Aristotle
Metaphysics
translated by W. D. Ross
1
All men by nature desire to know. An indication
of this is the delight we take in our senses; for even apart from their
usefulness they are loved for themselves; and above all others the sense of
sight. For not only with a view to action, but even when we are not going to do
anything, we prefer seeing (one might say) to everything else. The reason is
that this, most of all the senses, makes us know and brings to light many
differences between things.
By nature animals are born with the faculty of
sensation, and from sensation memory is produced in some of them, though not in
others. And therefore the former are more intelligent and apt at learning than
those which cannot remember; those which are incapable of hearing sounds are
intelligent though they cannot be taught, e.g. the bee, and any other race of
animals that may be like it; and those which besides memory have this sense of
hearing can be taught.
The animals other than man live by appearances
and memories, and have but little of connected experience; but the human race
lives also by art and reasonings. Now from memory experience is produced in men;
for the several memories of the same thing produce finally the capacity for a
single experience. And experience seems pretty much like science and art, but
really science and art come to men through experience; for ‘experience made
art’, as Polus says, ‘but inexperience luck.’ Now art arises when from many
notions gained by experience one universal judgement about a class of objects is
produced. For to have a judgement that when Callias was ill of this disease this
did him good, and similarly in the case of Socrates and in many individual
cases, is a matter of experience; but to judge that it has done good to all
persons of a certain constitution, marked off in one class, when they were ill
of this disease, e.g. to phlegmatic or bilious people when burning with fevers –
this is a matter of art.
With a view to action experience seems in no
respect inferior to art, and men of experience succeed even better than those
who have theory without experience. (The reason is that experience is knowledge
of individuals, art of universals, and actions and productions are all concerned
with the individual; for the physician does not cure man, except in an
incidental way, but Callias or Socrates or some other called by some such
individual name, who happens to be a man. If, then, a man has the theory without
the experience, and recognizes the universal but does not know the individual
included in this, he will often fail to cure; for it is the individual that is
to be cured.) But yet we think that knowledge and understanding belong to art
rather than to experience, and we suppose artists to be wiser than men of
experience (which implies that Wisdom depends in all cases rather on knowledge);
and this because the former know the cause, but the latter do not. For men of
experience know that the thing is so, but do not know why, while the others know
the ‘why’ and the cause. Hence we think also that the masterworkers in each
craft are more honourable and know in a truer sense and are wiser than the
manual workers, because they know the causes of the things that are done (we
think the manual workers are like certain lifeless things which act indeed, but
act without knowing what they do, as fire burns, – but while the lifeless things
perform each of their functions by a natural tendency, the labourers perform
them through habit); thus we view them as being wiser not in virtue of being
able to act, but of having the theory for themselves and knowing the causes. And
in general it is a sign of the man who knows and of the man who does not know,
that the former can teach, and therefore we think art more truly knowledge than
experience is; for artists can teach, and men of mere experience
cannot.
Again, we do not regard any of the senses as
Wisdom; yet surely these give the most authoritative knowledge of particulars.
But they do not tell us the ‘why’ of anything – e.g. why fire is hot; they only
say that it is hot.
At first he who invented any art whatever that
went beyond the common perceptions of man was naturally admired by men, not only
because there was something useful in the inventions, but because he was thought
wise and superior to the rest. But as more arts were invented, and some were
directed to the necessities of life, others to recreation, the inventors of the
latter were naturally always regarded as wiser than the inventors of the former,
because their branches of knowledge did not aim at utility. Hence when all such
inventions were already established, the sciences which do not aim at giving
pleasure or at the necessities of life were discovered, and first in the places
where men first began to have leisure. This is why the mathematical arts were
founded in Egypt; for there the priestly caste was allowed to be at
leisure.
We have said in the Ethics what the difference
is between art and science and the other kindred faculties; but the point of our
present discussion is this, that all men suppose what is called Wisdom to deal
with the first causes and the principles of things; so that, as has been said
before, the man of experience is thought to be wiser than the possessors of any
sense-perception whatever, the artist wiser than the men of experience, the
masterworker than the mechanic, and the theoretical kinds of knowledge to be
more of the nature of Wisdom than the productive. Clearly then Wisdom is
knowledge about certain principles and causes.
2
Since we are seeking this knowledge, we must
inquire of what kind are the causes and the principles, the knowledge of which
is Wisdom. If one were to take the notions we have about the wise man, this
might perhaps make the answer more evident. We suppose first, then, that the
wise man knows all things, as far as possible, although he has not knowledge of
each of them in detail; secondly, that he who can learn things that are
difficult, and not easy for man to know, is wise (sense-perception is common to
all, and therefore easy and no mark of Wisdom); again, that he who is more exact
and more capable of teaching the causes is wiser, in every branch of knowledge;
and that of the sciences, also, that which is desirable on its own account and
for the sake of knowing it is more of the nature of Wisdom than that which is
desirable on account of its results, and the superior science is more of the
nature of Wisdom than the ancillary; for the wise man must not be ordered but
must order, and he must not obey another, but the less wise must obey
him.
Such and so many are the notions, then, which
we have about Wisdom and the wise. Now of these characteristics that of knowing
all things must belong to him who has in the highest degree universal knowledge;
for he knows in a sense all the instances that fall under the universal. And
these things, the most universal, are on the whole the hardest for men to know;
for they are farthest from the senses. And the most exact of the sciences are
those which deal most with first principles; for those which involve fewer
principles are more exact than those which involve additional principles, e.g.
arithmetic than geometry. But the science which investigates causes is also
instructive, in a higher degree, for the people who instruct us are those who
tell the causes of each thing. And understanding and knowledge pursued for their
own sake are found most in the knowledge of that which is most knowable (for he
who chooses to know for the sake of knowing will choose most readily that which
is most truly knowledge, and such is the knowledge of that which is most
knowable); and the first principles and the causes are most knowable; for by
reason of these, and from these, all other things come to be known, and not
these by means of the things subordinate to them. And the science which knows to
what end each thing must be done is the most authoritative of the sciences, and
more authoritative than any ancillary science; and this end is the good of that
thing, and in general the supreme good in the whole of nature. Judged by all the
tests we have mentioned, then, the name in question falls to the same science;
this must be a science that investigates the first principles and causes; for
the good, i.e. the end, is one of the causes.
That it is not a science of production is clear
even from the history of the earliest philosophers. For it is owing to their
wonder that men both now begin and at first began to philosophize; they wondered
originally at the obvious difficulties, then advanced little by little and
stated difficulties about the greater matters, e.g. about the phenomena of the
moon and those of the sun and of the stars, and about the genesis of the
universe. And a man who is puzzled and wonders thinks himself ignorant (whence
even the lover of myth is in a sense a lover of Wisdom, for the myth is composed
of wonders); therefore since they philosophized order to escape from ignorance,
evidently they were pursuing science in order to know, and not for any
utilitarian end. And this is confirmed by the facts; for it was when almost all
the necessities of life and the things that make for comfort and recreation had
been secured, that such knowledge began to be sought. Evidently then we do not
seek it for the sake of any other advantage; but as the man is free, we say, who
exists for his own sake and not for another’s, so we pursue this as the only
free science, for it alone exists for its own sake.
Hence also the possession of it might be justly
regarded as beyond human power; for in many ways human nature is in bondage, so
that according to Simonides ‘God alone can have this privilege’, and it is
unfitting that man should not be content to seek the knowledge that is suited to
him. If, then, there is something in what the poets say, and jealousy is natural
to the divine power, it would probably occur in this case above all, and all who
excelled in this knowledge would be unfortunate. But the divine power cannot be
jealous (nay, according to the proverb, ‘bards tell a lie’), nor should any
other science be thought more honourable than one of this sort. For the most
divine science is also most honourable; and this science alone must be, in two
ways, most divine. For the science which it would be most meet for God to have
is a divine science, and so is any science that deals with divine objects; and
this science alone has both these qualities; for (1) God is thought to be among
the causes of all things and to be a first principle, and (2) such a science
either God alone can have, or God above all others. All the sciences, indeed,
are more necessary than this, but none is better.
Yet the acquisition of it must in a sense end
in something which is the opposite of our original inquiries. For all men begin,
as we said, by wondering that things are as they are, as they do about
self-moving marionettes, or about the solstices or the incommensurability of the
diagonal of a square with the side; for it seems wonderful to all who have not
yet seen the reason, that there is a thing which cannot be measured even by the
smallest unit. But we must end in the contrary and, according to the proverb,
the better state, as is the case in these instances too when men learn the
cause; for there is nothing which would surprise a geometer so much as if the
diagonal turned out to be commensurable.
We have stated, then, what is the nature of the
science we are searching for, and what is the mark which our search and our
whole investigation must reach.
3
Evidently we have to acquire knowledge of the
original causes (for we say we know each thing only when we think we recognize
its first cause), and causes are spoken of in four senses. In one of these we
mean the substance, i.e. the essence (for the ‘why’ is reducible finally to the
definition, and the ultimate ‘why’ is a cause and principle); in another the
matter or substratum, in a third the source of the change, and in a fourth the
cause opposed to this, the purpose and the good (for this is the end of all
generation and change). We have studied these causes sufficiently in our work on
nature, but yet let us call to our aid those who have attacked the investigation
of being and philosophized about reality before us. For obviously they too speak
of certain principles and causes; to go over their views, then, will be of
profit to the present inquiry, for we shall either find another kind of cause,
or be more convinced of the correctness of those which we now
maintain.
Of the first philosophers, then, most thought
the principles which were of the nature of matter were the only principles of
all things. That of which all things that are consist, the first from which they
come to be, the last into which they are resolved (the substance remaining, but
changing in its modifications), this they say is the element and this the
principle of things, and therefore they think nothing is either generated or
destroyed, since this sort of entity is always conserved, as we say Socrates
neither comes to be absolutely when he comes to be beautiful or musical, nor
ceases to be when loses these characteristics, because the substratum, Socrates
himself remains. just so they say nothing else comes to be or ceases to be; for
there must be some entity – either one or more than one – from which all other
things come to be, it being conserved.
Yet they do not all agree as to the number and
the nature of these principles. Thales, the founder of this type of philosophy,
says the principle is water (for which reason he declared that the earth rests
on water), getting the notion perhaps from seeing that the nutriment of all
things is moist, and that heat itself is generated from the moist and kept alive
by it (and that from which they come to be is a principle of all things). He got
his notion from this fact, and from the fact that the seeds of all things have a
moist nature, and that water is the origin of the nature of moist
things.
Some think that even the ancients who lived
long before the present generation, and first framed accounts of the gods, had a
similar view of nature; for they made Ocean and Tethys the parents of creation,
and described the oath of the gods as being by water, to which they give the
name of Styx; for what is oldest is most honourable, and the most honourable
thing is that by which one swears. It may perhaps be uncertain whether this
opinion about nature is primitive and ancient, but Thales at any rate is said to
have declared himself thus about the first cause. Hippo no one would think fit
to include among these thinkers, because of the paltriness of his
thought.
Anaximenes and Diogenes make air prior to
water, and the most primary of the simple bodies, while Hippasus of Metapontium
and Heraclitus of Ephesus say this of fire, and Empedocles says it of the four
elements (adding a fourth-earth to those which have been named); for these, he
says, always remain and do not come to be, except that they come to be more or
fewer, being aggregated into one and segregated out of
one.
Anaxagoras of Clazomenae, who, though older
than Empedocles, was later in his philosophical activity, says the principles
are infinite in number; for he says almost all the things that are made of parts
like themselves, in the manner of water or fire, are generated and destroyed in
this way, only by aggregation and segregation, and are not in any other sense
generated or destroyed, but remain eternally.
From these facts one might think that the only
cause is the so-called material cause; but as men thus advanced, the very facts
opened the way for them and joined in forcing them to investigate the subject.
However true it may be that all generation and destruction proceed from some one
or (for that matter) from more elements, why does this happen and what is the
cause? For at least the substratum itself does not make itself change; e.g.
neither the wood nor the bronze causes the change of either of them, nor does
the wood manufacture a bed and the bronze a statue, but something else is the
cause of the change. And to seek this is to seek the second cause, as we should
say, – that from which comes the beginning of the movement. Now those who at the
very beginning set themselves to this kind of inquiry, and said the substratum
was one, were not at all dissatisfied with themselves; but some at least of
those who maintain it to be one – as though defeated by this search for the
second cause – say the one and nature as a whole is unchangeable not only in
respect of generation and destruction (for this is a primitive belief, and all
agreed in it), but also of all other change; and this view is peculiar to them.
Of those who said the universe was one, then none succeeded in discovering a
cause of this sort, except perhaps Parmenides, and he only inasmuch as he
supposes that there is not only one but also in some sense two causes. But for
those who make more elements it is more possible to state the second cause, e.g.
for those who make hot and cold, or fire and earth, the elements; for they treat
fire as having a nature which fits it to move things, and water and earth and
such things they treat in the contrary way.
When these men and the principles of this kind
had had their day, as the latter were found inadequate to generate the nature of
things men were again forced by the truth itself, as we said, to inquire into
the next kind of cause. For it is not likely either that fire or earth or any
such element should be the reason why things manifest goodness and, beauty both
in their being and in their coming to be, or that those thinkers should have
supposed it was; nor again could it be right to entrust so great a matter to
spontaneity and chance. When one man said, then, that reason was present – as in
animals, so throughout nature – as the cause of order and of all arrangement, he
seemed like a sober man in contrast with the random talk of his predecessors. We
know that Anaxagoras certainly adopted these views, but Hermotimus of Clazomenae
is credited with expressing them earlier. Those who thought thus stated that
there is a principle of things which is at the same time the cause of beauty,
and that sort of cause from which things acquire movement.
4
One might suspect that Hesiod was the first to
look for such a thing – or some one else who put love or desire among existing
things as a principle, as Parmenides, too, does; for he, in constructing the
genesis of the universe, says: –
Love first of all the Gods she
planned.
And Hesiod says: –
First of all things was chaos made, and
then
Broad-breasted earth...
And love, mid all the gods
pre-eminent,
which implies that among existing things there
must be from the first a cause which will move things and bring them together.
How these thinkers should be arranged with regard to priority of discovery let
us be allowed to decide later; but since the contraries of the various forms of
good were also perceived to be present in nature – not only order and the
beautiful, but also disorder and the ugly, and bad things in greater number than
good, and ignoble things than beautiful – therefore another thinker introduced
friendship and strife, each of the two the cause of one of these two sets of
qualities. For if we were to follow out the view of Empedocles, and interpret it
according to its meaning and not to its lisping expression, we should find that
friendship is the cause of good things, and strife of bad. Therefore, if we said
that Empedocles in a sense both mentions, and is the first to mention, the bad
and the good as principles, we should perhaps be right, since the cause of all
goods is the good itself.
These thinkers, as we say, evidently grasped,
and to this extent, two of the causes which we distinguished in our work on
nature – the matter and the source of the movement – vaguely, however, and with
no clearness, but as untrained men behave in fights; for they go round their
opponents and often strike fine blows, but they do not fight on scientific
principles, and so too these thinkers do not seem to know what they say; for it
is evident that, as a rule, they make no use of their causes except to a small
extent. For Anaxagoras uses reason as a deus ex machina for the making of the
world, and when he is at a loss to tell from what cause something necessarily
is, then he drags reason in, but in all other cases ascribes events to anything
rather than to reason. And Empedocles, though he uses the causes to a greater
extent than this, neither does so sufficiently nor attains consistency in their
use. At least, in many cases he makes love segregate things, and strife
aggregate them. For whenever the universe is dissolved into its elements by
strife, fire is aggregated into one, and so is each of the other elements; but
whenever again under the influence of love they come together into one, the
parts must again be segregated out of each element.
Empedocles, then, in contrast with his
precessors, was the first to introduce the dividing of this cause, not positing
one source of movement, but different and contrary sources. Again, he was the
first to speak of four material elements; yet he does not use four, but treats
them as two only; he treats fire by itself, and its opposite – earth, air, and
water – as one kind of thing. We may learn this by study of his
verses.
This philosopher then, as we say, has spoken of
the principles in this way, and made them of this number. Leucippus and his
associate Democritus say that the full and the empty are the elements, calling
the one being and the other non-being – the full and solid being being, the
empty non-being (whence they say being no more is than non-being, because the
solid no more is than the empty); and they make these the material causes of
things. And as those who make the underlying substance one generate all other
things by its modifications, supposing the rare and the dense to be the sources
of the modifications, in the same way these philosophers say the differences in
the elements are the causes of all other qualities. These differences, they say,
are three-shape and order and position. For they say the real is differentiated
only by ‘rhythm and ‘inter-contact’ and ‘turning’; and of these rhythm is shape,
inter-contact is order, and turning is position; for A differs from N in shape,
AN from NA in order, M from W in position. The question of movement – whence or
how it is to belong to things – these thinkers, like the others, lazily
neglected.
Regarding the two causes, then, as we say, the
inquiry seems to have been pushed thus far by the early
philosophers.
5
Contemporaneously with these philosophers and
before them, the so-called Pythagoreans, who were the first to take up
mathematics, not only advanced this study, but also having been brought up in it
they thought its principles were the principles of all things. Since of these
principles numbers are by nature the first, and in numbers they seemed to see
many resemblances to the things that exist and come into being – more than in
fire and earth and water (such and such a modification of numbers being justice,
another being soul and reason, another being opportunity – and similarly almost
all other things being numerically expressible); since, again, they saw that the
modifications and the ratios of the musical scales were expressible in numbers;
– since, then, all other things seemed in their whole nature to be modelled on
numbers, and numbers seemed to be the first things in the whole of nature, they
supposed the elements of numbers to be the elements of all things, and the whole
heaven to be a musical scale and a number. And all the properties of numbers and
scales which they could show to agree with the attributes and parts and the
whole arrangement of the heavens, they collected and fitted into their scheme;
and if there was a gap anywhere, they readily made additions so as to make their
whole theory coherent. E.g. as the number 10 is thought to be perfect and to
comprise the whole nature of numbers, they say that the bodies which move
through the heavens are ten, but as the visible bodies are only nine, to meet
this they invent a tenth – the ‘counter-earth’. We have discussed these matters
more exactly elsewhere.
But the object of our review is that we may
learn from these philosophers also what they suppose to be the principles and
how these fall under the causes we have named. Evidently, then, these thinkers
also consider that number is the principle both as matter for things and as
forming both their modifications and their permanent states, and hold that the
elements of number are the even and the odd, and that of these the latter is
limited, and the former unlimited; and that the One proceeds from both of these
(for it is both even and odd), and number from the One; and that the whole
heaven, as has been said, is numbers.
Other members of this same school say there are
ten principles, which they arrange in two columns of cognates – limit and
unlimited, odd and even, one and plurality, right and left, male and female,
resting and moving, straight and curved, light and darkness, good and bad,
square and oblong. In this way Alcmaeon of Croton seems also to have conceived
the matter, and either he got this view from them or they got it from him; for
he expressed himself similarly to them. For he says most human affairs go in
pairs, meaning not definite contrarieties such as the Pythagoreans speak of, but
any chance contrarieties, e.g. white and black, sweet and bitter, good and bad,
great and small. He threw out indefinite suggestions about the other
contrarieties, but the Pythagoreans declared both how many and which their
contraricties are.
From both these schools, then, we can learn
this much, that the contraries are the principles of things; and how many these
principles are and which they are, we can learn from one of the two schools. But
how these principles can be brought together under the causes we have named has
not been clearly and articulately stated by them; they seem, however, to range
the elements under the head of matter; for out of these as immanent parts they
say substance is composed and moulded.
From these facts we may sufficiently perceive
the meaning of the ancients who said the elements of nature were more than one;
but there are some who spoke of the universe as if it were one entity, though
they were not all alike either in the excellence of their statement or in its
conformity to the facts of nature. The discussion of them is in no way
appropriate to our present investigation of causes, for. they do not, like some
of the natural philosophers, assume being to be one and yet generate it out of
the one as out of matter, but they speak in another way; those others add
change, since they generate the universe, but these thinkers say the universe is
unchangeable. Yet this much is germane to the present inquiry: Parmenides seems
to fasten on that which is one in definition, Melissus on that which is one in
matter, for which reason the former says that it is limited, the latter that it
is unlimited; while Xenophanes, the first of these partisans of the One (for
Parmenides is said to have been his pupil), gave no clear statement, nor does he
seem to have grasped the nature of either of these causes, but with reference to
the whole material universe he says the One is God. Now these thinkers, as we
said, must be neglected for the purposes of the present inquiry – two of them
entirely, as being a little too naive, viz. Xenophanes and Melissus; but
Parmenides seems in places to speak with more insight. For, claiming that,
besides the existent, nothing non-existent exists, he thinks that of necessity
one thing exists, viz. the existent and nothing else (on this we have spoken
more clearly in our work on nature), but being forced to follow the observed
facts, and supposing the existence of that which is one in definition, but more
than one according to our sensations, he now posits two causes and two
principles, calling them hot and cold, i.e. fire and earth; and of these he
ranges the hot with the existent, and the other with the
non-existent.
From what has been said, then, and from the
wise men who have now sat in council with us, we have got thus much – on the one
hand from the earliest philosophers, who regard the first principle as corporeal
(for water and fire and such things are bodies), and of whom some suppose that
there is one corporeal principle, others that there are more than one, but both
put these under the head of matter; and on the other hand from some who posit
both this cause and besides this the source of movement, which we have got from
some as single and from others as twofold.
Down to the Italian school, then, and apart
from it, philosophers have treated these subjects rather obscurely, except that,
as we said, they have in fact used two kinds of cause, and one of these – the
source of movement – some treat as one and others as two. But the Pythagoreans
have said in the same way that there are two principles, but added this much,
which is peculiar to them, that they thought that finitude and infinity were not
attributes of certain other things, e.g. of fire or earth or anything else of
this kind, but that infinity itself and unity itself were the substance of the
things of which they are predicated. This is why number was the substance of all
things. On this subject, then, they expressed themselves thus; and regarding the
question of essence they began to make statements and definitions, but treated
the matter too simply. For they both defined superficially and thought that the
first subject of which a given definition was predicable was the substance of
the thing defined, as if one supposed that ‘double’ and ‘2’ were the same,
because 2 is the first thing of which ‘double’ is predicable. But surely to be
double and to be 2 are not the same; if they are, one thing will be many – a
consequence which they actually drew. From the earlier philosophers, then, and
from their successors we can learn thus much.
6
After the systems we have named came the
philosophy of Plato, which in most respects followed these thinkers, but had
pecullarities that distinguished it from the philosophy of the Italians. For,
having in his youth first become familiar with Cratylus and with the Heraclitean
doctrines (that all sensible things are ever in a state of flux and there is no
knowledge about them), these views he held even in later years. Socrates,
however, was busying himself about ethical matters and neglecting the world of
nature as a whole but seeking the universal in these ethical matters, and fixed
thought for the first time on definitions; Plato accepted his teaching, but held
that the problem applied not to sensible things but to entities of another kind
– for this reason, that the common definition could not be a definition of any
sensible thing, as they were always changing. Things of this other sort, then,
he called Ideas, and sensible things, he said, were all named after these, and
in virtue of a relation to these; for the many existed by participation in the
Ideas that have the same name as they. Only the name ‘participation’ was new;
for the Pythagoreans say that things exist by ‘imitation’ of numbers, and Plato
says they exist by participation, changing the name. But what the participation
or the imitation of the Forms could be they left an open
question.
Further, besides sensible things and Forms he
says there are the objects of mathematics, which occupy an intermediate
position, differing from sensible things in being eternal and unchangeable, from
Forms in that there are many alike, while the Form itself is in each case
unique.
Since the Forms were the causes of all other
things, he thought their elements were the elements of all things. As matter,
the great and the small were principles; as essential reality, the One; for from
the great and the small, by participation in the One, come the
Numbers.
But he agreed with the Pythagoreans in saying
that the One is substance and not a predicate of something else; and in saying
that the Numbers are the causes of the reality of other things he agreed with
them; but positing a dyad and constructing the infinite out of great and small,
instead of treating the infinite as one, is peculiar to him; and so is his view
that the Numbers exist apart from sensible things, while they say that the
things themselves are Numbers, and do not place the objects of mathematics
between Forms and sensible things. His divergence from the Pythagoreans in
making the One and the Numbers separate from things, and his introduction of the
Forms, were due to his inquiries in the region of definitions (for the earlier
thinkers had no tincture of dialectic), and his making the other entity besides
the One a dyad was due to the belief that the numbers, except those which were
prime, could be neatly produced out of the dyad as out of some plastic material.
Yet what happens is the contrary; the theory is not a reasonable one. For they
make many things out of the matter, and the form generates only once, but what
we observe is that one table is made from one matter, while the man who applies
the form, though he is one, makes many tables. And the relation of the male to
the female is similar; for the latter is impregnated by one copulation, but the
male impregnates many females; yet these are analogues of those first
principles.
Plato, then, declared himself thus on the
points in question; it is evident from what has been said that he has used only
two causes, that of the essence and the material cause (for the Forms are the
causes of the essence of all other things, and the One is the cause of the
essence of the Forms); and it is evident what the underlying matter is, of which
the Forms are predicated in the case of sensible things, and the One in the case
of Forms, viz. that this is a dyad, the great and the small. Further, he has
assigned the cause of good and that of evil to the elements, one to each of the
two, as we say some of his predecessors sought to do, e.g. Empedocles and
Anaxagoras.
7
Our review of those who have spoken about first
principles and reality and of the way in which they have spoken, has been
concise and summary; but yet we have learnt this much from them, that of those
who speak about ‘principle’ and ‘cause’ no one has mentioned any principle
except those which have been distinguished in our work on nature, but all
evidently have some inkling of them, though only vaguely. For some speak of the
first principle as matter, whether they suppose one or more first principles,
and whether they suppose this to be a body or to be incorporeal; e.g. Plato
spoke of the great and the small, the Italians of the infinite, Empedocles of
fire, earth, water, and air, Anaxagoras of the infinity of things composed of
similar parts. These, then, have all had a notion of this kind of cause, and so
have all who speak of air or fire or water, or something denser than fire and
rarer than air; for some have said the prime element is of this
kind.
These thinkers grasped this cause only; but
certain others have mentioned the source of movement, e.g. those who make
friendship and strife, or reason, or love, a principle.
The essence, i.e. the substantial reality, no
one has expressed distinctly. It is hinted at chiefly by those who believe in
the Forms; for they do not suppose either that the Forms are the matter of
sensible things, and the One the matter of the Forms, or that they are the
source of movement (for they say these are causes rather of immobility and of
being at rest), but they furnish the Forms as the essence of every other thing,
and the One as the essence of the Forms.
That for whose sake actions and changes and
movements take place, they assert to be a cause in a way, but not in this way,
i.e. not in the way in which it is its nature to be a cause. For those who speak
of reason or friendship class these causes as goods; they do not speak, however,
as if anything that exists either existed or came into being for the sake of
these, but as if movements started from these. In the same way those who say the
One or the existent is the good, say that it is the cause of substance, but not
that substance either is or comes to be for the sake of this. Therefore it turns
out that in a sense they both say and do not say the good is a cause; for they
do not call it a cause qua good but only incidentally.
All these thinkers then, as they cannot pitch
on another cause, seem to testify that we have determined rightly both how many
and of what sort the causes are. Besides this it is plain that when the causes
are being looked for, either all four must be sought thus or they must be sought
in one of these four ways. Let us next discuss the possible difficulties with
regard to the way in which each of these thinkers has spoken, and with regard to
his situation relatively to the first principles.
8
Those, then, who say the universe is one and
posit one kind of thing as matter, and as corporeal matter which has spatial
magnitude, evidently go astray in many ways. For they posit the elements of
bodies only, not of incorporeal things, though there are also incorporeal
things. And in trying to state the causes of generation and destruction, and in
giving a physical account of all things, they do away with the cause of
movement. Further, they err in not positing the substance, i.e. the essence, as
the cause of anything, and besides this in lightly calling any of the simple
bodies except earth the first principle, without inquiring how they are produced
out of one anothers – I mean fire, water, earth, and air. For some things are
produced out of each other by combination, others by separation, and this makes
the greatest difference to their priority and posteriority. For (1) in a way the
property of being most elementary of all would seem to belong to the first thing
from which they are produced by combination, and this property would belong to
the most fine-grained and subtle of bodies. For this reason those who make fire
the principle would be most in agreement with this argument. But each of the
other thinkers agrees that the element of corporeal things is of this sort. At
least none of those who named one element claimed that earth was the element,
evidently because of the coarseness of its grain. (Of the other three elements
each has found some judge on its side; for some maintain that fire, others that
water, others that air is the element. Yet why, after all, do they not name
earth also, as most men do? For people say all things are earth Hesiod says
earth was produced first of corporeal things; so primitive and popular has the
opinion been.) According to this argument, then, no one would be right who
either says the first principle is any of the elements other than fire, or
supposes it to be denser than air but rarer than water. But (2) if that which is
later in generation is prior in nature, and that which is concocted and
compounded is later in generation, the contrary of what we have been saying must
be true, – water must be prior to air, and earth to water.
So much, then, for those who posit one cause
such as we mentioned; but the same is true if one supposes more of these, as
Empedocles says matter of things is four bodies. For he too is confronted by
consequences some of which are the same as have been mentioned, while others are
peculiar to him. For we see these bodies produced from one another, which
implies that the same body does not always remain fire or earth (we have spoken
about this in our works on nature); and regarding the cause of movement and the
question whether we must posit one or two, he must be thought to have spoken
neither correctly nor altogether plausibly. And in general, change of quality is
necessarily done away with for those who speak thus, for on their view cold will
not come from hot nor hot from cold. For if it did there would be something that
accepted the contraries themselves, and there would be some one entity that
became fire and water, which Empedocles denies.
As regards Anaxagoras, if one were to suppose
that he said there were two elements, the supposition would accord thoroughly
with an argument which Anaxagoras himself did not state articulately, but which
he must have accepted if any one had led him on to it. True, to say that in the
beginning all things were mixed is absurd both on other grounds and because it
follows that they must have existed before in an unmixed form, and because
nature does not allow any chance thing to be mixed with any chance thing, and
also because on this view modifications and accidents could be separated from
substances (for the same things which are mixed can be separated); yet if one
were to follow him up, piecing together what he means, he would perhaps be seen
to be somewhat modern in his views. For when nothing was separated out,
evidently nothing could be truly asserted of the substance that then existed. I
mean, e.g. that it was neither white nor black, nor grey nor any other colour,
but of necessity colourless; for if it had been coloured, it would have had one
of these colours. And similarly, by this same argument, it was flavourless, nor
had it any similar attribute; for it could not be either of any quality or of
any size, nor could it be any definite kind of thing. For if it were, one of the
particular forms would have belonged to it, and this is impossible, since all
were mixed together; for the particular form would necessarily have been already
separated out, but he all were mixed except reason, and this alone was unmixed
and pure. From this it follows, then, that he must say the principles are the
One (for this is simple and unmixed) and the Other, which is of such a nature as
we suppose the indefinite to be before it is defined and partakes of some form.
Therefore, while expressing himself neither rightly nor clearly, he means
something like what the later thinkers say and what is now more clearly seen to
be the case.
But these thinkers are, after all, at home only
in arguments about generation and destruction and movement; for it is
practically only of this sort of substance that they seek the principles and the
causes. But those who extend their vision to all things that exist, and of
existing things suppose some to be perceptible and others not perceptible,
evidently study both classes, which is all the more reason why one should devote
some time to seeing what is good in their views and what bad from the standpoint
of the inquiry we have now before us.
The ‘Pythagoreans’ treat of principles and
elements stranger than those of the physical philosophers (the reason is that
they got the principles from non-sensible things, for the objects of
mathematics, except those of astronomy, are of the class of things without
movement); yet their discussions and investigations are all about nature; for
they generate the heavens, and with regard to their parts and attributes and
functions they observe the phenomena, and use up the principles and the causes
in explaining these, which implies that they agree with the others, the physical
philosophers, that the real is just all that which is perceptible and contained
by the so-called ‘heavens’. But the causes and the principles which they mention
are, as we said, sufficient to act as steps even up to the higher realms of
reality, and are more suited to these than to theories about nature. They do not
tell us at all, however, how there can be movement if limit and unlimited and
odd and even are the only things assumed, or how without movement and change
there can be generation and destruction, or the bodies that move through the
heavens can do what they do.
Further, if one either granted them that
spatial magnitude consists of these elements, or this were proved, still how
would some bodies be light and others have weight? To judge from what they
assume and maintain they are speaking no more of mathematical bodies than of
perceptible; hence they have said nothing whatever about fire or earth or the
other bodies of this sort, I suppose because they have nothing to say which
applies peculiarly to perceptible things.
Further, how are we to combine the beliefs that
the attributes of number, and number itself, are causes of what exists and
happens in the heavens both from the beginning and now, and that there is no
other number than this number out of which the world is composed? When in one
particular region they place opinion and opportunity, and, a little above or
below, injustice and decision or mixture, and allege, as proof, that each of
these is a number, and that there happens to be already in this place a
plurality of the extended bodies composed of numbers, because these attributes
of number attach to the various places, – this being so, is this number, which
we must suppose each of these abstractions to be, the same number which is
exhibited in the material universe, or is it another than this? Plato says it is
different; yet even he thinks that both these bodies and their causes are
numbers, but that the intelligible numbers are causes, while the others are
sensible.
9
Let us leave the Pythagoreans for the present;
for it is enough to have touched on them as much as we have done. But as for
those who posit the Ideas as causes, firstly, in seeking to grasp the causes of
the things around us, they introduced others equal in number to these, as if a
man who wanted to count things thought he would not be able to do it while they
were few, but tried to count them when he had added to their number. For the
Forms are practically equal to – or not fewer than – the things, in trying to
explain which these thinkers proceeded from them to the Forms. For to each thing
there answers an entity which has the same name and exists apart from the
substances, and so also in the case of all other groups there is a one over
many, whether the many are in this world or are eternal.
Further, of the ways in which we prove that the
Forms exist, none is convincing; for from some no inference necessarily follows,
and from some arise Forms even of things of which we think there are no Forms.
For according to the arguments from the existence of the sciences there will be
Forms of all things of which there are sciences and according to the ‘one over
many’ argument there will be Forms even of negations, and according to the
argument that there is an object for thought even when the thing has perished,
there will be Forms of perishable things; for we have an image of these.
Further, of the more accurate arguments, some lead to Ideas of relations, of
which we say there is no independent class, and others introduce the ‘third
man’.
And in general the arguments for the Forms
destroy the things for whose existence we are more zealous than for the
existence of the Ideas; for it follows that not the dyad but number is first,
i.e. that the relative is prior to the absolute, – besides all the other points
on which certain people by following out the opinions held about the Ideas have
come into conflict with the principles of the theory.
Further, according to the assumption on which
our belief in the Ideas rests, there will be Forms not only of substances but
also of many other things (for the concept is single not only in the case of
substances but also in the other cases, and there are sciences not only of
substance but also of other things, and a thousand other such difficulties
confront them). But according to the necessities of the case and the opinions
held about the Forms, if Forms can be shared in there must be Ideas of
substances only. For they are not shared in incidentally, but a thing must share
in its Form as in something not predicated of a subject (by ‘being shared in
incidentally’ I mean that e.g. if a thing shares in ‘double itself’, it shares
also in ‘eternal’, but incidentally; for ‘eternal’ happens to be predicable of
the ‘double’). Therefore the Forms will be substance; but the same terms
indicate substance in this and in the ideal world (or what will be the meaning
of saying that there is something apart from the particulars – the one over
many?). And if the Ideas and the particulars that share in them have the same
form, there will be something common to these; for why should ‘2’ be one and the
same in the perishable 2’s or in those which are many but eternal, and not the
same in the ‘2’ itself’ as in the particular 2? But if they have not the same
form, they must have only the name in common, and it is as if one were to call
both Callias and a wooden image a ‘man’, without observing any community between
them.
Above all one might discuss the question what
on earth the Forms contribute to sensible things, either to those that are
eternal or to those that come into being and cease to be. For they cause neither
movement nor any change in them. But again they help in no wise either towards
the knowledge of the other things (for they are not even the substance of these,
else they would have been in them), or towards their being, if they are not in
the particulars which share in them; though if they were, they might be thought
to be causes, as white causes whiteness in a white object by entering into its
composition. But this argument, which first Anaxagoras and later Eudoxus and
certain others used, is very easily upset; for it is not difficult to collect
many insuperable objections to such a view.
But, further, all other things cannot come from
the Forms in any of the usual senses of ‘from’. And to say that they are
patterns and the other things share in them is to use empty words and poetical
metaphors. For what is it that works, looking to the Ideas? And anything can
either be, or become, like another without being copied from it, so that whether
Socrates or not a man Socrates like might come to be; and evidently this might
be so even if Socrates were eternal. And there will be several patterns of the
same thing, and therefore several Forms; e.g. ‘animal’ and ‘two-footed’ and also
‘man himself’ will be Forms of man. Again, the Forms are patterns not only
sensible things, but of Forms themselves also; i.e. the genus, as genus of
various species, will be so; therefore the same thing will be pattern and
copy.
Again, it would seem impossible that the
substance and that of which it is the substance should exist apart; how,
therefore, could the Ideas, being the substances of things, exist apart? In the
Phaedo’ the case is stated in this way – that the Forms are causes both of being
and of becoming; yet when the Forms exist, still the things that share in them
do not come into being, unless there is something to originate movement; and
many other things come into being (e.g. a house or a ring) of which we say there
are no Forms. Clearly, therefore, even the other things can both be and come
into being owing to such causes as produce the things just
mentioned.
Again, if the Forms are numbers, how can they
be causes? Is it because existing things are other numbers, e.g. one number is
man, another is Socrates, another Callias? Why then are the one set of numbers
causes of the other set? It will not make any difference even if the former are
eternal and the latter are not. But if it is because things in this sensible
world (e.g. harmony) are ratios of numbers, evidently the things between which
they are ratios are some one class of things. If, then, this – the matter – is
some definite thing, evidently the numbers themselves too will be ratios of
something to something else. E.g. if Callias is a numerical ratio between fire
and earth and water and air, his Idea also will be a number of certain other
underlying things; and man himself, whether it is a number in a sense or not,
will still be a numerical ratio of certain things and not a number proper, nor
will it be a of number merely because it is a numerical
ratio.
Again, from many numbers one number is
produced, but how can one Form come from many Forms? And if the number comes not
from the many numbers themselves but from the units in them, e.g. in 10,000, how
is it with the units? If they are specifically alike, numerous absurdities will
follow, and also if they are not alike (neither the units in one number being
themselves like one another nor those in other numbers being all like to all);
for in what will they differ, as they are without quality? This is not a
plausible view, nor is it consistent with our thought on the
matter.
Further, they must set up a second kind of
number (with which arithmetic deals), and all the objects which are called
‘intermediate’ by some thinkers; and how do these exist or from what principles
do they proceed? Or why must they be intermediate between the things in this
sensible world and the things-themselves?
Further, the units in must each come from a
prior but this is impossible.
Further, why is a number, when taken all
together, one?
Again, besides what has been said, if the units
are diverse the Platonists should have spoken like those who say there are four,
or two, elements; for each of these thinkers gives the name of element not to
that which is common, e.g. to body, but to fire and earth, whether there is
something common to them, viz. body, or not. But in fact the Platonists speak as
if the One were homogeneous like fire or water; and if this is so, the numbers
will not be substances. Evidently, if there is a One itself and this is a first
principle, ‘one’ is being used in more than one sense; for otherwise the theory
is impossible.
When we wish to reduce substances to their
principles, we state that lines come from the short and long (i.e. from a kind
of small and great), and the plane from the broad and narrow, and body from the
deep and shallow. Yet how then can either the plane contain a line, or the solid
a line or a plane? For the broad and narrow is a different class from the deep
and shallow. Therefore, just as number is not present in these, because the many
and few are different from these, evidently no other of the higher classes will
be present in the lower. But again the broad is not a genus which includes the
deep, for then the solid would have been a species of plane. Further, from what
principle will the presence of the points in the line be derived? Plato even
used to object to this class of things as being a geometrical fiction. He gave
the name of principle of the line – and this he often posited – to the
indivisible lines. Yet these must have a limit; therefore the argument from
which the existence of the line follows proves also the existence of the
point.
In general, though philosophy seeks the cause
of perceptible things, we have given this up (for we say nothing of the cause
from which change takes its start), but while we fancy we are stating the
substance of perceptible things, we assert the existence of a second class of
substances, while our account of the way in which they are the substances of
perceptible things is empty talk; for ‘sharing’, as we said before, means
nothing.
Nor have the Forms any connexion with what we
see to be the cause in the case of the arts, that for whose sake both all mind
and the whole of nature are operative, – with this cause which we assert to be
one of the first principles; but mathematics has come to be identical with
philosophy for modern thinkers, though they say that it should be studied for
the sake of other things. Further, one might suppose that the substance which
according to them underlies as matter is too mathematical, and is a predicate
and differentia of the substance, ie. of the matter, rather than matter itself;
i.e. the great and the small are like the rare and the dense which the physical
philosophers speak of, calling these the primary differentiae of the substratum;
for these are a kind of excess and defect. And regarding movement, if the great
and the small are to he movement, evidently the Forms will be moved; but if they
are not to be movement, whence did movement come? The whole study of nature has
been annihilated.
And what is thought to be easy – to show that
all things are one – is not done; for what is proved by the method of setting
out instances is not that all things are one but that there is a One itself, –
if we grant all the assumptions. And not even this follows, if we do not grant
that the universal is a genus; and this in some cases it cannot
be.
Nor can it be explained either how the lines
and planes and solids that come after the numbers exist or can exist, or what
significance they have; for these can neither be Forms (for they are not
numbers), nor the intermediates (for those are the objects of mathematics), nor
the perishable things. This is evidently a distinct fourth
class.
In general, if we search for the elements of
existing things without distinguishing the many senses in which things are said
to exist, we cannot find them, especially if the search for the elements of
which things are made is conducted in this manner. For it is surely impossible
to discover what ‘acting’ or ‘being acted on’, or ‘the straight’, is made of,
but if elements can be discovered at all, it is only the elements of substances;
therefore either to seek the elements of all existing things or to think one has
them is incorrect.
And how could we learn the elements of all
things? Evidently we cannot start by knowing anything before. For as he who is
learning geometry, though he may know other things before, knows none of the
things with which the science deals and about which he is to learn, so is it in
all other cases. Therefore if there is a science of all things, such as some
assert to exist, he who is learning this will know nothing before. Yet all
learning is by means of premisses which are (either all or some of them) known
before, – whether the learning be by demonstration or by definitions; for the
elements of the definition must be known before and be familiar; and learning by
induction proceeds similarly. But again, if the science were actually innate, it
were strange that we are unaware of our possession of the greatest of
sciences.
Again, how is one to come to know what all
things are made of, and how is this to be made evident? This also affords a
difficulty; for there might be a conflict of opinion, as there is about certain
syllables; some say za is made out of s and d and a, while others say it is a
distinct sound and none of those that are familiar.
Further, how could we know the objects of sense
without having the sense in question? Yet we ought to, if the elements of which
all things consist, as complex sounds consist of the clements proper to sound,
are the same.
10
It is evident, then, even from what we have
said before, that all men seem to seek the causes named in the Physics, and that
we cannot name any beyond these; but they seek these vaguely; and though in a
sense they have all been described before, in a sense they have not been
described at all. For the earliest philosophy is, on all subjects, like one who
lisps, since it is young and in its beginnings. For even Empedocles says bone
exists by virtue of the ratio in it. Now this is the essence and the substance
of the thing. But it is similarly necessary that flesh and each of the other
tissues should be the ratio of its elements, or that not one of them should; for
it is on account of this that both flesh and bone and everything else will
exist, and not on account of the matter, which he names, – fire and earth and
water and air. But while he would necessarily have agreed if another had said
this, he has not said it clearly.
On these questions our views have been
expressed before; but let us return to enumerate the difficulties that might be
raised on these same points; for perhaps we may get from them some help towards
our later difficulties.
1
The investigation of the truth is in one way
hard, in another easy. An indication of this is found in the fact that no one is
able to attain the truth adequately, while, on the other hand, we do not
collectively fail, but every one says something true about the nature of things,
and while individually we contribute little or nothing to the truth, by the
union of all a considerable amount is amassed. Therefore, since the truth seems
to be like the proverbial door, which no one can fail to hit, in this respect it
must be easy, but the fact that we can have a whole truth and not the particular
part we aim at shows the difficulty of it.
Perhaps, too, as difficulties are of two kinds,
the cause of the present difficulty is not in the facts but in us. For as the
eyes of bats are to the blaze of day, so is the reason in our soul to the things
which are by nature most evident of all.
It is just that we should be grateful, not only
to those with whose views we may agree, but also to those who have expressed
more superficial views; for these also contributed something, by developing
before us the powers of thought. It is true that if there had been no Timotheus
we should have been without much of our lyric poetry; but if there had been no
Phrynis there would have been no Timotheus. The same holds good of those who
have expressed views about the truth; for from some thinkers we have inherited
certain opinions, while the others have been responsible for the appearance of
the former.
It is right also that philosophy should be
called knowledge of the truth. For the end of theoretical knowledge is truth,
while that of practical knowledge is action (for even if they consider how
things are, practical men do not study the eternal, but what is relative and in
the present). Now we do not know a truth without its cause; and a thing has a
quality in a higher degree than other things if in virtue of it the similar
quality belongs to the other things as well (e.g. fire is the hottest of things;
for it is the cause of the heat of all other things); so that that causes
derivative truths to be true is most true. Hence the principles of eternal
things must be always most true (for they are not merely sometimes true, nor is
there any cause of their being, but they themselves are the cause of the being
of other things), so that as each thing is in respect of being, so is it in
respect of truth.
2
But evidently there is a first principle, and
the causes of things are neither an infinite series nor infinitely various in
kind. For neither can one thing proceed from another, as from matter, ad
infinitum (e.g. flesh from earth, earth from air, air from fire, and so on
without stopping), nor can the sources of movement form an endless series (man
for instance being acted on by air, air by the sun, the sun by Strife, and so on
without limit). Similarly the final causes cannot go on ad infinitum, – walking
being for the sake of health, this for the sake of happiness, happiness for the
sake of something else, and so one thing always for the sake of another. And the
case of the essence is similar. For in the case of intermediates, which have a
last term and a term prior to them, the prior must be the cause of the later
terms. For if we had to say which of the three is the cause, we should say the
first; surely not the last, for the final term is the cause of none; nor even
the intermediate, for it is the cause only of one. (It makes no difference
whether there is one intermediate or more, nor whether they are infinite or
finite in number.) But of series which are infinite in this way, and of the
infinite in general, all the parts down to that now present are alike
intermediates; so that if there is no first there is no cause at
all.
Nor can there be an infinite process downwards,
with a beginning in the upward direction, so that water should proceed from
fire, earth from water, and so always some other kind should be produced. For
one thing comes from another in two ways – not in the sense in which ‘from’
means ‘after’ (as we say ‘from the Isthmian games come the Olympian’), but
either (i) as the man comes from the boy, by the boy’s changing, or (ii) as air
comes from water. By ‘as the man comes from the boy’ we mean ‘as that which has
come to be from that which is coming to be’ or ‘as that which is finished from
that which is being achieved’ (for as becoming is between being and not being,
so that which is becoming is always between that which is and that which is not;
for the learner is a man of science in the making, and this is what is meant
when we say that from a learner a man of science is being made); on the other
hand, coming from another thing as water comes from air implies the destruction
of the other thing. This is why changes of the former kind are not reversible,
and the boy does not come from the man (for it is not that which comes to be
something that comes to be as a result of coming to be, but that which exists
after the coming to be; for it is thus that the day, too, comes from the morning
– in the sense that it comes after the morning; which is the reason why the
morning cannot come from the day); but changes of the other kind are reversible.
But in both cases it is impossible that the number of terms should be infinite.
For terms of the former kind, being intermediates, must have an end, and terms
of the latter kind change back into one another, for the destruction of either
is the generation of the other.
At the same time it is impossible that the
first cause, being eternal, should be destroyed; for since the process of
becoming is not infinite in the upward direction, that which is the first thing
by whose destruction something came to be must be
non-eternal.
Further, the final cause is an end, and that
sort of end which is not for the sake of something else, but for whose sake
everything else is; so that if there is to be a last term of this sort, the
process will not be infinite; but if there is no such term, there will be no
final cause, but those who maintain the infinite series eliminate the Good
without knowing it (yet no one would try to do anything if he were not going to
come to a limit); nor would there be reason in the world; the reasonable man, at
least, always acts for a purpose, and this is a limit; for the end is a
limit.
But the essence, also, cannot be reduced to
another definition which is fuller in expression. For the original definition is
always more of a definition, and not the later one; and in a series in which the
first term has not the required character, the next has not it either. Further,
those who speak thus destroy science; for it is not possible to have this till
one comes to the unanalysable terms. And knowledge becomes impossible; for how
can one apprehend things that are infinite in this way? For this is not like the
case of the line, to whose divisibility there is no stop, but which we cannot
think if we do not make a stop (for which reason one who is tracing the
infinitely divisible line cannot be counting the possibilities of section), but
the whole line also must be apprehended by something in us that does not move
from part to part. – Again, nothing infinite can exist; and if it could, at
least the notion of infinity is not infinite.
But if the kinds of causes had been infinite in
number, then also knowledge would have been impossible; for we think we know,
only when we have ascertained the causes, that but that which is infinite by
addition cannot be gone through in a finite time.
3
The effect which lectures produce on a hearer
depends on his habits; for we demand the language we are accustomed to, and that
which is different from this seems not in keeping but somewhat unintelligible
and foreign because of its unwontedness. For it is the customary that is
intelligible. The force of habit is shown by the laws, in which the legendary
and childish elements prevail over our knowledge about them, owing to habit.
Thus some people do not listen to a speaker unless he speaks mathematically,
others unless he gives instances, while others expect him to cite a poet as
witness. And some want to have everything done accurately, while others are
annoyed by accuracy, either because they cannot follow the connexion of thought
or because they regard it as pettifoggery. For accuracy has something of this
character, so that as in trade so in argument some people think it mean. Hence
one must be already trained to know how to take each sort of argument, since it
is absurd to seek at the same time knowledge and the way of attaining knowledge;
and it is not easy to get even one of the two.
The minute accuracy of mathematics is not to be
demanded in all cases, but only in the case of things which have no matter.
Hence method is not that of natural science; for presumably the whole of nature
has matter. Hence we must inquire first what nature is: for thus we shall also
see what natural science treats of (and whether it belongs to one science or to
more to investigate the causes and the principles of
things).
1
We must, with a view to the science which we
are seeking, first recount the subjects that should be first discussed. These
include both the other opinions that some have held on the first principles, and
any point besides these that happens to have been overlooked. For those who wish
to get clear of difficulties it is advantageous to discuss the difficulties
well; for the subsequent free play of thought implies the solution of the
previous difficulties, and it is not possible to untie a knot of which one does
not know. But the difficulty of our thinking points to a ‘knot’ in the object;
for in so far as our thought is in difficulties, it is in like case with those
who are bound; for in either case it is impossible to go forward. Hence one
should have surveyed all the difficulties beforehand, both for the purposes we
have stated and because people who inquire without first stating the
difficulties are like those who do not know where they have to go; besides, a
man does not otherwise know even whether he has at any given time found what he
is looking for or not; for the end is not clear to such a man, while to him who
has first discussed the difficulties it is clear. Further, he who has heard all
the contending arguments, as if they were the parties to a case, must be in a
better position for judging.
The first problem concerns the subject which we
discussed in our prefatory remarks. It is this – (1) whether the investigation
of the causes belongs to one or to more sciences, and (2) whether such a science
should survey only the first principles of substance, or also the principles on
which all men base their proofs, e.g. whether it is possible at the same time to
assert and deny one and the same thing or not, and all other such questions; and
(3) if the science in question deals with substance, whether one science deals
with all substances, or more than one, and if more, whether all are akin, or
some of them must be called forms of Wisdom and the others something else. And
(4) this itself is also one of the things that must be discussed – whether
sensible substances alone should be said to exist or others also besides them,
and whether these others are of one kind or there are several classes of
substances, as is supposed by those who believe both in Forms and in
mathematical objects intermediate between these and sensible things. Into these
questions, then, as we say, we must inquire, and also (5) whether our
investigation is concerned only with substances or also with the essential
attributes of substances. Further, with regard to the same and other and like
and unlike and contrariety, and with regard to prior and posterior and all other
such terms about which the dialecticians try to inquire, starting their
investigation from probable premises only, – whose business is it to inquire
into all these? Further, we must discuss the essential attributes of these
themselves; and we must ask not only what each of these is, but also whether one
thing always has one contrary. Again (6), are the principles and elements of
things the genera, or the parts present in each thing, into which it is divided;
and (7) if they are the genera, are they the genera that are predicated
proximately of the individuals, or the highest genera, e.g. is animal or man the
first principle and the more independent of the individual instance? And (8) we
must inquire and discuss especially whether there is, besides the matter, any
thing that is a cause in itself or not, and whether this can exist apart or not,
and whether it is one or more in number, and whether there is something apart
from the concrete thing (by the concrete thing I mean the matter with something
already predicated of it), or there is nothing apart, or there is something in
some cases though not in others, and what sort of cases these are. Again (9) we
ask whether the principles are limited in number or in kind, both those in the
definitions and those in the substratum; and (10) whether the principles of
perishable and of imperishable things are the same or different; and whether
they are all imperishable or those of perishable things are perishable. Further
(11) there is the question which is hardest of all and most perplexing, whether
unity and being, as the Pythagoreans and Plato said, are not attributes of
something else but the substance of existing things, or this is not the case,
but the substratum is something else, – as Empedocles says, love; as some one
else says, fire; while another says water or air. Again (12) we ask whether the
principles are universal or like individual things, and (13) whether they exist
potentially or actually, and further, whether they are potential or actual in
any other sense than in reference to movement; for these questions also would
present much difficulty. Further (14), are numbers and lines and figures and
points a kind of substance or not, and if they are substances are they separate
from sensible things or present in them? With regard to all these matters not
only is it hard to get possession of the truth, but it is not easy even to think
out the difficulties well.
2
(1) First then with regard to what we mentioned
first, does it belong to one or to more sciences to investigate all the kinds of
causes? How could it belong to one science to recognize the principles if these
are not contrary?
Further, there are many things to which not all
the principles pertain. For how can a principle of change or the nature of the
good exist for unchangeable things, since everything that in itself and by its
own nature is good is an end, and a cause in the sense that for its sake the
other things both come to be and are, and since an end or purpose is the end of
some action, and all actions imply change? So in the case of unchangeable things
this principle could not exist, nor could there be a good itself. This is why in
mathematics nothing is proved by means of this kind of cause, nor is there any
demonstration of this kind – ‘because it is better, or worse’; indeed no one
even mentions anything of the kind. And so for this reason some of the Sophists,
e.g. Aristippus, used to ridicule mathematics; for in the arts (he maintained),
even in the industrial arts, e.g. in carpentry and cobbling, the reason always
given is ‘because it is better, or worse,’ but the mathematical sciences take no
account of goods and evils.
But if there are several sciences of the
causes, and a different science for each different principle, which of these
sciences should be said to be that which we seek, or which of the people who
possess them has the most scientific knowledge of the object in question? The
same thing may have all the kinds of causes, e.g. the moving cause of a house is
the art or the builder, the final cause is the function it fulfils, the matter
is earth and stones, and the form is the definition. To judge from our previous
discussion of the question which of the sciences should be called Wisdom, there
is reason for applying the name to each of them. For inasmuch as it is most
architectonic and authoritative and the other sciences, like slavewomen, may not
even contradict it, the science of the end and of the good is of the nature of
Wisdom (for the other things are for the sake of the end). But inasmuch as it
was described’ as dealing with the first causes and that which is in the highest
sense object of knowledge, the science of substance must be of the nature of
Wisdom. For since men may know the same thing in many ways, we say that he who
recognizes what a thing is by its being so and so knows more fully than he who
recognizes it by its not being so and so, and in the former class itself one
knows more fully than another, and he knows most fully who knows what a thing
is, not he who knows its quantity or quality or what it can by nature do or have
done to it. And further in all cases also we think that the knowledge of each
even of the things of which demonstration is possible is present only when we
know what the thing is, e.g. what squaring a rectangle is, viz. that it is the
finding of a mean; and similarly in all other cases. And we know about becomings
and actions and about every change when we know the source of the movement; and
this is other than and opposed to the end. Therefore it would seem to belong to
different sciences to investigate these causes severally.
But (2), taking the starting-points of
demonstration as well as the causes, it is a disputable question whether they
are the object of one science or of more (by the starting-points of
demonstration I mean the common beliefs, on which all men base their proofs);
e.g. that everything must be either affirmed or denied, and that a thing cannot
at the same time be and not be, and all other such premisses: – the question is
whether the same science deals with them as with substance, or a different
science, and if it is not one science, which of the two must be identified with
that which we now seek. – It is not reasonable that these topics should be the
object of one science; for why should it be peculiarly appropriate to geometry
or to any other science to understand these matters? If then it belongs to every
science alike, and cannot belong to all, it is not peculiar to the science which
investigates substances, any more than to any other science, to know about these
topics. – And, at the same time, in what way can there be a science of the first
principles? For we are aware even now what each of them in fact is (at least
even other sciences use them as familiar); but if there is a demonstrative
science which deals with them, there will have to be an underlying kind, and
some of them must be demonstrable attributes and others must be axioms (for it
is impossible that there should be demonstration about all of them); for the
demonstration must start from certain premisses and be about a certain subject
and prove certain attributes. Therefore it follows that all attributes that are
proved must belong to a single class; for all demonstrative sciences use the
axioms.
But if the science of substance and the science
which deals with the axioms are different, which of them is by nature more
authoritative and prior? The axioms are most universal and are principles of all
things. And if it is not the business of the philosopher, to whom else will it
belong to inquire what is true and what is untrue about
them?
(3) In general, do all substances fall under
one science or under more than one? If the latter, to what sort of substance is
the present science to be assigned? – On the other hand, it is not reasonable
that one science should deal with all. For then there would be one demonstrative
science dealing with all attributes. For ever demonstrative science investigates
with regard to some subject its essential attributes, starting from the common
beliefs. Therefore to investigate the essential attributes of one class of
things, starting from one set of beliefs, is the business of one science. For
the subject belongs to one science, and the premisses belong to one, whether to
the same or to another; so that the attributes do so too, whether they are
investigated by these sciences or by one compounded out of
them.
(5) Further, does our investigation deal with
substances alone or also with their attributes? I mean for instance, if the
solid is a substance and so are lines and planes, is it the business of the same
science to know these and to know the attributes of each of these classes (the
attributes about which the mathematical sciences offer proofs), or of a
different science? If of the same, the science of substance also must be a
demonstrative science, but it is thought that there is no demonstration of the
essence of things. And if of another, what will be the science that investigates
the attributes of substance? This is a very difficult
question.
(4) Further, must we say that sensible
substances alone exist, or that there are others besides these? And are
substances of one kind or are there in fact several kinds of substances, as
those say who assert the existence both of the Forms and of the intermediates,
with which they say the mathematical sciences deal? – The sense in which we say
the Forms are both causes and self-dependent substances has been explained in
our first remarks about them; while the theory presents difficulties in many
ways, the most paradoxical thing of all is the statement that there are certain
things besides those in the material universe, and that these are the same as
sensible things except that they are eternal while the latter are perishable.
For they say there is a man-himself and a horse-itself and health-itself, with
no further qualification, – a procedure like that of the people who said there
are gods, but in human form. For they were positing nothing but eternal men, nor
are the Platonists making the Forms anything other than eternal sensible
things.
Further, if we are to posit besides the Forms
and the sensibles the intermediates between them, we shall have many
difficulties. For clearly on the same principle there will be lines besides the
lines-themselves and the sensible lines, and so with each of the other classes
of things; so that since astronomy is one of these mathematical sciences there
will also be a heaven besides the sensible heaven, and a sun and a moon (and so
with the other heavenly bodies) besides the sensible. Yet how are we to believe
in these things? It is not reasonable even to suppose such a body immovable, but
to suppose it moving is quite impossible. – And similarly with the things of
which optics and mathematical harmonics treat; for these also cannot exist apart
from the sensible things, for the same reasons. For if there are sensible things
and sensations intermediate between Form and individual, evidently there will
also be animals intermediate between animals-themselves and the perishable
animals. – We might also raise the question, with reference to which kind of
existing things we must look for these sciences of intermediates. If geometry is
to differ from mensuration only in this, that the latter deals with things that
we perceive, and the former with things that are not perceptible, evidently
there will also be a science other than medicine, intermediate between
medical-science-itself and this individual medical science, and so with each of
the other sciences. Yet how is this possible? There would have to be also
healthy things besides the perceptible healthy things and the healthy-itself. –
And at the same time not even this is true, that mensuration deals with
perceptible and perishable magnitudes; for then it would have perished when they
perished.
But on the other hand astronomy cannot be
dealing with perceptible magnitudes nor with this heaven above us. For neither
are perceptible lines such lines as the geometer speaks of (for no perceptible
thing is straight or round in the way in which he defines ‘straight’ and
‘round’; for a hoop touches a straight edge not at a point, but as Protagoras
used to say it did, in his refutation of the geometers), nor are the movements
and spiral orbits in the heavens like those of which astronomy treats, nor have
geometrical points the same nature as the actual stars. – Now there are some who
say that these so-called intermediates between the Forms and the perceptible
things exist, not apart from the perceptible things, however, but in these; the
impossible results of this view would take too long to enumerate, but it is
enough to consider even such points as the following: – It is not reasonable
that this should be so only in the case of these intermediates, but clearly the
Forms also might be in the perceptible things; for both statements are parts of
the same theory. Further, it follows from this theory that there are two solids
in the same place, and that the intermediates are not immovable, since they are
in the moving perceptible things. And in general to what purpose would one
suppose them to exist indeed, but to exist in perceptible things? For the same
paradoxical results will follow which we have already mentioned; there will be a
heaven besides the heaven, only it will be not apart but in the same place;
which is still more impossible.
3
(6) Apart from the great difficulty of stating
the case truly with regard to these matters, it is very hard to say, with regard
to the first principles, whether it is the genera that should be taken as
elements and principles, or rather the primary constituents of a thing; e.g. it
is the primary parts of which articulate sounds consist that are thought to be
elements and principles of articulate sound, not the common genus-articulate
sound; and we give the name of ‘elements’ to those geometrical propositions, the
proofs of which are implied in the proofs of the others, either of all or of
most. Further, both those who say there are several elements of corporeal things
and those who say there is one, say the parts of which bodies are compounded and
consist are principles; e.g. Empedocles says fire and water and the rest are the
constituent elements of things, but does not describe these as genera of
existing things. Besides this, if we want to examine the nature of anything
else, we examine the parts of which, e.g. a bed consists and how they are put
together, and then we know its nature.
To judge from these arguments, then, the
principles of things would not be the genera; but if we know each thing by its
definition, and the genera are the principles or starting-points of definitions,
the genera must also be the principles of definable things. And if to get the
knowledge of the species according to which things are named is to get the
knowledge of things, the genera are at least starting-points of the species. And
some also of those who say unity or being, or the great and the small, are
elements of things, seem to treat them as genera.
But, again, it is not possible to describe the
principles in both ways. For the formula of the essence is one; but definition
by genera will be different from that which states the constituent parts of a
thing.
(7) Besides this, even if the genera are in the
highest degree principles, should one regard the first of the genera as
principles, or those which are predicated directly of the individuals? This also
admits of dispute. For if the universals are always more of the nature of
principles, evidently the uppermost of the genera are the principles; for these
are predicated of all things. There will, then, be as many principles of things
as there are primary genera, so that both being and unity will be principles and
substances; for these are most of all predicated of all existing things. But it
is not possible that either unity or being should be a single genus of things;
for the differentiae of any genus must each of them both have being and be one,
but it is not possible for the genus taken apart from its species (any more than
for the species of the genus) to be predicated of its proper differentiae; so
that if unity or being is a genus, no differentia will either have being or be
one. But if unity and being are not genera, neither will they be principles, if
the genera are the principles. Again, the intermediate kinds, in whose nature
the differentiae are included, will on this theory be genera, down to the
indivisible species; but as it is, some are thought to be genera and others are
not thought to be so. Besides this, the differentiae are principles even more
than the genera; and if these also are principles, there comes to be practically
an infinite number of principles, especially if we suppose the highest genus to
be a principle. – But again, if unity is more of the nature of a principle, and
the indivisible is one, and everything indivisible is so either in quantity or
in species, and that which is so in species is the prior, and genera are
divisible into species for man is not the genus of individual men), that which
is predicated directly of the individuals will have more unity. – Further, in
the case of things in which the distinction of prior and posterior is present,
that which is predicable of these things cannot be something apart from them
(e.g. if two is the first of numbers, there will not be a Number apart from the
kinds of numbers; and similarly there will not be a Figure apart from the kinds
of figures; and if the genera of these things do not exist apart from the
species, the genera of other things will scarcely do so; for genera of these
things are thought to exist if any do). But among the individuals one is not
prior and another posterior. Further, where one thing is better and another
worse, the better is always prior; so that of these also no genus can exist.
From these considerations, then, the species predicated of individuals seem to
be principles rather than the genera. But again, it is not easy to say in what
sense these are to be taken as principles. For the principle or cause must exist
alongside of the things of which it is the principle, and must be capable of
existing in separation from them; but for what reason should we suppose any such
thing to exist alongside of the individual, except that it is predicated
universally and of all? But if this is the reason, the things that are more
universal must be supposed to be more of the nature of principles; so that the
highest genera would be the principles.
4
(8) There is a difficulty connected with these,
the hardest of all and the most necessary to examine, and of this the discussion
now awaits us. If, on the one hand, there is nothing apart from individual
things, and the individuals are infinite in number, how then is it possible to
get knowledge of the infinite individuals? For all things that we come to know,
we come to know in so far as they have some unity and identity, and in so far as
some attribute belongs to them universally.
But if this is necessary, and there must be
something apart from the individuals, it will be necessary that the genera exist
apart from the individuals, either the lowest or the highest genera; but we
found by discussion just now that this is impossible.
Further, if we admit in the fullest sense that
something exists apart from the concrete thing, whenever something is predicated
of the matter, must there, if there is something apart, be something apart from
each set of individuals, or from some and not from others, or from none? (A) If
there is nothing apart from individuals, there will be no object of thought, but
all things will be objects of sense, and there will not be knowledge of
anything, unless we say that sensation is knowledge. Further, nothing will be
eternal or unmovable; for all perceptible things perish and are in movement. But
if there is nothing eternal, neither can there be a process of coming to be; for
there must be something that comes to be, i.e. from which something comes to be,
and the ultimate term in this series cannot have come to be, since the series
has a limit and since nothing can come to be out of that which is not. Further,
if generation and movement exist there must also be a limit; for no movement is
infinite, but every movement has an end, and that which is incapable of
completing its coming to be cannot be in process of coming to be; and that which
has completed its coming to be must he as soon as it has come to be. Further,
since the matter exists, because it is ungenerated, it is a fortiori reasonable
that the substance or essence, that which the matter is at any time coming to
be, should exist; for if neither essence nor matter is to be, nothing will be at
all, and since this is impossible there must be something besides the concrete
thing, viz. the shape or form.
But again (B) if we are to suppose this, it is
hard to say in which cases we are to suppose it and in which not. For evidently
it is not possible to suppose it in all cases; we could not suppose that there
is a house besides the particular houses. – Besides this, will the substance of
all the individuals, e.g. of all men, be one? This is paradoxical, for all the
things whose substance is one are one. But are the substances many and
different? This also is unreasonable. – At the same time, how does the matter
become each of the individuals, and how is the concrete thing these two
elements?
(9) Again, one might ask the following question
also about the first principles. If they are one in kind only, nothing will be
numerically one, not even unity-itself and being-itself; and how will knowing
exist, if there is not to be something common to a whole set of
individuals?
But if there is a common element which is
numerically one, and each of the principles is one, and the principles are not
as in the case of perceptible things different for different things (e.g. since
this particular syllable is the same in kind whenever it occurs, the elements it
are also the same in kind; only in kind, for these also, like the syllable, are
numerically different in different contexts), – if it is not like this but the
principles of things are numerically one, there will be nothing else besides the
elements (for there is no difference of meaning between ‘numerically one’ and
‘individual’; for this is just what we mean by the individual – the numerically
one, and by the universal we mean that which is predicable of the individuals).
Therefore it will be just as if the elements of articulate sound were limited in
number; all the language in the world would be confined to the ABC, since there
could not be two or more letters of the same kind.
(10) One difficulty which is as great as any
has been neglected both by modern philosophers and by their predecessors –
whether the principles of perishable and those of imperishable things are the
same or different. If they are the same, how are some things perishable and
others imperishable, and for what reason? The school of Hesiod and all the
theologians thought only of what was plausible to themselves, and had no regard
to us. For, asserting the first principles to be gods and born of gods, they say
that the beings which did not taste of nectar and ambrosia became mortal; and
clearly they are using words which are familiar to themselves, yet what they
have said about the very application of these causes is above our comprehension.
For if the gods taste of nectar and ambrosia for their pleasure, these are in no
wise the causes of their existence; and if they taste them to maintain their
existence, how can gods who need food be eternal? – But into the subtleties of
the mythologists it is not worth our while to inquire seriously; those, however,
who use the language of proof we must cross-examine and ask why, after all,
things which consist of the same elements are, some of them, eternal in nature,
while others perish. Since these philosophers mention no cause, and it is
unreasonable that things should be as they say, evidently the principles or
causes of things cannot be the same. Even the man whom one might suppose to
speak most consistently – Empedocles, even he has made the same mistake; for he
maintains that strife is a principle that causes destruction, but even strife
would seem no less to produce everything, except the One; for all things
excepting God proceed from strife. At least he says: –
From which all that was and is and will be
hereafter –
Trees, and men and women, took their
growth,
And beasts and birds and water-nourished
fish,
And long-aged gods.
The implication is evident even apart from
these words; for if strife had not been present in things, all things would have
been one, according to him; for when they have come together, ‘then strife stood
outermost.’ Hence it also follows on his theory that God most blessed is less
wise than all others; for he does not know all the elements; for he has in him
no strife, and knowledge is of the like by the like. ‘For by earth,’ he
says,
We see earth, by water
water,
By ether godlike ether, by fire wasting
fire,
Love by love, and strife by gloomy
strife.
But – and this is the point we started from
this at least is evident, that on his theory it follows that strife is as much
the cause of existence as of destruction. And similarly love is not specially
the cause of existence; for in collecting things into the One it destroys all
other things. And at the same time Empedocles mentions no cause of the change
itself, except that things are so by nature.
But when strife at last waxed great in the
limbs of the Sphere,
And sprang to assert its rights as the time was
fulfilled
Which is fixed for them in turn by a mighty
oath.
This implies that change was necessary; but he
shows no cause of the necessity. But yet so far at least he alone speaks
consistently; for he does not make some things perishable and others
imperishable, but makes all perishable except the elements. The difficulty we
are speaking of now is, why some things are perishable and others are not, if
they consist of the same principles.
Let this suffice as proof of the fact that the
principles cannot be the same. But if there are different principles, one
difficulty is whether these also will be imperishable or perishable. For if they
are perishable, evidently these also must consist of certain elements (for all
things that perish, perish by being resolved into the elements of which they
consist); so that it follows that prior to the principles there are other
principles. But this is impossible, whether the process has a limit or proceeds
to infinity. Further, how will perishable things exist, if their principles are
to be annulled? But if the principles are imperishable, why will things composed
of some imperishable principles be perishable, while those composed of the
others are imperishable? This is not probable, but is either impossible or needs
much proof. Further, no one has even tried to maintain different principles;
they maintain the same principles for all things. But they swallow the
difficulty we stated first as if they took it to be something
trifling.
(11) The inquiry that is both the hardest of
all and the most necessary for knowledge of the truth is whether being and unity
are the substances of things, and whether each of them, without being anything
else, is being or unity respectively, or we must inquire what being and unity
are, with the implication that they have some other underlying nature. For some
people think they are of the former, others think they are of the latter
character. Plato and the Pythagoreans thought being and unity were nothing else,
but this was their nature, their essence being just unity and being. But the
natural philosophers take a different line; e.g. Empedocles – as though reducing
to something more intelligible – says what unity is; for he would seem to say it
is love: at least, this is for all things the cause of their being one. Others
say this unity and being, of which things consist and have been made, is fire,
and others say it is air. A similar view is expressed by those who make the
elements more than one; for these also must say that unity and being are
precisely all the things which they say are principles.
(A) If we do not suppose unity and being to be
substances, it follows that none of the other universals is a substance; for
these are most universal of all, and if there is no unity-itself or
being-itself, there will scarcely be in any other case anything apart from what
are called the individuals. Further, if unity is not a substance, evidently
number also will not exist as an entity separate from the individual things; for
number is units, and the unit is precisely a certain kind of
one.
But (B) if there is a unity-itself and a
being-itself, unity and being must be their substance; for it is not something
else that is predicated universally of the things that are and are one, but just
unity and being. But if there is to be a being-itself and a unity-itself, there
is much difficulty in seeing how there will be anything else besides these, – I
mean, how things will be more than one in number. For what is different from
being does not exist, so that it necessarily follows, according to the argument
of Parmenides, that all things that are are one and this is
being.
There are objections to both views. For whether
unity is not a substance or there is a unity-itself, number cannot be a
substance. We have already said why this result follows if unity is not a
substance; and if it is, the same difficulty arises as arose with regard to
being. For whence is there to be another one besides unity-itself? It must be
not-one; but all things are either one or many, and of the many each is
one.
Further, if unity-itself is indivisible,
according to Zeno’s postulate it will be nothing. For that which neither when
added makes a thing greater nor when subtracted makes it less, he asserts to
have no being, evidently assuming that whatever has being is a spatial
magnitude. And if it is a magnitude, it is corporeal; for the corporeal has
being in every dimension, while the other objects of mathematics, e.g. a plane
or a line, added in one way will increase what they are added to, but in another
way will not do so, and a point or a unit does so in no way. But, since his
theory is of a low order, and an indivisible thing can exist in such a way as to
have a defence even against him (for the indivisible when added will make the
number, though not the size, greater), – yet how can a magnitude proceed from
one such indivisible or from many? It is like saying that the line is made out
of points.
But even if ore supposes the case to be such
that, as some say, number proceeds from unity-itself and something else which is
not one, none the less we must inquire why and how the product will be sometimes
a number and sometimes a magnitude, if the not-one was inequality and was the
same principle in either case. For it is not evident how magnitudes could
proceed either from the one and this principle, or from some number and this
principle.
5
(14) A question connected with these is whether
numbers and bodies and planes and points are substances of a kind, or not. If
they are not, it baffles us to say what being is and what the substances of
things are. For modifications and movements and relations and dispositions and
ratios do not seem to indicate the substance of anything; for all are predicated
of a subject, and none is a ‘this’. And as to the things which might seem most
of all to indicate substance, water and earth and fire and air, of which
composite bodies consist, heat and cold and the like are modifications of these,
not substances, and the body which is thus modified alone persists as something
real and as a substance. But, on the other hand, the body is surely less of a
substance than the surface, and the surface than the line, and the line than the
unit and the point. For the body is bounded by these; and they are thought to be
capable of existing without body, but body incapable of existing without these.
This is why, while most of the philosophers and the earlier among them thought
that substance and being were identical with body, and that all other things
were modifications of this, so that the first principles of the bodies were the
first principles of being, the more recent and those who were held to be wiser
thought numbers were the first principles. As we said, then, if these are not
substance, there is no substance and no being at all; for the accidents of these
it cannot be right to call beings.
But if this is admitted, that lines and points
are substance more than bodies, but we do not see to what sort of bodies these
could belong (for they cannot be in perceptible bodies), there can be no
substance. – Further, these are all evidently divisions of body, – one in
breadth, another in depth, another in length. Besides this, no sort of shape is
present in the solid more than any other; so that if the Hermes is not in the
stone, neither is the half of the cube in the cube as something determinate;
therefore the surface is not in it either; for if any sort of surface were in
it, the surface which marks off the half of the cube would be in it too. And the
same account applies to the line and to the point and the unit. Therefore, if on
the one hand body is in the highest degree substance, and on the other hand
these things are so more than body, but these are not even instances of
substance, it baffles us to say what being is and what the substance of things
is. – For besides what has been said, the questions of generation and
instruction confront us with further paradoxes. For if substance, not having
existed before, now exists, or having existed before, afterwards does not exist,
this change is thought to be accompanied by a process of becoming or perishing;
but points and lines and surfaces cannot be in process either of becoming or of
perishing, when they at one time exist and at another do not. For when bodies
come into contact or are divided, their boundaries simultaneously become one in
the one case when they touch, and two in the other – when they are divided; so
that when they have been put together one boundary does not exist but has
perished, and when they have been divided the boundaries exist which before did
not exist (for it cannot be said that the point, which is indivisible, was
divided into two). And if the boundaries come into being and cease to be, from
what do they come into being? A similar account may also be given of the ‘now’
in time; for this also cannot be in process of coming into being or of ceasing
to be, but yet seems to be always different, which shows that it is not a
substance. And evidently the same is true of points and lines and planes; for
the same argument applies, since they are all alike either limits or
divisions.
6
In general one might raise the question why
after all, besides perceptible things and the intermediates, we have to look for
another class of things, i.e. the Forms which we posit. If it is for this
reason, because the objects of mathematics, while they differ from the things in
this world in some other respect, differ not at all in that there are many of
the same kind, so that their first principles cannot be limited in number (just
as the elements of all the language in this sensible world are not limited in
number, but in kind, unless one takes the elements of this individual syllable
or of this individual articulate sound – whose elements will be limited even in
number; so is it also in the case of the intermediates; for there also the
members of the same kind are infinite in number), so that if there are not –
besides perceptible and mathematical objects – others such as some maintain the
Forms to be, there will be no substance which is one in number, but only in
kind, nor will the first principles of things be determinate in number, but only
in kind: – if then this must be so, the Forms also must therefore be held to
exist. Even if those who support this view do not express it articulately, still
this is what they mean, and they must be maintaining the Forms just because each
of the Forms is a substance and none is by accident.
But if we are to suppose both that the Forms
exist and that the principles are one in number, not in kind, we have mentioned
the impossible results that necessarily follow.
(13) Closely connected with this is the
question whether the elements exist potentially or in some other manner. If in
some other way, there will be something else prior to the first principles; for
the potency is prior to the actual cause, and it is not necessary for everything
potential to be actual. – But if the elements exist potentially, it is possible
that everything that is should not be. For even that which is not yet is capable
of being; for that which is not comes to be, but nothing that is incapable of
being comes to be.
(12) We must not only raise these questions
about the first principles, but also ask whether they are universal or what we
call individuals. If they are universal, they will not be substances; for
everything that is common indicates not a ‘this’ but a ‘such’, but substance is
a ‘this’. And if we are to be allowed to lay it down that a common predicate is
a ‘this’ and a single thing, Socrates will be several animals – himself and
‘man’ and ‘animal’, if each of these indicates a ‘this’ and a single
thing.
If, then, the principles are universals, these
universal. Therefore if there is to be results follow; if they are not
universals but of knowledge of the principles there must be the nature of
individuals, they will not be other principles prior to them, namely those
knowable; for the knowledge of anything is that are universally predicated of
them.
1
There is a science which investigates being as being and the attributes which belong to this in virtue of its own nature. Now this is not the same as any of the so-called special sciences; for none of these others treats universally of being as being. They cut off a part of being and investigate the attribute of this part; this is what the mathematical sciences for instance do. Now since we are seeking the first principles and the highest causes, clearly there must be some thing to which these belong in virtue of its own nature. If then those who sought the elements of existing things were seeking these same principles, it is necessary that the elements must be elements of being not by accident but just because it is being. Therefore it is of being as being that we also must grasp the first causes.
2
There are many senses in which a thing may be
said to ‘be’, but all that ‘is’ is related to one central point, one definite
kind of thing, and is not said to ‘be’ by a mere ambiguity. Everything which is
healthy is related to health, one thing in the sense that it preserves health,
another in the sense that it produces it, another in the sense that it is a
symptom of health, another because it is capable of it. And that which is
medical is relative to the medical art, one thing being called medical because
it possesses it, another because it is naturally adapted to it, another because
it is a function of the medical art. And we shall find other words used
similarly to these. So, too, there are many senses in which a thing is said to
be, but all refer to one starting-point; some things are said to be because they
are substances, others because they are affections of substance, others because
they are a process towards substance, or destructions or privations or qualities
of substance, or productive or generative of substance, or of things which are
relative to substance, or negations of one of these thing of substance itself.
It is for this reason that we say even of non-being that it is nonbeing. As,
then, there is one science which deals with all healthy things, the same applies
in the other cases also. For not only in the case of things which have one
common notion does the investigation belong to one science, but also in the case
of things which are related to one common nature; for even these in a sense have
one common notion. It is clear then that it is the work of one science also to
study the things that are, qua being. – But everywhere science deals chiefly
with that which is primary, and on which the other things depend, and in virtue
of which they get their names. If, then, this is substance, it will be of
substances that the philosopher must grasp the principles and the
causes.
Now for each one class of things, as there is
one perception, so there is one science, as for instance grammar, being one
science, investigates all articulate sounds. Hence to investigate all the
species of being qua being is the work of a science which is generically one,
and to investigate the several species is the work of the specific parts of the
science.
If, now, being and unity are the same and are
one thing in the sense that they are implied in one another as principle and
cause are, not in the sense that they are explained by the same definition
(though it makes no difference even if we suppose them to be like that – in fact
this would even strengthen our case); for ‘one man’ and ‘man’ are the same
thing, and so are ‘existent man’ and ‘man’, and the doubling of the words in
‘one man and one existent man’ does not express anything different (it is clear
that the two things are not separated either in coming to be or in ceasing to
be); and similarly ‘one existent man’ adds nothing to ‘existent man’, and that
it is obvious that the addition in these cases means the same thing, and unity
is nothing apart from being; and if, further, the substance of each thing is one
in no merely accidental way, and similarly is from its very nature something
that is: – all this being so, there must be exactly as many species of being as
of unity. And to investigate the essence of these is the work of a science which
is generically one – I mean, for instance, the discussion of the same and the
similar and the other concepts of this sort; and nearly all contraries may be
referred to this origin; let us take them as having been investigated in the
‘Selection of Contraries’.
And there are as many parts of philosophy as
there are kinds of substance, so that there must necessarily be among them a
first philosophy and one which follows this. For being falls immediately into
genera; for which reason the sciences too will correspond to these genera. For
the philosopher is like the mathematician, as that word is used; for mathematics
also has parts, and there is a first and a second science and other successive
ones within the sphere of mathematics.
Now since it is the work of one science to
investigate opposites, and plurality is opposed to unity – and it belongs to one
science to investigate the negation and the privation because in both cases we
are really investigating the one thing of which the negation or the privation is
a negation or privation (for we either say simply that that thing is not
present, or that it is not present in some particular class; in the latter case
difference is present over and above what is implied in negation; for negation
means just the absence of the thing in question, while in privation there is
also employed an underlying nature of which the privation is asserted): – in
view of all these facts, the contraries of the concepts we named above, the
other and the dissimilar and the unequal, and everything else which is derived
either from these or from plurality and unity, must fall within the province of
the science above named. And contrariety is one of these concepts; for
contrariety is a kind of difference, and difference is a kind of otherness.
Therefore, since there are many senses in which a thing is said to be one, these
terms also will have many senses, but yet it belongs to one science to know them
all; for a term belongs to different sciences not if it has different senses,
but if it has not one meaning and its definitions cannot be referred to one
central meaning. And since all things are referred to that which is primary, as
for instance all things which are called one are referred to the primary one, we
must say that this holds good also of the same and the other and of contraries
in general; so that after distinguishing the various senses of each, we must
then explain by reference to what is primary in the case of each of the
predicates in question, saying how they are related to it; for some will be
called what they are called because they possess it, others because they produce
it, and others in other such ways.
It is evident, then, that it belongs to one
science to be able to give an account of these concepts as well as of substance
(this was one of the questions in our book of problems), and that it is the
function of the philosopher to be able to investigate all things. For if it is
not the function of the philosopher, who is it who will inquire whether Socrates
and Socrates seated are the same thing, or whether one thing has one contrary,
or what contrariety is, or how many meanings it has? And similarly with all
other such questions. Since, then, these are essential modifications of unity
qua unity and of being qua being, not qua numbers or lines or fire, it is clear
that it belongs to this science to investigate both the essence of these
concepts and their properties. And those who study these properties err not by
leaving the sphere of philosophy, but by forgetting that substance, of which
they have no correct idea, is prior to these other things. For number qua number
has peculiar attributes, such as oddness and evenness, commensurability and
equality, excess and defect, and these belong to numbers either in themselves or
in relation to one another. And similarly the solid and the motionless and that
which is in motion and the weightless and that which has weight have other
peculiar properties. So too there are certain properties peculiar to being as
such, and it is about these that the philosopher has to investigate the truth. –
An indication of this may be mentioned: dialecticians and sophists assume the
same guise as the philosopher, for sophistic is Wisdom which exists only in
semblance, and dialecticians embrace all things in their dialectic, and being is
common to all things; but evidently their dialectic embraces these subjects
because these are proper to philosophy. – For sophistic and dialectic turn on
the same class of things as philosophy, but this differs from dialectic in the
nature of the faculty required and from sophistic in respect of the purpose of
the philosophic life. Dialectic is merely critical where philosophy claims to
know, and sophistic is what appears to be philosophy but is
not.
Again, in the list of contraries one of the two
columns is privative, and all contraries are reducible to being and non-being,
and to unity and plurality, as for instance rest belongs to unity and movement
to plurality. And nearly all thinkers agree that being and substance are
composed of contraries; at least all name contraries as their first principles –
some name odd and even, some hot and cold, some limit and the unlimited, some
love and strife. And all the others as well are evidently reducible to unity and
plurality (this reduction we must take for granted), and the principles stated
by other thinkers fall entirely under these as their genera. It is obvious then
from these considerations too that it belongs to one science to examine being
qua being. For all things are either contraries or composed of contraries, and
unity and plurality are the starting-points of all contraries. And these belong
to one science, whether they have or have not one single meaning. Probably the
truth is that they have not; yet even if ‘one’ has several meanings, the other
meanings will be related to the primary meaning (and similarly in the case of
the contraries), even if being or unity is not a universal and the same in every
instance or is not separable from the particular instances (as in fact it
probably is not; the unity is in some cases that of common reference, in some
cases that of serial succession). And for this reason it does not belong to the
geometer to inquire what is contrariety or completeness or unity or being or the
same or the other, but only to presuppose these concepts and reason from this
starting-point. – Obviously then it is the work of one science to examine being
qua being, and the attributes which belong to it qua being, and the same science
will examine not only substances but also their attributes, both those above
named and the concepts ‘prior’ and ‘posterior’, ‘genus’ and ‘species’, ‘whole’
and ‘part’, and the others of this sort.
3
We must state whether it belongs to one or to
different sciences to inquire into the truths which are in mathematics called
axioms, and into substance. Evidently, the inquiry into these also belongs to
one science, and that the science of the philosopher; for these truths hold good
for everything that is, and not for some special genus apart from others. And
all men use them, because they are true of being qua being and each genus has
being. But men use them just so far as to satisfy their purposes; that is, as
far as the genus to which their demonstrations refer extends. Therefore since
these truths clearly hold good for all things qua being (for this is what is
common to them), to him who studies being qua being belongs the inquiry into
these as well. And for this reason no one who is conducting a special inquiry
tries to say anything about their truth or falsity, – neither the geometer nor
the arithmetician. Some natural philosophers indeed have done so, and their
procedure was intelligible enough; for they thought that they alone were
inquiring about the whole of nature and about being. But since there is one kind
of thinker who is above even the natural philosopher (for nature is only one
particular genus of being), the discussion of these truths also will belong to
him whose inquiry is universal and deals with primary substance. Physics also is
a kind of Wisdom, but it is not the first kind. – And the attempts of some of
those who discuss the terms on which truth should be accepted, are due to a want
of training in logic; for they should know these things already when they come
to a special study, and not be inquiring into them while they are listening to
lectures on it.
Evidently then it belongs to the philosopher,
i.e. to him who is studying the nature of all substance, to inquire also into
the principles of syllogism. But he who knows best about each genus must be able
to state the most certain principles of his subject, so that he whose subject is
existing things qua existing must be able to state the most certain principles
of all things. This is the philosopher, and the most certain principle of all is
that regarding which it is impossible to be mistaken; for such a principle must
be both the best known (for all men may be mistaken about things which they do
not know), and non-hypothetical. For a principle which every one must have who
understands anything that is, is not a hypothesis; and that which every one must
know who knows anything, he must already have when he comes to a special study.
Evidently then such a principle is the most certain of all; which principle this
is, let us proceed to say. It is, that the same attribute cannot at the same
time belong and not belong to the same subject and in the same respect; we must
presuppose, to guard against dialectical objections, any further qualifications
which might be added. This, then, is the most certain of all principles, since
it answers to the definition given above. For it is impossible for any one to
believe the same thing to be and not to be, as some think Heraclitus says. For
what a man says, he does not necessarily believe; and if it is impossible that
contrary attributes should belong at the same time to the same subject (the
usual qualifications must be presupposed in this premiss too), and if an opinion
which contradicts another is contrary to it, obviously it is impossible for the
same man at the same time to believe the same thing to be and not to be; for if
a man were mistaken on this point he would have contrary opinions at the same
time. It is for this reason that all who are carrying out a demonstration reduce
it to this as an ultimate belief; for this is naturally the starting-point even
for all the other axioms.
4
There are some who, as we said, both themselves
assert that it is possible for the same thing to be and not to be, and say that
people can judge this to be the case. And among others many writers about nature
use this language. But we have now posited that it is impossible for anything at
the same time to be and not to be, and by this means have shown that this is the
most indisputable of all principles. – Some indeed demand that even this shall
be demonstrated, but this they do through want of education, for not to know of
what things one should demand demonstration, and of what one should not, argues
want of education. For it is impossible that there should be demonstration of
absolutely everything (there would be an infinite regress, so that there would
still be no demonstration); but if there are things of which one should not
demand demonstration, these persons could not say what principle they maintain
to be more self-evident than the present one.
We can, however, demonstrate negatively even
that this view is impossible, if our opponent will only say something; and if he
says nothing, it is absurd to seek to give an account of our views to one who
cannot give an account of anything, in so far as he cannot do so. For such a
man, as such, is from the start no better than a vegetable. Now negative
demonstration I distinguish from demonstration proper, because in a
demonstration one might be thought to be begging the question, but if another
person is responsible for the assumption we shall have negative proof, not
demonstration. The starting-point for all such arguments is not the demand that
our opponent shall say that something either is or is not (for this one might
perhaps take to be a begging of the question), but that he shall say something
which is significant both for himself and for another; for this is necessary, if
he really is to say anything. For, if he means nothing, such a man will not be
capable of reasoning, either with himself or with another. But if any one grants
this, demonstration will be possible; for we shall already have something
definite. The person responsible for the proof, however, is not he who
demonstrates but he who listens; for while disowning reason he listens to
reason. And again he who admits this has admitted that something is true apart
from demonstration (so that not everything will be ‘so and not
so’).
First then this at least is obviously true,
that the word ‘be’ or ‘not be’ has a definite meaning, so that not everything
will be ‘so and not so’. Again, if ‘man’ has one meaning, let this be
‘two-footed animal’; by having one meaning I understand this: – if ‘man’ means
‘X’, then if A is a man ‘X’ will be what ‘being a man’ means for him. (It makes
no difference even if one were to say a word has several meanings, if only they
are limited in number; for to each definition there might be assigned a
different word. For instance, we might say that ‘man’ has not one meaning but
several, one of which would have one definition, viz. ‘two-footed animal’, while
there might be also several other definitions if only they were limited in
number; for a peculiar name might be assigned to each of the definitions. If,
however, they were not limited but one were to say that the word has an infinite
number of meanings, obviously reasoning would be impossible; for not to have one
meaning is to have no meaning, and if words have no meaning our reasoning with
one another, and indeed with ourselves, has been annihilated; for it is
impossible to think of anything if we do not think of one thing; but if this is
possible, one name might be assigned to this thing.)
Let it be assumed then, as was said at the
beginning, that the name has a meaning and has one meaning; it is impossible,
then, that ‘being a man’ should mean precisely ‘not being a man’, if ‘man’ not
only signifies something about one subject but also has one significance (for we
do not identify ‘having one significance’ with ‘signifying something about one
subject’, since on that assumption even ‘musical’ and ‘white’ and ‘man’ would
have had one significance, so that all things would have been one; for they
would all have had the same significance).
And it will not be possible to be and not to be
the same thing, except in virtue of an ambiguity, just as if one whom we call
‘man’, others were to call ‘not-man’; but the point in question is not this,
whether the same thing can at the same time be and not be a man in name, but
whether it can in fact. Now if ‘man’ and ‘not-man’ mean nothing different,
obviously ‘not being a man’ will mean nothing different from ‘being a man’; so
that ‘being a man’ will be ‘not being a man’; for they will be one. For being
one means this – being related as ‘raiment’ and ‘dress’ are, if their definition
is one. And if ‘being a man’ and ‘being a not-man’ are to be one, they must mean
one thing. But it was shown earlier that they mean different things. –
Therefore, if it is true to say of anything that it is a man, it must be a
two-footed animal (for this was what ‘man’ meant); and if this is necessary, it
is impossible that the same thing should not at that time be a two-footed
animal; for this is what ‘being necessary’ means – that it is impossible for the
thing not to be. It is, then, impossible that it should be at the same time true
to say the same thing is a man and is not a man.
The same account holds good with regard to ‘not
being a man’, for ‘being a man’ and ‘being a not-man’ mean different things,
since even ‘being white’ and ‘being a man’ are different; for the former terms
are much more different so that they must a fortiori mean different things. And
if any one says that ‘white’ means one and the same thing as ‘man’, again we
shall say the same as what was said before, that it would follow that all things
are one, and not only opposites. But if this is impossible, then what we have
maintained will follow, if our opponent will only answer our
question.
And if, when one asks the question simply, he
adds the contradictories, he is not answering the question. For there is nothing
to prevent the same thing from being both a man and white and countless other
things: but still, if one asks whether it is or is not true to say that this is
a man, our opponent must give an answer which means one thing, and not add that
‘it is also white and large’. For, besides other reasons, it is impossible to
enumerate its accidental attributes, which are infinite in number; let him,
then, enumerate either all or none. Similarly, therefore, even if the same thing
is a thousand times a man and a not-man, he must not, in answering the question
whether this is a man, add that it is also at the same time a not-man, unless he
is bound to add also all the other accidents, all that the subject is or is not;
and if he does this, he is not observing the rules of
argument.
And in general those who say this do away with
substance and essence. For they must say that all attributes are accidents, and
that there is no such thing as ‘being essentially a man’ or ‘an animal’. For if
there is to be any such thing as ‘being essentially a man’ this will not be
‘being a not-man’ or ‘not being a man’ (yet these are negations of it); for
there was one thing which it meant, and this was the substance of something. And
denoting the substance of a thing means that the essence of the thing is nothing
else. But if its being essentially a man is to be the same as either being
essentially a not-man or essentially not being a man, then its essence will be
something else. Therefore our opponents must say that there cannot be such a
definition of anything, but that all attributes are accidental; for this is the
distinction between substance and accident – ‘white’ is accidental to man,
because though he is white, whiteness is not his essence. But if all statements
are accidental, there will be nothing primary about which they are made, if the
accidental always implies predication about a subject. The predication, then,
must go on ad infinitum. But this is impossible; for not even more than two
terms can be combined in accidental predication. For (1) an accident is not an
accident of an accident, unless it be because both are accidents of the same
subject. I mean, for instance, that the white is musical and the latter is
white, only because both are accidental to man. But (2) Socrates is musical, not
in this sense, that both terms are accidental to something else. Since then some
predicates are accidental in this and some in that sense, (a) those which are
accidental in the latter sense, in which white is accidental to Socrates, cannot
form an infinite series in the upward direction; e.g. Socrates the white has not
yet another accident; for no unity can be got out of such a sum. Nor again (b)
will ‘white’ have another term accidental to it, e.g. ‘musical’. For this is no
more accidental to that than that is to this; and at the same time we have drawn
the distinction, that while some predicates are accidental in this sense, others
are so in the sense in which ‘musical’ is accidental to Socrates; and the
accident is an accident of an accident not in cases of the latter kind, but only
in cases of the other kind, so that not all terms will be accidental. There
must, then, even so be something which denotes substance. And if this is so, it
has been shown that contradictories cannot be predicated at the same
time.
Again, if all contradictory statements are true
of the same subject at the same time, evidently all things will be one. For the
same thing will be a trireme, a wall, and a man, if of everything it is possible
either to affirm or to deny anything (and this premiss must be accepted by those
who share the views of Protagoras). For if any one thinks that the man is not a
trireme, evidently he is not a trireme; so that he also is a trireme, if, as
they say, contradictory statements are both true. And we thus get the doctrine
of Anaxagoras, that all things are mixed together; so that nothing really
exists. They seem, then, to be speaking of the indeterminate, and, while
fancying themselves to be speaking of being, they are speaking about non-being;
for it is that which exists potentially and not in complete reality that is
indeterminate. But they must predicate of every subject the affirmation or the
negation of every attribute. For it is absurd if of each subject its own
negation is to be predicable, while the negation of something else which cannot
be predicated of it is not to be predicable of it; for instance, if it is true
to say of a man that he is not a man, evidently it is also true to say that he
is either a trireme or not a trireme. If, then, the affirmative can be
predicated, the negative must be predicable too; and if the affirmative is not
predicable, the negative, at least, will be more predicable than the negative of
the subject itself. If, then, even the latter negative is predicable, the
negative of ‘trireme’ will be also predicable; and, if this is predicable, the
affirmative will be so too.
Those, then, who maintain this view are driven
to this conclusion, and to the further conclusion that it is not necessary
either to assert or to deny. For if it is true that a thing is a man and a
not-man, evidently also it will be neither a man nor a not-man. For to the two
assertions there answer two negations, and if the former is treated as a single
proposition compounded out of two, the latter also is a single proposition
opposite to the former.
Again, either the theory is true in all cases,
and a thing is both white and not-white, and existent and non-existent, and all
other assertions and negations are similarly compatible or the theory is true of
some statements and not of others. And if not of all, the exceptions will be
contradictories of which admittedly only one is true; but if of all, again
either the negation will be true wherever the assertion is, and the assertion
true wherever the negation is, or the negation will be true where the assertion
is, but the assertion not always true where the negation is. And (a) in the
latter case there will be something which fixedly is not, and this will be an
indisputable belief; and if non-being is something indisputable and knowable,
the opposite assertion will be more knowable. But (b) if it is equally possible
also to assert all that it is possible to deny, one must either be saying what
is true when one separates the predicates (and says, for instance, that a thing
is white, and again that it is not-white), or not. And if (i) it is not true to
apply the predicates separately, our opponent is not saying what he professes to
say, and also nothing at all exists; but how could non-existent things speak or
walk, as he does? Also all things would on this view be one, as has been already
said, and man and God and trireme and their contradictories will be the same.
For if contradictories can be predicated alike of each subject, one thing will
in no wise differ from another; for if it differ, this difference will be
something true and peculiar to it. And (ii) if one may with truth apply the
predicates separately, the above-mentioned result follows none the less, and,
further, it follows that all would then be right and all would be in error, and
our opponent himself confesses himself to be in error. – And at the same time
our discussion with him is evidently about nothing at all; for he says nothing.
For he says neither ‘yes’ nor ‘no’, but ‘yes and no’; and again he denies both
of these and says ‘neither yes nor no’; for otherwise there would already be
something definite.
Again if when the assertion is true, the
negation is false, and when this is true, the affirmation is false, it will not
be possible to assert and deny the same thing truly at the same time. But
perhaps they might say this was the very question at
issue.
Again, is he in error who judges either that
the thing is so or that it is not so, and is he right who judges both? If he is
right, what can they mean by saying that the nature of existing things is of
this kind? And if he is not right, but more right than he who judges in the
other way, being will already be of a definite nature, and this will be true,
and not at the same time also not true. But if all are alike both wrong and
right, one who is in this condition will not be able either to speak or to say
anything intelligible; for he says at the same time both ‘yes’ and ‘no.’ And if
he makes no judgement but ‘thinks’ and ‘does not think’, indifferently, what
difference will there be between him and a vegetable? – Thus, then, it is in the
highest degree evident that neither any one of those who maintain this view nor
any one else is really in this position. For why does a man walk to Megara and
not stay at home, when he thinks he ought to be walking there? Why does he not
walk early some morning into a well or over a precipice, if one happens to be in
his way? Why do we observe him guarding against this, evidently because he does
not think that falling in is alike good and not good? Evidently, then, he judges
one thing to be better and another worse. And if this is so, he must also judge
one thing to be a man and another to be not-a-man, one thing to be sweet and
another to be not-sweet. For he does not aim at and judge all things alike,
when, thinking it desirable to drink water or to see a man, he proceeds to aim
at these things; yet he ought, if the same thing were alike a man and not-a-man.
But, as was said, there is no one who does not obviously avoid some things and
not others. Therefore, as it seems, all men make unqualified judgements, if not
about all things, still about what is better and worse. And if this is not
knowledge but opinion, they should be all the more anxious about the truth, as a
sick man should be more anxious about his health than one who is healthy; for he
who has opinions is, in comparison with the man who knows, not in a healthy
state as far as the truth is concerned.
Again, however much all things may be ‘so and
not so’, still there is a more and a less in the nature of things; for we should
not say that two and three are equally even, nor is he who thinks four things
are five equally wrong with him who thinks they are a thousand. If then they are
not equally wrong, obviously one is less wrong and therefore more right. If then
that which has more of any quality is nearer the norm, there must be some truth
to which the more true is nearer. And even if there is not, still there is
already something better founded and liker the truth, and we shall have got rid
of the unqualified doctrine which would prevent us from determining anything in
our thought.
5
From the same opinion proceeds the doctrine of
Protagoras, and both doctrines must be alike true or alike untrue. For on the
one hand, if all opinions and appearances are true, all statements must be at
the same time true and false. For many men hold beliefs in which they conflict
with one another, and think those mistaken who have not the same opinions as
themselves; so that the same thing must both be and not be. And on the other
hand, if this is so, all opinions must be true; for those who are mistaken and
those who are right are opposed to one another in their opinions; if, then,
reality is such as the view in question supposes, all will be right in their
beliefs.
Evidently, then, both doctrines proceed from
the same way of thinking. But the same method of discussion must not be used
with all opponents; for some need persuasion, and others compulsion. Those who
have been driven to this position by difficulties in their thinking can easily
be cured of their ignorance; for it is not their expressed argument but their
thought that one has to meet. But those who argue for the sake of argument can
be cured only by refuting the argument as expressed in speech and in
words.
Those who really feel the difficulties have
been led to this opinion by observation of the sensible world. (1) They think
that contradictories or contraries are true at the same time, because they see
contraries coming into existence out of the same thing. If, then, that which is
not cannot come to be, the thing must have existed before as both contraries
alike, as Anaxagoras says all is mixed in all, and Democritus too; for he says
the void and the full exist alike in every part, and yet one of these is being,
and the other non-being. To those, then, whose belief rests on these grounds, we
shall say that in a sense they speak rightly and in a sense they err. For ‘that
which is’ has two meanings, so that in some sense a thing can come to be out of
that which is not, while in some sense it cannot, and the same thing can at the
same time be in being and not in being – but not in the same respect. For the
same thing can be potentially at the same time two contraries, but it cannot
actually. And again we shall ask them to believe that among existing things
there is also another kind of substance to which neither movement nor
destruction nor generation at all belongs.
And (2) similarly some have inferred from
observation of the sensible world the truth of appearances. For they think that
the truth should not be determined by the large or small number of those who
hold a belief, and that the same thing is thought sweet by some when they taste
it, and bitter by others, so that if all were ill or all were mad, and only two
or three were well or sane, these would be thought ill and mad, and not the
others.
And again, they say that many of the other
animals receive impressions contrary to ours; and that even to the senses of
each individual, things do not always seem the same. Which, then, of these
impressions are true and which are false is not obvious; for the one set is no
more true than the other, but both are alike. And this is why Democritus, at any
rate, says that either there is no truth or to us at least it is not
evident.
And in general it is because these thinkers
suppose knowledge to be sensation, and this to be a physical alteration, that
they say that what appears to our senses must be true; for it is for these
reasons that both Empedocles and Democritus and, one may almost say, all the
others have fallen victims to opinions of this sort. For Empedocles says that
when men change their condition they change their
knowledge;
For wisdom increases in men according to what
is before them.
And elsewhere he says that: –
So far as their nature changed, so far to them
always
Came changed thoughts into
mind.
And Parmenides also expresses himself in the
same way:
For as at each time the much-bent limbs are
composed,
So is the mind of men; for in each and all
men
‘Tis one thing thinks – the substance of their
limbs:
For that of which there is more is
thought.
A saying of Anaxagoras to some of his friends
is also related, – that things would be for them such as they supposed them to
be. And they say that Homer also evidently had this opinion, because he made
Hector, when he was unconscious from the blow, lie ‘thinking other thoughts’, –
which implies that even those who are bereft of thought have thoughts, though
not the same thoughts. Evidently, then, if both are forms of knowledge, the real
things also are at the same time ‘both so and not so’. And it is in this
direction that the consequences are most difficult. For if those who have seen
most of such truth as is possible for us (and these are those who seek and love
it most) – if these have such opinions and express these views about the truth,
is it not natural that beginners in philosophy should lose heart? For to seek
the truth would be to follow flying game.
But the reason why these thinkers held this
opinion is that while they were inquiring into the truth of that which is, they
thought, ‘that which is’ was identical with the sensible world; in this,
however, there is largely present the nature of the indeterminate – of that
which exists in the peculiar sense which we have explained; and therefore, while
they speak plausibly, they do not say what is true (for it is fitting to put the
matter so rather than as Epicharmus put it against Xenophanes). And again,
because they saw that all this world of nature is in movement and that about
that which changes no true statement can be made, they said that of course,
regarding that which everywhere in every respect is changing, nothing could
truly be affirmed. It was this belief that blossomed into the most extreme of
the views above mentioned, that of the professed Heracliteans, such as was held
by Cratylus, who finally did not think it right to say anything but only moved
his finger, and criticized Heraclitus for saying that it is impossible to step
twice into the same river; for he thought one could not do it even
once.
But we shall say in answer to this argument
also that while there is some justification for their thinking that the
changing, when it is changing, does not exist, yet it is after all disputable;
for that which is losing a quality has something of that which is being lost,
and of that which is coming to be, something must already be. And in general if
a thing is perishing, will be present something that exists; and if a thing is
coming to be, there must be something from which it comes to be and something by
which it is generated, and this process cannot go on ad infinitum. – But,
leaving these arguments, let us insist on this, that it is not the same thing to
change in quantity and in quality. Grant that in quantity a thing is not
constant; still it is in respect of its form that we know each thing. – And
again, it would be fair to criticize those who hold this view for asserting
about the whole material universe what they saw only in a minority even of
sensible things. For only that region of the sensible world which immediately
surrounds us is always in process of destruction and generation; but this is –
so to speak – not even a fraction of the whole, so that it would have been
juster to acquit this part of the world because of the other part, than to
condemn the other because of this. – And again, obviously we shall make to them
also the same reply that we made long ago; we must show them and persuade them
that there is something whose nature is changeless. Indeed, those who say that
things at the same time are and are not, should in consequence say that all
things are at rest rather than that they are in movement; for there is nothing
into which they can change, since all attributes belong already to all
subjects.
Regarding the nature of truth, we must maintain
that not everything which appears is true; firstly, because even if sensation –
at least of the object peculiar to the sense in question – is not false, still
appearance is not the same as sensation. – Again, it is fair to express surprise
at our opponents’ raising the question whether magnitudes are as great, and
colours are of such a nature, as they appear to people at a distance, or as they
appear to those close at hand, and whether they are such as they appear to the
healthy or to the sick, and whether those things are heavy which appear so to
the weak or those which appear so to the strong, and those things true which
appear to the slee ing or to the waking. For obviously they do not think these
to be open questions; no one, at least, if when he is in Libya he has fancied
one night that he is in Athens, starts for the concert hall. – And again with
regard to the future, as Plato says, surely the opinion of the physician and
that of the ignorant man are not equally weighty, for instance, on the question
whether a man will get well or not. – And again, among sensations themselves the
sensation of a foreign object and that of the appropriate object, or that of a
kindred object and that of the object of the sense in question, are not equally
authoritative, but in the case of colour sight, not taste, has the authority,
and in the case of flavour taste, not sight; each of which senses never says at
the same time of the same object that it simultaneously is ‘so and not so’. –
But not even at different times does one sense disagree about the quality, but
only about that to which the quality belongs. I mean, for instance, that the
same wine might seem, if either it or one’s body changed, at one time sweet and
at another time not sweet; but at least the sweet, such as it is when it exists,
has never yet changed, but one is always right about it, and that which is to be
sweet is of necessity of such and such a nature. Yet all these views destroy
this necessity, leaving nothing to be of necessity, as they leave no essence of
anything; for the necessary cannot be in this way and also in that, so that if
anything is of necessity, it will not be ‘both so and not
so’.
And, in general, if only the sensible exists,
there would be nothing if animate things were not; for there would be no faculty
of sense. Now the view that neither the sensible qualities nor the sensations
would exist is doubtless true (for they are affections of the perceiver), but
that the substrata which cause the sensation should not exist even apart from
sensation is impossible. For sensation is surely not the sensation of itself,
but there is something beyond the sensation, which must be prior to the
sensation; for that which moves is prior in nature to that which is moved, and
if they are correlative terms, this is no less the case.
6
There are, both among those who have these
convictions and among those who merely profess these views, some who raise a
difficulty by asking, who is to be the judge of the healthy man, and in general
who is likely to judge rightly on each class of questions. But such inquiries
are like puzzling over the question whether we are now asleep or awake. And all
such questions have the same meaning. These people demand that a reason shall be
given for everything; for they seek a starting-point, and they seek to get this
by demonstration, while it is obvious from their actions that they have no
conviction. But their mistake is what we have stated it to be; they seek a
reason for things for which no reason can be given; for the starting-point of
demonstration is not demonstration.
These, then, might be easily persuaded of this
truth, for it is not difficult to grasp; but those who seek merely compulsion in
argument seek what is impossible; for they demand to be allowed to contradict
themselves – a claim which contradicts itself from the very first. – But if not
all things are relative, but some are self-existent, not everything that appears
will be true; for that which appears is apparent to some one; so that he who
says all things that appear are true, makes all things relative. And, therefore,
those who ask for an irresistible argument, and at the same time demand to be
called to account for their views, must guard themselves by saying that the
truth is not that what appears exists, but that what appears exists for him to
whom it appears, and when, and to the sense to which, and under the conditions
under which it appears. And if they give an account of their view, but do not
give it in this way, they will soon find themselves contradicting themselves.
For it is possible that the same thing may appear to be honey to the sight, but
not to the taste, and that, since we have two eyes, things may not appear the
same to each, if their sight is unlike. For to those who for the reasons named
some time ago say that what appears is true, and therefore that all things are
alike false and true, for things do not appear either the same to all men or
always the same to the same man, but often have contrary appearances at the same
time (for touch says there are two objects when we cross our fingers, while
sight says there is one) – to these we shall say ‘yes, but not to the same sense
and in the same part of it and under the same conditions and at the same time’,
so that what appears will be with these qualifications true. But perhaps for
this reason those who argue thus not because they feel a difficulty but for the
sake of argument, should say that this is not true, but true for this man. And
as has been said before, they must make everything relative – relative to
opinion and perception, so that nothing either has come to be or will be without
some one’s first thinking so. But if things have come to be or will be,
evidently not all things will be relative to opinion. – Again, if a thing is
one, it is in relation to one thing or to a definite number of things; and if
the same thing is both half and equal, it is not to the double that the equal is
correlative. If, then, in relation to that which thinks, man and that which is
thought are the same, man will not be that which thinks, but only that which is
thought. And if each thing is to be relative to that which thinks, that which
thinks will be relative to an infinity of specifically different
things.
Let this, then, suffice to show (1) that the
most indisputable of all beliefs is that contradictory statements are not at the
same time true, and (2) what consequences follow from the assertion that they
are, and (3) why people do assert this. Now since it is impossible that
contradictories should be at the same time true of the same thing, obviously
contraries also cannot belong at the same time to the same thing. For of
contraries, one is a privation no less than it is a contrary – and a privation
of the essential nature; and privation is the denial of a predicate to a
determinate genus. If, then, it is impossible to affirm and deny truly at the
same time, it is also impossible that contraries should belong to a subject at
the same time, unless both belong to it in particular relations, or one in a
particular relation and one without qualification.
7
But on the other hand there cannot be an
intermediate between contradictories, but of one subject we must either affirm
or deny any one predicate. This is clear, in the first place, if we define what
the true and the false are. To say of what is that it is not, or of what is not
that it is, is false, while to say of what is that it is, and of what is not
that it is not, is true; so that he who says of anything that it is, or that it
is not, will say either what is true or what is false; but neither what is nor
what is not is said to be or not to be. – Again, the intermediate between the
contradictories will be so either in the way in which grey is between black and
white, or as that which is neither man nor horse is between man and horse. (a)
If it were of the latter kind, it could not change into the extremes (for change
is from not-good to good, or from good to not-good), but as a matter of fact
when there is an intermediate it is always observed to change into the extremes.
For there is no change except to opposites and to their intermediates. (b) But
if it is really intermediate, in this way too there would have to be a change to
white, which was not from not-white; but as it is, this is never seen. – Again,
every object of understanding or reason the understanding either affirms or
denies – this is obvious from the definition – whenever it says what is true or
false. When it connects in one way by assertion or negation, it says what is
true, and when it does so in another way, what is false. – Again, there must be
an intermediate between all contradictories, if one is not arguing merely for
the sake of argument; so that it will be possible for a man to say what is
neither true nor untrue, and there will be a middle between that which is and
that which is not, so that there will also be a kind of change intermediate
between generation and destruction. – Again, in all classes in which the
negation of an attribute involves the assertion of its contrary, even in these
there will be an intermediate; for instance, in the sphere of numbers there will
be number which is neither odd nor not-odd. But this is impossible, as is
obvious from the definition. – Again, the process will go on ad infinitum, and
the number of realities will be not only half as great again, but even greater.
For again it will be possible to deny this intermediate with reference both to
its assertion and to its negation, and this new term will be some definite
thing; for its essence is something different. – Again, when a man, on being
asked whether a thing is white, says ‘no’, he has denied nothing except that it
is; and its not being is a negation.
Some people have acquired this opinion as other
paradoxical opinions have been acquired; when men cannot refute eristical
arguments, they give in to the argument and agree that the conclusion is true.
This, then, is why some express this view; others do so because they demand a
reason for everything. And the starting-point in dealing with all such people is
definition. Now the definition rests on the necessity of their meaning
something; for the form of words of which the word is a sign will be its
definition. – While the doctrine of Heraclitus, that all things are and are not,
seems to make everything true, that of Anaxagoras, that there is an intermediate
between the terms of a contradiction, seems to make everything false; for when
things are mixed, the mixture is neither good nor not-good, so that one cannot
say anything that is true.
8
In view of these distinctions it is obvious
that the one-sided theories which some people express about all things cannot be
valid – on the one hand the theory that nothing is true (for, say they, there is
nothing to prevent every statement from being like the statement ‘the diagonal
of a square is commensurate with the side’), on the other hand the theory that
everything is true. These views are practically the same as that of Heraclitus;
for he who says that all things are true and all are false also makes each of
these statements separately, so that since they are impossible, the double
statement must be impossible too. – Again, there are obviously contradictories
which cannot be at the same time true – nor on the other hand can all statements
be false; yet this would seem more possible in the light of what has been said.
– But against all such views we must postulate, as we said above,’ not that
something is or is not, but that something has a meaning, so that we must argue
from a definition, viz. by assuming what falsity or truth means. If that which
it is true to affirm is nothing other than that which it is false to deny, it is
impossible that all statements should be false; for one side of the
contradiction must be true. Again, if it is necessary with regard to everything
either to assert or to deny it, it is impossible that both should be false; for
it is one side of the contradiction that is false. – Therefore all such views
are also exposed to the often expressed objection, that they destroy themselves.
For he who says that everything is true makes even the statement contrary to his
own true, and therefore his own not true (for the contrary statement denies that
it is true), while he who says everything is false makes himself also false. –
And if the former person excepts the contrary statement, saying it alone is not
true, while the latter excepts his own as being not false, none the less they
are driven to postulate the truth or falsity of an infinite number of
statements; for that which says the true statement is true is true, and this
process will go on to infinity.
Evidently, again, those who say all things are
at rest are not right, nor are those who say all things are in movement. For if
all things are at rest, the same statements will always be true and the same
always false, – but this obviously changes; for he who makes a statement,
himself at one time was not and again will not be. And if all things are in
motion, nothing will be true; everything therefore will be false. But it has
been shown that this is impossible. Again, it must be that which is that
changes; for change is from something to something. But again it is not the case
that all things are at rest or in motion sometimes, and nothing for ever; for
there is something which always moves the things that are in motion, and the
first mover is itself unmoved.
1
‘Beginning’ means (1) that part of a thing from which one would start first, e.g a line or a road has a beginning in either of the contrary directions. (2) That from which each thing would best be originated, e.g. even in learning we must sometimes begin not from the first point and the beginning of the subject, but from the point from which we should learn most easily. (4) That from which, as an immanent part, a thing first comes to be, e,g, as the keel of a ship and the foundation of a house, while in animals some suppose the heart, others the brain, others some other part, to be of this nature. (4) That from which, not as an immanent part, a thing first comes to be, and from which the movement or the change naturally first begins, as a child comes from its father and its mother, and a fight from abusive language. (5) That at whose will that which is moved is moved and that which changes changes, e.g. the magistracies in cities, and oligarchies and monarchies and tyrannies, are called arhchai, and so are the arts, and of these especially the architectonic arts. (6) That from which a thing can first be known, – this also is called the beginning of the thing, e.g. the hypotheses are the beginnings of demonstrations. (Causes are spoken of in an equal number of senses; for all causes are beginnings.) It is common, then, to all beginnings to be the first point from which a thing either is or comes to be or is known; but of these some are immanent in the thing and others are outside. Hence the nature of a thing is a beginning, and so is the element of a thing, and thought and will, and essence, and the final cause – for the good and the beautiful are the beginning both of the knowledge and of the movement of many things.
2
‘Cause’ means (1) that from which, as immanent
material, a thing comes into being, e.g. the bronze is the cause of the statue
and the silver of the saucer, and so are the classes which include these. (2)
The form or pattern, i.e. the definition of the essence, and the classes which
include this (e.g. the ratio 2:1 and number in general are causes of the
octave), and the parts included in the definition. (3) That from which the
change or the resting from change first begins; e.g. the adviser is a cause of
the action, and the father a cause of the child, and in general the maker a
cause of the thing made and the change-producing of the changing. (4) The end,
i.e. that for the sake of which a thing is; e.g. health is the cause of walking.
For ‘Why does one walk?’ we say; ‘that one may be healthy’; and in speaking thus
we think we have given the cause. The same is true of all the means that
intervene before the end, when something else has put the process in motion, as
e.g. thinning or purging or drugs or instruments intervene before health is
reached; for all these are for the sake of the end, though they differ from one
another in that some are instruments and others are
actions.
These, then, are practically all the senses in
which causes are spoken of, and as they are spoken of in several senses it
follows both that there are several causes of the same thing, and in no
accidental sense (e.g. both the art of sculpture and the bronze are causes of
the statue not in respect of anything else but qua statue; not, however, in the
same way, but the one as matter and the other as source of the movement), and
that things can be causes of one another (e.g. exercise of good condition, and
the latter of exercise; not, however, in the same way, but the one as end and
the other as source of movement). – Again, the same thing is the cause of
contraries; for that which when present causes a particular thing, we sometimes
charge, when absent, with the contrary, e.g. we impute the shipwreck to the
absence of the steersman, whose presence was the cause of safety; and both – the
presence and the privation – are causes as sources of
movement.
All the causes now mentioned fall under four
senses which are the most obvious. For the letters are the cause of syllables,
and the material is the cause of manufactured things, and fire and earth and all
such things are the causes of bodies, and the parts are causes of the whole, and
the hypotheses are causes of the conclusion, in the sense that they are that out
of which these respectively are made; but of these some are cause as the
substratum (e.g. the parts), others as the essence (the whole, the synthesis,
and the form). The semen, the physician, the adviser, and in general the agent,
are all sources of change or of rest. The remainder are causes as the end and
the good of the other things; for that for the sake of which other things are
tends to be the best and the end of the other things; let us take it as making
no difference whether we call it good or apparent good.
These, then, are the causes, and this is the
number of their kinds, but the varieties of causes are many in number, though
when summarized these also are comparatively few. Causes are spoken of in many
senses, and even of those which are of the same kind some are causes in a prior
and others in a posterior sense, e.g. both ‘the physician’ and ‘the professional
man’ are causes of health, and both ‘the ratio 2:1’ and ‘number’ are causes of
the octave, and the classes that include any particular cause are always causes
of the particular effect. Again, there are accidental causes and the classes
which include these; e.g. while in one sense ‘the sculptor’ causes the statue,
in another sense ‘Polyclitus’ causes it, because the sculptor happens to be
Polyclitus; and the classes that include the accidental cause are also causes,
e.g. ‘man’ – or in general ‘animal’ – is the cause of the statue, because
Polyclitus is a man, and man is an animal. Of accidental causes also some are
more remote or nearer than others, as, for instance, if ‘the white’ and ‘the
musical’ were called causes of the statue, and not only ‘Polyclitus’ or ‘man’.
But besides all these varieties of causes, whether proper or accidental, some
are called causes as being able to act, others as acting; e.g. the cause of the
house’s being built is a builder, or a builder who is building. – The same
variety of language will be found with regard to the effects of causes; e.g. a
thing may be called the cause of this statue or of a statue or in general of an
image, and of this bronze or of bronze or of matter in general; and similarly in
the case of accidental effects. Again, both accidental and proper causes may be
spoken of in combination; e.g. we may say not ‘Polyclitus’ nor ‘the sculptor’
but ‘Polyclitus the sculptor’. Yet all these are but six in number, while each
is spoken of in two ways; for (A) they are causes either as the individual, or
as the genus, or as the accidental, or as the genus that includes the
accidental, and these either as combined, or as taken simply; and (B) all may be
taken as acting or as having a capacity. But they differ inasmuch as the acting
causes, i.e. the individuals, exist, or do not exist, simultaneously with the
things of which they are causes, e.g. this particular man who is healing, with
this particular man who is recovering health, and this particular builder with
this particular thing that is being built; but the potential causes are not
always in this case; for the house does not perish at the same time as the
builder.
3
‘Element’ means (1) the primary component
immanent in a thing, and indivisible in kind into other kinds; e.g. the elements
of speech are the parts of which speech consists and into which it is ultimately
divided, while they are no longer divided into other forms of speech different
in kind from them. If they are divided, their parts are of the same kind, as a
part of water is water (while a part of the syllable is not a syllable).
Similarly those who speak of the elements of bodies mean the things into which
bodies are ultimately divided, while they are no longer divided into other
things differing in kind; and whether the things of this sort are one or more,
they call these elements. The so-called elements of geometrical proofs, and in
general the elements of demonstrations, have a similar character; for the
primary demonstrations, each of which is implied in many demonstrations, are
called elements of demonstrations; and the primary syllogisms, which have three
terms and proceed by means of one middle, are of this
nature.
(2) People also transfer the word ‘element’
from this meaning and apply it to that which, being one and small, is useful for
many purposes; for which reason what is small and simple and indivisible is
called an element. Hence come the facts that the most universal things are
elements (because each of them being one and simple is present in a plurality of
things, either in all or in as many as possible), and that unity and the point
are thought by some to be first principles. Now, since the so-called genera are
universal and indivisible (for there is no definition of them), some say the
genera are elements, and more so than the differentia, because the genus is more
universal; for where the differentia is present, the genus accompanies it, but
where the genus is present, the differentia is not always so. It is common to
all the meanings that the element of each thing is the first component immanent
in each.
4
‘Nature’ means (1) the genesis of growing
things – the meaning which would be suggested if one were to pronounce the ‘u’
in phusis long. – (2) That immanent part of a growing thing, from which its
growth first proceeds. – (3) The source from which the primary movement in each
natural object is present in it in virtue of its own essence. Those things are
said to grow which derive increase from something else by contact and either by
organic unity, or by organic adhesion as in the case of embryos. Organic unity
differs from contact; for in the latter case there need not be anything besides
the contact, but in organic unities there is something identical in both parts,
which makes them grow together instead of merely touching, and be one in respect
of continuity and quantity, though not of quality. – (4) ‘Nature’ means the
primary material of which any natural object consists or out of which it is
made, which is relatively unshaped and cannot be changed from its own potency,
as e.g. bronze is said to be the nature of a statue and of bronze utensils, and
wood the nature of wooden things; and so in all other cases; for when a product
is made out of these materials, the first matter is preserved throughout. For it
is in this way that people call the elements of natural objects also their
nature, some naming fire, others earth, others air, others water, others
something else of the sort, and some naming more than one of these, and others
all of them. – (5) ‘Nature’ means the essence of natural objects, as with those
who say the nature is the primary mode of composition, or as Empedocles says: –
Nothing that is has a
nature,
But only mixing and parting of the
mixed,
And nature is but a name given them by
men.
Hence as regards the things that are or come to
be by nature, though that from which they naturally come to be or are is already
present, we say they have not their nature yet, unless they have their form or
shape. That which comprises both of these exists by nature, e.g. the animals and
their parts; and not only is the first matter nature (and this in two senses,
either the first, counting from the thing, or the first in general; e.g. in the
case of works in bronze, bronze is first with reference to them, but in general
perhaps water is first, if all things that can be melted are water), but also
the form or essence, which is the end of the process of becoming. – (6) By an
extension of meaning from this sense of ‘nature’ every essence in general has
come to be called a ‘nature’, because the nature of a thing is one kind of
essence.
From what has been said, then, it is plain that
nature in the primary and strict sense is the essence of things which have in
themselves, as such, a source of movement; for the matter is called the nature
because it is qualified to receive this, and processes of becoming and growing
are called nature because they are movements proceeding from this. And nature in
this sense is the source of the movement of natural objects, being present in
them somehow, either potentially or in complete reality.
5
We call ‘necessary’ (1) (a) that without which,
as a condition, a thing cannot live; e.g. breathing and food are necessary for
an animal; for it is incapable of existing without these; (b) the conditions
without which good cannot be or come to be, or without which we cannot get rid
or be freed of evil; e.g. drinking the medicine is necessary in order that we
may be cured of disease, and a man’s sailing to Aegina is necessary in order
that he may get his money. – (2) The compulsory and compulsion, i.e. that which
impedes and tends to hinder, contrary to impulse and purpose. For the compulsory
is called necessary (whence the necessary is painful, as Evenus says: ‘For every
necessary thing is ever irksome’), and compulsion is a form of necessity, as
Sophocles says: ‘But force necessitates me to this act’. And necessity is held
to be something that cannot be persuaded – and rightly, for it is contrary to
the movement which accords with purpose and with reasoning. – (3) We say that
that which cannot be otherwise is necessarily as it is. And from this sense of
‘necessary’ all the others are somehow derived; for a thing is said to do or
suffer what is necessary in the sense of compulsory, only when it cannot act
according to its impulse because of the compelling forces – which implies that
necessity is that because of which a thing cannot be otherwise; and similarly as
regards the conditions of life and of good; for when in the one case good, in
the other life and being, are not possible without certain conditions, these are
necessary, and this kind of cause is a sort of necessity. Again, demonstration
is a necessary thing because the conclusion cannot be otherwise, if there has
been demonstration in the unqualified sense; and the causes of this necessity
are the first premisses, i.e. the fact that the propositions from which the
syllogism proceeds cannot be otherwise.
Now some things owe their necessity to
something other than themselves; others do not, but are themselves the source of
necessity in other things. Therefore the necessary in the primary and strict
sense is the simple; for this does not admit of more states than one, so that it
cannot even be in one state and also in another; for if it did it would already
be in more than one. If, then, there are any things that are eternal and
unmovable, nothing compulsory or against their nature attaches to
them.
6
‘One’ means (1) that which is one by accident,
(2) that which is one by its own nature. (1) Instances of the accidentally one
are ‘Coriscus and what is musical’, and ‘musical Coriscus’ (for it is the same
thing to say ‘Coriscus and what is musical’, and ‘musical Coriscus’), and ‘what
is musical and what is just’, and ‘musical Coriscus and just Coriscus’. For all
of these are called one by virtue of an accident, ‘what is just and what is
musical’ because they are accidents of one substance, ‘what is musical and
Coriscus’ because the one is an accident of the other; and similarly in a sense
‘musical Coriscus’ is one with ‘Coriscus’ because one of the parts of the phrase
is an accident of the other, i.e. ‘musical’ is an accident of Coriscus; and
‘musical Coriscus’ is one with ‘just Coriscus’ because one part of each is an
accident of one and the same subject. The case is similar if the accident is
predicated of a genus or of any universal name, e.g. if one says that man is the
same as ‘musical man’; for this is either because ‘musical’ is an accident of
man, which is one substance, or because both are accidents of some individual,
e.g. Coriscus. Both, however, do not belong to him in the same way, but one
presumably as genus and included in his substance, the other as a state or
affection of the substance.
The things, then, that are called one in virtue
of an accident, are called so in this way. (2) Of things that are called one in
virtue of their own nature some (a) are so called because they are continuous,
e.g. a bundle is made one by a band, and pieces of wood are made one by glue;
and a line, even if it is bent, is called one if it is continuous, as each part
of the body is, e.g. the leg or the arm. Of these themselves, the continuous by
nature are more one than the continuous by art. A thing is called continuous
which has by its own nature one movement and cannot have any other; and the
movement is one when it is indivisible, and it is indivisible in respect of
time. Those things are continuous by their own nature which are one not merely
by contact; for if you put pieces of wood touching one another, you will not say
these are one piece of wood or one body or one continuum of any other sort.
Things, then, that are continuous in any way called one, even if they admit of
being bent, and still more those which cannot be bent; e.g. the shin or the
thigh is more one than the leg, because the movement of the leg need not be one.
And the straight line is more one than the bent; but that which is bent and has
an angle we call both one and not one, because its movement may be either
simultaneous or not simultaneous; but that of the straight line is always
simultaneous, and no part of it which has magnitude rests while another moves,
as in the bent line.
(b)(i) Things are called one in another sense
because their substratum does not differ in kind; it does not differ in the case
of things whose kind is indivisible to sense. The substratum meant is either the
nearest to, or the farthest from, the final state. For, one the one hand, wine
is said to be one and water is said to be one, qua indivisible in kind; and, on
the other hand, all juices, e.g. oil and wine, are said to be one, and so are
all things that can be melted, because the ultimate substratum of all is the
same; for all of these are water or air.
(ii) Those things also are called one whose
genus is one though distinguished by opposite differentiae – these too are all
called one because the genus which underlies the differentiae is one (e.g.
horse, man, and dog form a unity, because all are animals), and indeed in a way
similar to that in which the matter is one. These are sometimes called one in
this way, but sometimes it is the higher genus that is said to be the same (if
they are infimae species of their genus) – the genus above the proximate genera;
e.g. the isosceles and the equilateral are one and the same figure because both
are triangles; but they are not the same triangles.
(c) Two things are called one, when the
definition which states the essence of one is indivisible from another
definition which shows us the other (though in itself every definition is
divisible). Thus even that which has increased or is diminishing is one, because
its definition is one, as, in the case of plane figures, is the definition of
their form. In general those things the thought of whose essence is indivisible,
and cannot separate them either in time or in place or in definition, are most
of all one, and of these especially those which are substances. For in general
those things that do not admit of division are called one in so far as they do
not admit of it; e.g. if two things are indistinguishable qua man, they are one
kind of man; if qua animal, one kind of animal; if qua magnitude, one kind of
magnitude. – Now most things are called one because they either do or have or
suffer or are related to something else that is one, but the things that are
primarily called one are those whose substance is one, – and one either in
continuity or in form or in definition; for we count as more than one either
things that are not continuous, or those whose form is not one, or those whose
definition is not one.
While in a sense we call anything one if it is
a quantity and continuous, in a sense we do not unless it is a whole, i.e.
unless it has unity of form; e.g. if we saw the parts of a shoe put together
anyhow we should not call them one all the same (unless because of their
continuity); we do this only if they are put together so as to be a shoe and to
have already a certain single form. This is why the circle is of all lines most
truly one, because it is whole and complete.
(3) The essence of what is one is to be some
kind of beginning of number; for the first measure is the beginning, since that
by which we first know each class is the first measure of the class; the one,
then, is the beginning of the knowable regarding each class. But the one is not
the same in all classes. For here it is a quarter-tone, and there it is the
vowel or the consonant; and there is another unit of weight and another of
movement. But everywhere the one is indivisible either in quantity or in kind.
Now that which is indivisible in quantity is called a unit if it is not
divisible in any dimension and is without position, a point if it is not
divisible in any dimension and has position, a line if it is divisible in one
dimension, a plane if in two, a body if divisible in quantity in all – i.e. in
three – dimensions. And, reversing the order, that which is divisible in two
dimensions is a plane, that which is divisible in one a line, that which is in
no way divisible in quantity is a point or a unit, – that which has not position
a unit, that which has position a point.
Again, some things are one in number, others in
species, others in genus, others by analogy; in number those whose matter is
one, in species those whose definition is one, in genus those to which the same
figure of predication applies, by analogy those which are related as a third
thing is to a fourth. The latter kinds of unity are always found when the former
are; e.g. things that are one in number are also one in species, while things
that are one in species are not all one in number; but things that are one in
species are all one in genus, while things that are so in genus are not all one
in species but are all one by analogy; while things that are one by analogy are
not all one in genus.
Evidently ‘many’ will have meanings opposite to
those of ‘one’; some things are many because they are not continuous, others
because their matter – either the proximate matter or the ultimate – is
divisible in kind, others because the definitions which state their essence are
more than one.
7
Things are said to ‘be’ (1) in an accidental
sense, (2) by their own nature.
(1) In an accidental sense, e.g. we say ‘the
righteous doer is musical’, and ‘the man is musical’, and ‘the musician is a
man’, just as we say ‘the musician builds’, because the builder happens to be
musical or the musician to be a builder; for here ‘one thing is another’ means
‘one is an accident of another’. So in the cases we have mentioned; for when we
say ‘the man is musical’ and ‘the musician is a man’, or ‘he who is pale is
musical’ or ‘the musician is pale’, the last two mean that both attributes are
accidents of the same thing; the first that the attribute is an accident of that
which is, while ‘the musical is a man’ means that ‘musical’ is an accident of a
man. (In this sense, too, the not-pale is said to be, because that of which it
is an accident is.) Thus when one thing is said in an accidental sense to be
another, this is either because both belong to the same thing, and this is, or
because that to which the attribute belongs is, or because the subject which has
as an attribute that of which it is itself predicated, itself
is.
(2) The kinds of essential being are precisely
those that are indicated by the figures of predication; for the senses of
‘being’ are just as many as these figures. Since, then, some predicates indicate
what the subject is, others its quality, others quantity, others relation,
others activity or passivity, others its ‘where’, others its ‘when’, ‘being’ has
a meaning answering to each of these. For there is no difference between ‘the
man is recovering’ and ‘the man recovers’, nor between ‘the man is walking or
cutting’ and ‘the man walks’ or ‘cuts’; and similarly in all other
cases.
(3) Again, ‘being’ and ‘is’ mean that a
statement is true, ‘not being’ that it is not true but false – and this alike in
the case of affirmation and of negation; e.g. ‘Socrates is musical’ means that
this is true, or ‘Socrates is not-pale’ means that this is true; but ‘the
diagonal of the square is not commensurate with the side’ means that it is false
to say it is.
(4) Again, ‘being’ and ‘that which is’ mean
that some of the things we have mentioned ‘are’ potentially, others in complete
reality. For we say both of that which sees potentially and of that which sees
actually, that it is ‘seeing’, and both of that which can actualize its
knowledge and of that which is actualizing it, that it knows, and both of that
to which rest is already present and of that which can rest, that it rests. And
similarly in the case of substances; we say the Hermes is in the stone, and the
half of the line is in the line, and we say of that which is not yet ripe that
it is corn. When a thing is potential and when it is not yet potential must be
explained elsewhere.
8
We call ‘substance’ (1) the simple bodies, i.e.
earth and fire and water and everything of the sort, and in general bodies and
the things composed of them, both animals and divine beings, and the parts of
these. All these are called substance because they are not predicated of a
subject but everything else is predicated of them. – (2) That which, being
present in such things as are not predicated of a subject, is the cause of their
being, as the soul is of the being of an animal. – (3) The parts which are
present in such things, limiting them and marking them as individuals, and by
whose destruction the whole is destroyed, as the body is by the destruction of
the plane, as some say, and the plane by the destruction of the line; and in
general number is thought by some to be of this nature; for if it is destroyed,
they say, nothing exists, and it limits all things. – (4) The essence, the
formula of which is a definition, is also called the substance of each
thing.
It follows, then, that ‘substance’ has two
senses, (A) ultimate substratum, which is no longer predicated of anything else,
and (B) that which, being a ‘this’, is also separable and of this nature is the
shape or form of each thing.
9
‘The same’ means (1) that which is the same in
an accidental sense, e.g. ‘the pale’ and ‘the musical’ are the same because they
are accidents of the same thing, and ‘a man’ and ‘musical’ because the one is an
accident of the other; and ‘the musical’ is ‘a man’ because it is an accident of
the man. (The complex entity is the same as either of the simple ones and each
of these is the same as it; for both ‘the man’ and ‘the musical’ are said to be
the same as ‘the musical man’, and this the same as they.) This is why all of
these statements are made not universally; for it is not true to say that every
man is the same as ‘the musical’ (for universal attributes belong to things in
virtue of their own nature, but accidents do not belong to them in virtue of
their own nature); but of the individuals the statements are made without
qualification. For ‘Socrates’ and ‘musical Socrates’ are thought to be the same;
but ‘Socrates’ is not predicable of more than one subject, and therefore we do
not say ‘every Socrates’ as we say ‘every man’.
Some things are said to be the same in this
sense, others (2) are the same by their own nature, in as many senses as that
which is one by its own nature is so; for both the things whose matter is one
either in kind or in number, and those whose essence is one, are said to be the
same. Clearly, therefore, sameness is a unity of the being either of more than
one thing or of one thing when it is treated as more than one, ie. when we say a
thing is the same as itself; for we treat it as two.
Things are called ‘other’ if either their kinds
or their matters or the definitions of their essence are more than one; and in
general ‘other’ has meanings opposite to those of ‘the
same’.
‘Different’ is applied (1) to those things
which though other are the same in some respect, only not in number but either
in species or in genus or by analogy; (2) to those whose genus is other, and to
contraries, and to an things that have their otherness in their
essence.
Those things are called ‘like’ which have the
same attributes in every respect, and those which have more attributes the same
than different, and those whose quality is one; and that which shares with
another thing the greater number or the more important of the attributes (each
of them one of two contraries) in respect of which things are capable of
altering, is like that other thing. The senses of ‘unlike’ are opposite to those
of ‘like’.
10
The term ‘opposite’ is applied to
contradictories, and to contraries, and to relative terms, and to privation and
possession, and to the extremes from which and into which generation and
dissolution take place; and the attributes that cannot be present at the same
time in that which is receptive of both, are said to be opposed, – either
themselves of their constituents. Grey and white colour do not belong at the
same time to the same thing; hence their constituents are
opposed.
The term ‘contrary’ is applied (1) to those
attributes differing in genus which cannot belong at the same time to the same
subject, (2) to the most different of the things in the same genus, (3) to the
most different of the attributes in the same recipient subject, (4) to the most
different of the things that fall under the same faculty, (5) to the things
whose difference is greatest either absolutely or in genus or in species. The
other things that are called contrary are so called, some because they possess
contraries of the above kind, some because they are receptive of such, some
because they are productive of or susceptible to such, or are producing or
suffering them, or are losses or acquisitions, or possessions or privations, of
such. Since ‘one’ and ‘being’ have many senses, the other terms which are
derived from these, and therefore ‘same’, ‘other’, and ‘contrary’, must
correspond, so that they must be different for each
category.
The term ‘other in species’ is applied to
things which being of the same genus are not subordinate the one to the other,
or which being in the same genus have a difference, or which have a contrariety
in their substance; and contraries are other than one another in species (either
all contraries or those which are so called in the primary sense), and so are
those things whose definitions differ in the infima species of the genus (e.g.
man and horse are indivisible in genus, but their definitions are different),
and those which being in the same substance have a difference. ‘The same in
species’ has the various meanings opposite to these.
11
The words ‘prior’ and ‘posterior’ are applied
(1) to some things (on the assumption that there is a first, i.e. a beginning,
in each class) because they are nearer some beginning determined either
absolutely and by nature, or by reference to something or in some place or by
certain people; e.g. things are prior in place because they are nearer either to
some place determined by nature (e.g. the middle or the last place), or to some
chance object; and that which is farther is posterior. – Other things are prior
in time; some by being farther from the present, i.e. in the case of past events
(for the Trojan war is prior to the Persian, because it is farther from the
present), others by being nearer the present, i.e. in the case of future events
(for the Nemean games are prior to the Pythian, if we treat the present as
beginning and first point, because they are nearer the present). – Other things
are prior in movement; for that which is nearer the first mover is prior (e.g.
the boy is prior to the man); and the prime mover also is a beginning
absolutely. – Others are prior in power; for that which exceeds in power, i.e.
the more powerful, is prior; and such is that according to whose will the other
– i.e. the posterior – must follow, so that if the prior does not set it in
motion the other does not move, and if it sets it in motion it does move; and
here will is a beginning. – Others are prior in arrangement; these are the
things that are placed at intervals in reference to some one definite thing
according to some rule, e.g. in the chorus the second man is prior to the third,
and in the lyre the second lowest string is prior to the lowest; for in the one
case the leader and in the other the middle string is the
beginning.
These, then, are called prior in this sense,
but (2) in another sense that which is prior for knowledge is treated as also
absolutely prior; of these, the things that are prior in definition do not
coincide with those that are prior in relation to perception. For in definition
universals are prior, in relation to perception individuals. And in definition
also the accident is prior to the whole, e.g. ‘musical’ to ‘musical man’, for
the definition cannot exist as a whole without the part; yet musicalness cannot
exist unless there is some one who is musical.
(3) The attributes of prior things are called
prior, e.g. straightness is prior to smoothness; for one is an attribute of a
line as such, and the other of a surface.
Some things then are called prior and posterior
in this sense, others (4) in respect of nature and substance, i.e. those which
can be without other things, while the others cannot be without them, – a
distinction which Plato used. (If we consider the various senses of ‘being’,
firstly the subject is prior, so that substance is prior; secondly, according as
potency or complete reality is taken into account, different things are prior,
for some things are prior in respect of potency, others in respect of complete
reality, e.g. in potency the half line is prior to the whole line, and the part
to the whole, and the matter to the concrete substance, but in complete reality
these are posterior; for it is only when the whole has been dissolved that they
will exist in complete reality.) In a sense, therefore, all things that are
called prior and posterior are so called with reference to this fourth sense;
for some things can exist without others in respect of generation, e.g. the
whole without the parts, and others in respect of dissolution, e.g. the part
without the whole. And the same is true in all other
cases.
12
‘Potency’ means (1) a source of movement or
change, which is in another thing than the thing moved or in the same thing qua
other; e.g. the art of building is a potency which is not in the thing built,
while the art of healing, which is a potency, may be in the man healed, but not
in him qua healed. ‘Potency’ then means the source, in general, of change or
movement in another thing or in the same thing qua other, and also (2) the
source of a thing’s being moved by another thing or by itself qua other. For in
virtue of that principle, in virtue of which a patient suffers anything, we call
it ‘capable’ of suffering; and this we do sometimes if it suffers anything at
all, sometimes not in respect of everything it suffers, but only if it suffers a
change for the better – (3) The capacity of performing this well or according to
intention; for sometimes we say of those who merely can walk or speak but not
well or not as they intend, that they cannot speak or walk. So too (4) in the
case of passivity. – (5) The states in virtue of which things are absolutely
impassive or unchangeable, or not easily changed for the worse, are called
potencies; for things are broken and crushed and bent and in general destroyed
not by having a potency but by not having one and by lacking something, and
things are impassive with respect to such processes if they are scarcely and
slightly affected by them, because of a ‘potency’ and because they ‘can’ do
something and are in some positive state.
‘Potency’ having this variety of meanings, so
too the ‘potent’ or ‘capable’ in one sense will mean that which can begin a
movement (or a change in general, for even that which can bring things to rest
is a ‘potent’ thing) in another thing or in itself qua other; and in one sense
that over which something else has such a potency; and in one sense that which
has a potency of changing into something, whether for the worse or for the
better (for even that which perishes is thought to be ‘capable’ of perishing,
for it would not have perished if it had not been capable of it; but, as a
matter of fact, it has a certain disposition and cause and principle which fits
it to suffer this; sometimes it is thought to be of this sort because it has
something, sometimes because it is deprived of something; but if privation is in
a sense ‘having’ or ‘habit’, everything will be capable by having something, so
that things are capable both by having a positive habit and principle, and by
having the privation of this, if it is possible to have a privation; and if
privation is not in a sense ‘habit’, ‘capable’ is used in two distinct senses);
and a thing is capable in another sense because neither any other thing, nor
itself qua other, has a potency or principle which can destroy it. Again, all of
these are capable either merely because the thing might chance to happen or not
to happen, or because it might do so well. This sort of potency is found even in
lifeless things, e.g. in instruments; for we say one lyre can speak, and another
cannot speak at all, if it has not a good tone.
Incapacity is privation of capacity – i.e. of
such a principle as has been described either in general or in the case of
something that would naturally have the capacity, or even at the time when it
would naturally already have it; for the senses in which we should call a boy
and a man and a eunuch ‘incapable of begetting’ are distinct. – Again, to either
kind of capacity there is an opposite incapacity – both to that which only can
produce movement and to that which can produce it well.
Some things, then, are called adunata in virtue
of this kind of incapacity, while others are so in another sense; i.e. both
dunaton and adunaton are used as follows. The impossible is that of which the
contrary is of necessity true, e.g. that the diagonal of a square is
commensurate with the side is impossible, because such a statement is a falsity
of which the contrary is not only true but also necessary; that it is
commensurate, then, is not only false but also of necessity false. The contrary
of this, the possible, is found when it is not necessary that the contrary is
false, e.g. that a man should be seated is possible; for that he is not seated
is not of necessity false. The possible, then, in one sense, as has been said,
means that which is not of necessity false; in one, that which is true; in one,
that which may be true. – A ‘potency’ or ‘power’ in geometry is so called by a
change of meaning. – These senses of ‘capable’ or ‘possible’ involve no
reference to potency. But the senses which involve a reference to potency all
refer to the primary kind of potency; and this is a source of change in another
thing or in the same thing qua other. For other things are called ‘capable’,
some because something else has such a potency over them, some because it has
not, some because it has it in a particular way. The same is true of the things
that are incapable. Therefore the proper definition of the primary kind of
potency will be ‘a source of change in another thing or in the same thing qua
other’.
13
‘Quantum’ means that which is divisible into
two or more constituent parts of which each is by nature a ‘one’ and a ‘this’. A
quantum is a plurality if it is numerable, a magnitude if it is a measurable.
‘Plurality’ means that which is divisible potentially into non-continuous parts,
‘magnitude’ that which is divisible into continuous parts; of magnitude, that
which is continuous in one dimension is length; in two breadth, in three depth.
Of these, limited plurality is number, limited length is a line, breadth a
surface, depth a solid.
Again, some things are called quanta in virtue
of their own nature, others incidentally; e.g. the line is a quantum by its own
nature, the musical is one incidentally. Of the things that are quanta by their
own nature some are so as substances, e.g. the line is a quantum (for ‘a certain
kind of quantum’ is present in the definition which states what it is), and
others are modifications and states of this kind of substance, e.g. much and
little, long and short, broad and narrow, deep and shallow, heavy and light, and
all other such attributes. And also great and small, and greater and smaller,
both in themselves and when taken relatively to each other, are by their own
nature attributes of what is quantitative; but these names are transferred to
other things also. Of things that are quanta incidentally, some are so called in
the sense in which it was said that the musical and the white were quanta, viz.
because that to which musicalness and whiteness belong is a quantum, and some
are quanta in the way in which movement and time are so; for these also are
called quanta of a sort and continuous because the things of which these are
attributes are divisible. I mean not that which is moved, but the space through
which it is moved; for because that is a quantum movement also is a quantum, and
because this is a quantum time is one.
14
‘Quality’ means (1) the differentia of the
essence, e.g. man is an animal of a certain quality because he is two-footed,
and the horse is so because it is four-footed; and a circle is a figure of
particular quality because it is without angles, – which shows that the
essential differentia is a quality. – This, then, is one meaning of quality –
the differentia of the essence, but (2) there is another sense in which it
applies to the unmovable objects of mathematics, the sense in which the numbers
have a certain quality, e.g. the composite numbers which are not in one
dimension only, but of which the plane and the solid are copies (these are those
which have two or three factors); and in general that which exists in the
essence of numbers besides quantity is quality; for the essence of each is what
it is once, e.g. that of is not what it is twice or thrice, but what it is once;
for 6 is once 6.
(3) All the modifications of substances that
move (e.g. heat and cold, whiteness and blackness, heaviness and lightness, and
the others of the sort) in virtue of which, when they change, bodies are said to
alter. (4) Quality in respect of virtue and vice, and in general, of evil and
good.
Quality, then, seems to have practically two
meanings, and one of these is the more proper. The primary quality is the
differentia of the essence, and of this the quality in numbers is a part; for it
is a differentia of essences, but either not of things that move or not of them
qua moving. Secondly, there are the modifications of things that move, qua
moving, and the differentiae of movements. Virtue and vice fall among these
modifications; for they indicate differentiae of the movement or activity,
according to which the things in motion act or are acted on well or badly; for
that which can be moved or act in one way is good, and that which can do so in
another – the contrary – way is vicious. Good and evil indicate quality
especially in living things, and among these especially in those which have
purpose.
15
Things are ‘relative’ (1) as double to half,
and treble to a third, and in general that which contains something else many
times to that which is contained many times in something else, and that which
exceeds to that which is exceeded; (2) as that which can heat to that which can
be heated, and that which can cut to that which can be cut, and in general the
active to the passive; (3) as the measurable to the measure, and the knowable to
knowledge, and the perceptible to perception.
(1) Relative terms of the first kind are
numerically related either indefinitely or definitely, to numbers themselves or
to 1. E.g. the double is in a definite numerical relation to 1, and that which
is ‘many times as great’ is in a numerical, but not a definite, relation to 1,
i.e. not in this or in that numerical relation to it; the relation of that which
is half as big again as something else to that something is a definite numerical
relation to a number; that which is n+I/n times something else is in an
indefinite relation to that something, as that which is ‘many times as great’ is
in an indefinite relation to 1; the relation of that which exceeds to that which
is exceeded is numerically quite indefinite; for number is always commensurate,
and ‘number’ is not predicated of that which is not commensurate, but that which
exceeds is, in relation to that which is exceeded, so much and something more;
and this something is indefinite; for it can, indifferently, be either equal or
not equal to that which is exceeded. – All these relations, then, are
numerically expressed and are determinations of number, and so in another way
are the equal and the like and the same. For all refer to unity. Those things
are the same whose substance is one; those are like whose quality is one; those
are equal whose quantity is one; and 1 is the beginning and measure of number,
so that all these relations imply number, though not in the same
way.
(2) Things that are active or passive imply an
active or a passive potency and the actualizations of the potencies; e.g. that
which is capable of heating is related to that which is capable of being heated,
because it can heat it, and, again, that which heats is related to that which is
heated and that which cuts to that which is cut, in the sense that they actually
do these things. But numerical relations are not actualized except in the sense
which has been elsewhere stated; actualizations in the sense of movement they
have not. Of relations which imply potency some further imply particular periods
of time, e.g. that which has made is relative to that which has been made, and
that which will make to that which will be made. For it is in this way that a
father is called the father of his son; for the one has acted and the other has
been acted on in a certain way. Further, some relative terms imply privation of
potency, i.e. ‘incapable’ and terms of this sort, e.g.
‘invisible’.
Relative terms which imply number or potency,
therefore, are all relative because their very essence includes in its nature a
reference to something else, not because something else involves a reference to
it; but (3) that which is measurable or knowable or thinkable is called relative
because something else involves a reference to it. For ‘that which is thinkable’
implies that the thought of it is possible, but the thought is not relative to
‘that of which it is the thought’; for we should then have said the same thing
twice. Similarly sight is the sight of something, not ‘of that of which it is
the sight’ (though of course it is true to say this); in fact it is relative to
colour or to something else of the sort. But according to the other way of
speaking the same thing would be said twice, – ’the sight is of that of which it
is.’
Things that are by their own nature called
relative are called so sometimes in these senses, sometimes if the classes that
include them are of this sort; e.g. medicine is a relative term because its
genus, science, is thought to be a relative term. Further, there are the
properties in virtue of which the things that have them are called relative,
e.g. equality is relative because the equal is, and likeness because the like
is. Other things are relative by accident; e.g. a man is relative because he
happens to be double of something and double is a relative term; or the white is
relative, if the same thing happens to be double and
white.
16
What is called ‘complete’ is (1) that outside
which it is not possible to find any, even one, of its parts; e.g. the complete
time of each thing is that outside which it is not possible to find any time
which is a part proper to it. – (2) That which in respect of excellence and
goodness cannot be excelled in its kind; e.g. we have a complete doctor or a
complete flute-player, when they lack nothing in respect of the form of their
proper excellence. And thus, transferring the word to bad things, we speak of a
complete scandal-monger and a complete thief; indeed we even call them good,
i.e. a good thief and a good scandal-monger. And excellence is a completion; for
each thing is complete and every substance is complete, when in respect of the
form of its proper excellence it lacks no part of its natural magnitude. – (3)
The things which have attained their end, this being good, are called complete;
for things are complete in virtue of having attained their end. Therefore, since
the end is something ultimate, we transfer the word to bad things and say a
thing has been completely spoilt, and completely destroyed, when it in no wise
falls short of destruction and badness, but is at its last point. This is why
death, too, is by a figure of speech called the end, because both are last
things. But the ultimate purpose is also an end. – Things, then, that are called
complete in virtue of their own nature are so called in all these senses, some
because in respect of goodness they lack nothing and cannot be excelled and no
part proper to them can be found outside them, others in general because they
cannot be exceeded in their several classes and no part proper to them is
outside them; the others presuppose these first two kinds, and are called
complete because they either make or have something of the sort or are adapted
to it or in some way or other involve a reference to the things that are called
complete in the primary sense.
17
‘Limit’ means (1) the last point of each thing,
i.e. the first point beyond which it is not possible to find any part, and the
first point within which every part is; (2) the form, whatever it may be, of a
spatial magnitude or of a thing that has magnitude; (3) the end of each thing
(and of this nature is that towards which the movement and the action are, not
that from which they are – though sometimes it is both, that from which and that
to which the movement is, i.e. the final cause); (4) the substance of each
thing, and the essence of each; for this is the limit of knowledge; and if of
knowledge, of the object also. Evidently, therefore, ‘limit’ has as many senses
as ‘beginning’, and yet more; for the beginning is a limit, but not every limit
is a beginning.
18
‘That in virtue of which’ has several meanings:
– (1) the form or substance of each thing, e.g. that in virtue of which a man is
good is the good itself, (2) the proximate subject in which it is the nature of
an attribute to be found, e.g. colour in a surface. ‘That in virtue of which’,
then, in the primary sense is the form, and in a secondary sense the matter of
each thing and the proximate substratum of each. – In general ‘that in virtue of
which’ will found in the same number of senses as ‘cause’; for we say
indifferently (3) in virtue of what has he come?’ or ‘for what end has he
come?’; and (4) in virtue of what has he inferred wrongly, or inferred?’ or
‘what is the cause of the inference, or of the wrong inference?’ – Further (5)
Kath’ d is used in reference to position, e.g. ‘at which he stands’ or ‘along
which he walks; for all such phrases indicate place and
position.
Therefore ‘in virtue of itself’ must likewise
have several meanings. The following belong to a thing in virtue of itself: –
(1) the essence of each thing, e.g. Callias is in virtue of himself Callias and
what it was to be Callias; – (2) whatever is present in the ‘what’, e.g. Callias
is in virtue of himself an animal. For ‘animal’ is present in his definition;
Callias is a particular animal. – (3) Whatever attribute a thing receives in
itself directly or in one of its parts; e.g. a surface is white in virtue of
itself, and a man is alive in virtue of himself; for the soul, in which life
directly resides, is a part of the man. – (4) That which has no cause other than
itself; man has more than one cause – animal, two-footed – but yet man is man in
virtue of himself. – (5) Whatever attributes belong to a thing alone, and in so
far as they belong to it merely by virtue of itself considered apart by
itself.
19
‘Disposition’ means the arrangement of that
which has parts, in respect either of place or of potency or of kind; for there
must be a certain position, as even the word ‘disposition’
shows.
20
‘Having’ means (1) a kind of activity of the
haver and of what he has – something like an action or movement. For when one
thing makes and one is made, between them there is a making; so too between him
who has a garment and the garment which he has there is a having. This sort of
having, then, evidently we cannot have; for the process will go on to infinity,
if it is to be possible to have the having of what we have. – (2) ‘Having’ or
‘habit’ means a disposition according to which that which is disposed is either
well or ill disposed, and either in itself or with reference to something else;
e.g. health is a ‘habit’; for it is such a disposition. – (3) We speak of a
‘habit’ if there is a portion of such a disposition; and so even the excellence
of the parts is a ‘habit’ of the whole thing.
21
‘Affection’ means (1) a quality in respect of
which a thing can be altered, e.g. white and black, sweet and bitter, heaviness
and lightness, and all others of the kind. – (2) The actualization of these –
the already accomplished alterations. – (3) Especially, injurious alterations
and movements, and, above all painful injuries. – (4) Misfortunes and painful
experiences when on a large scale are called affections.
22
We speak of ‘privation’ (1) if something has
not one of the attributes which a thing might naturally have, even if this thing
itself would not naturally have it; e.g. a plant is said to be ‘deprived’ of
eyes. – (2) If, though either the thing itself or its genus would naturally have
an attribute, it has it not; e.g. a blind man and a mole are in different senses
‘deprived’ of sight; the latter in contrast with its genus, the former in
contrast with his own normal nature. – (3) If, though it would naturally have
the attribute, and when it would naturally have it, it has it not; for blindness
is a privation, but one is not ‘blind’ at any and every age, but only if one has
not sight at the age at which one would naturally have it. Similarly a thing is
called blind if it has not sight in the medium in which, and in respect of the
organ in respect of which, and with reference to the object with reference to
which, and in the circumstances in which, it would naturally have it. – (4) The
violent taking away of anything is called privation.
Indeed there are just as many kinds of
privations as there are of words with negative prefixes; for a thing is called
unequal because it has not equality though it would naturally have it, and
invisible either because it has no colour at all or because it has a poor
colour, and apodous either because it has no feet at all or because it has
imperfect feet. Again, a privative term may be used because the thing has little
of the attribute (and this means having it in a sense imperfectly), e.g.
‘kernel-less’; or because it has it not easily or not well (e.g. we call a thing
uncuttable not only if it cannot be cut but also if it cannot be cut easily or
well); or because it has not the attribute at all; for it is not the one-eyed
man but he who is sightless in both eyes that is called blind. This is why not
every man is ‘good’ or ‘bad’, ‘just’ or ‘unjust’, but there is also an
intermediate state.
23
To ‘have’ or ‘hold’ means many things: – (1) to
treat a thing according to one’s own nature or according to one’s own impulse;
so that fever is said to have a man, and tyrants to have their cities, and
people to have the clothes they wear. – (2) That in which a thing is present as
in something receptive of it is said to have the thing; e.g. the bronze has the
form of the statue, and the body has the disease. – (3) As that which contains
holds the things contained; for a thing is said to be held by that in which it
is as in a container; e.g. we say that the vessel holds the liquid and the city
holds men and the ship sailors; and so too that the whole holds the parts. – (4)
That which hinders a thing from moving or acting according to its own impulse is
said to hold it, as pillars hold the incumbent weights, and as the poets make
Atlas hold the heavens, implying that otherwise they would collapse on the
earth, as some of the natural philosophers also say. In this way also that which
holds things together is said to hold the things it holds together, since they
would otherwise separate, each according to its own
impulse.
‘Being in something’ has similar and
corresponding meanings to ‘holding’ or ‘having’.
24
‘To come from something’ means (1) to come from
something as from matter, and this in two senses, either in respect of the
highest genus or in respect of the lowest species; e.g. in a sense all things
that can be melted come from water, but in a sense the statue comes from bronze.
– (2) As from the first moving principle; e.g. ‘what did the fight come from?’
From abusive language, because this was the origin of the fight. – (3) From the
compound of matter and shape, as the parts come from the whole, and the verse
from the Iliad, and the stones from the house; (in every such case the whole is
a compound of matter and shape,) for the shape is the end, and only that which
attains an end is complete. – (4) As the form from its part, e.g. man from
‘two-footed’and syllable from ‘letter’; for this is a different sense from that
in which the statue comes from bronze; for the composite substance comes from
the sensible matter, but the form also comes from the matter of the form. – Some
things, then, are said to come from something else in these senses; but (5)
others are so described if one of these senses is applicable to a part of that
other thing; e.g. the child comes from its father and mother, and plants come
from the earth, because they come from a part of those things. – (6) It means
coming after a thing in time, e.g. night comes from day and storm from fine
weather, because the one comes after the other. Of these things some are so
described because they admit of change into one another, as in the cases now
mentioned; some merely because they are successive in time, e.g. the voyage took
place ‘from’ the equinox, because it took place after the equinox, and the
festival of the Thargelia comes ‘from’ the Dionysia, because after the
Dionysia.
25
‘Part’ means (1) (a) that into which a quantum
can in any way be divided; for that which is taken from a quantum qua quantum is
always called a part of it, e.g. two is called in a sense a part of three. It
means (b), of the parts in the first sense, only those which measure the whole;
this is why two, though in one sense it is, in another is not, called a part of
three. – (2) The elements into which a kind might be divided apart from the
quantity are also called parts of it; for which reason we say the species are
parts of the genus. – (3) The elements into which a whole is divided, or of
which it consists – the ‘whole’ meaning either the form or that which has the
form; e.g. of the bronze sphere or of the bronze cube both the bronze – i.e. the
matter in which the form is – and the characteristic angle are parts. – (4) The
elements in the definition which explains a thing are also parts of the whole;
this is why the genus is called a part of the species, though in another sense
the species is part of the genus.
26
‘A whole’ means (1) that from which is absent
none of the parts of which it is said to be naturally a whole, and (2) that
which so contains the things it contains that they form a unity; and this in two
senses – either as being each severally one single thing, or as making up the
unity between them. For (a) that which is true of a whole class and is said to
hold good as a whole (which implies that it is a kind whole) is true of a whole
in the sense that it contains many things by being predicated of each, and by
all of them, e.g. man, horse, god, being severally one single thing, because all
are living things. But (b) the continuous and limited is a whole, when it is a
unity consisting of several parts, especially if they are present only
potentially, but, failing this, even if they are present actually. Of these
things themselves, those which are so by nature are wholes in a higher degree
than those which are so by art, as we said in the case of unity also, wholeness
being in fact a sort of oneness.
Again (3) of quanta that have a beginning and a
middle and an end, those to which the position does not make a difference are
called totals, and those to which it does, wholes. Those which admit of both
descriptions are both wholes and totals. These are the things whose nature
remains the same after transposition, but whose form does not, e.g. wax or a
coat; they are called both wholes and totals; for they have both
characteristics. Water and all liquids and number are called totals, but ‘the
whole number’ or ‘the whole water’ one does not speak of, except by an extension
of meaning. To things, to which qua one the term ‘total’ is applied, the term
‘all’ is applied when they are treated as separate; ‘this total number,’ ‘all
these units.’
27
It is not any chance quantitative thing that
can be said to be ‘mutilated’; it must be a whole as well as divisible. For not
only is two not ‘mutilated’ if one of the two ones is taken away (for the part
removed by mutilation is never equal to the remainder), but in general no number
is thus mutilated; for it is also necessary that the essence remain; if a cup is
mutilated, it must still be a cup; but the number is no longer the same.
Further, even if things consist of unlike parts, not even these things can all
be said to be mutilated, for in a sense a number has unlike parts (e.g. two and
three) as well as like; but in general of the things to which their position
makes no difference, e.g. water or fire, none can be mutilated; to be mutilated,
things must be such as in virtue of their essence have a certain position.
Again, they must be continuous; for a musical scale consists of unlike parts and
has position, but cannot become mutilated. Besides, not even the things that are
wholes are mutilated by the privation of any part. For the parts removed must be
neither those which determine the essence nor any chance parts, irrespective of
their position; e.g. a cup is not mutilated if it is bored through, but only if
the handle or a projecting part is removed, and a man is mutilated not if the
flesh or the spleen is removed, but if an extremity is, and that not every
extremity but one which when completely removed cannot grow again. Therefore
baldness is not a mutilation.
28
The term ‘race’ or ‘genus’ is used (1) if
generation of things which have the same form is continuous, e.g. ‘while the
race of men lasts’ means ‘while the generation of them goes on continuously’. –
(2) It is used with reference to that which first brought things into existence;
for it is thus that some are called Hellenes by race and others Ionians, because
the former proceed from Hellen and the latter from Ion as their first begetter.
And the word is used in reference to the begetter more than to the matter,
though people also get a race-name from the female, e.g. ‘the descendants of
Pyrrha’. – (3) There is genus in the sense in which ‘plane’ is the genus of
plane figures and solid’ of solids; for each of the figures is in the one case a
plane of such and such a kind, and in the other a solid of such and such a kind;
and this is what underlies the differentiae. Again (4) in definitions the first
constituent element, which is included in the ‘what’, is the genus, whose
differentiae the qualities are said to be ‘Genus’ then is used in all these
ways, (1) in reference to continuous generation of the same kind, (2) in
reference to the first mover which is of the same kind as the things it moves,
(3) as matter; for that to which the differentia or quality belongs is the
substratum, which we call matter.
Those things are said to be ‘other in genus’
whose proximate substratum is different, and which are not analysed the one into
the other nor both into the same thing (e.g. form and matter are different in
genus); and things which belong to different categories of being (for some of
the things that are said to ‘be’ signify essence, others a quality, others the
other categories we have before distinguished); these also are not analysed
either into one another or into some one thing.
29
‘The false’ means (1) that which is false as a
thing, and that (a) because it is not put together or cannot be put together,
e.g. ‘that the diagonal of a square is commensurate with the side’ or ‘that you
are sitting’; for one of these is false always, and the other sometimes; it is
in these two senses that they are non-existent. (b) There are things which
exist, but whose nature it is to appear either not to be such as they are or to
be things that do not exist, e.g. a sketch or a dream; for these are something,
but are not the things the appearance of which they produce in us. We call
things false in this way, then, – either because they themselves do not exist,
or because the appearance which results from them is that of something that does
not exist.
(2) A false account is the account of
non-existent objects, in so far as it is false. Hence every account is false
when applied to something other than that of which it is true; e.g. the account
of a circle is false when applied to a triangle. In a sense there is one account
of each thing, i.e. the account of its essence, but in a sense there are many,
since the thing itself and the thing itself with an attribute are in a sense the
same, e.g. Socrates and musical Socrates (a false account is not the account of
anything, except in a qualified sense). Hence Antisthenes was too simple-minded
when he claimed that nothing could be described except by the account proper to
it, – one predicate to one subject; from which the conclusion used to be drawn
that there could be no contradiction, and almost that there could be no error.
But it is possible to describe each thing not only by the account of itself, but
also by that of something else. This may be done altogether falsely indeed, but
there is also a way in which it may be done truly; e.g. eight may be described
as a double number by the use of the definition of two.
These things, then, are called false in these
senses, but (3) a false man is one who is ready at and fond of such accounts,
not for any other reason but for their own sake, and one who is good at
impressing such accounts on other people, just as we say things are which
produce a false appearance. This is why the proof in the Hippias that the same
man is false and true is misleading. For it assumes that he is false who can
deceive (i.e. the man who knows and is wise); and further that he who is
willingly bad is better. This is a false result of induction – for a man who
limps willingly is better than one who does so unwillingly – by ‘limping’ Plato
means ‘mimicking a limp’, for if the man were lame willingly, he would
presumably be worse in this case as in the corresponding case of moral
character.
30
‘Accident’ means (1) that which attaches to
something and can be truly asserted, but neither of necessity nor usually, e.g.
if some one in digging a hole for a plant has found treasure. This – the finding
of treasure – is for the man who dug the hole an accident; for neither does the
one come of necessity from the other or after the other, nor, if a man plants,
does he usually find treasure. And a musical man might be pale; but since this
does not happen of necessity nor usually, we call it an accident. Therefore
since there are attributes and they attach to subjects, and some of them attach
to these only in a particular place and at a particular time, whatever attaches
to a subject, but not because it was this subject, or the time this time, or the
place this place, will be an accident. Therefore, too, there is no definite
cause for an accident, but a chance cause, i.e. an indefinite one. Going to
Aegina was an accident for a man, if he went not in order to get there, but
because he was carried out of his way by a storm or captured by pirates. The
accident has happened or exists, – not in virtue of the subject’s nature,
however, but of something else; for the storm was the cause of his coming to a
place for which he was not sailing, and this was Aegina.
‘Accident’ has also (2) another meaning, i.e.
all that attaches to each thing in virtue of itself but is not in its essence,
as having its angles equal to two right angles attaches to the triangle. And
accidents of this sort may be eternal, but no accident of the other sort is.
This is explained elsewhere.
1
We are seeking the principles and the causes of the things that are, and obviously of them qua being. For, while there is a cause of health and of good condition, and the objects of mathematics have first principles and elements and causes, and in general every science which is ratiocinative or at all involves reasoning deals with causes and principles, more or less precise, all these sciences mark off some particular being – some genus, and inquire into this, but not into being simply nor qua being, nor do they offer any discussion of the essence of the things of which they treat; but starting from the essence – some making it plain to the senses, others assuming it as a hypothesis – they then demonstrate, more or less cogently, the essential attributes of the genus with which they deal. It is obvious, therefore, that such an induction yields no demonstration of substance or of the essence, but some other way of exhibiting it. And similarly the sciences omit the question whether the genus with which they deal exists or does not exist, because it belongs to the same kind of thinking to show what it is and that it is.
And since natural science, like other sciences,
is in fact about one class of being, i.e. to that sort of substance which has
the principle of its movement and rest present in itself, evidently it is
neither practical nor productive. For in the case of things made the principle
is in the maker – it is either reason or art or some faculty, while in the case
of things done it is in the doer – viz. will, for that which is done and that
which is willed are the same. Therefore, if all thought is either practical or
productive or theoretical, physics must be a theoretical science, but it will
theorize about such being as admits of being moved, and about substance – as
defined for the most part only as not separable from matter. Now, we must not
fail to notice the mode of being of the essence and of its definition, for,
without this, inquiry is but idle. Of things defined, i.e. of ‘whats’, some are
like ‘snub’, and some like ‘concave’. And these differ because ‘snub’ is bound
up with matter (for what is snub is a concave nose), while concavity is
independent of perceptible matter. If then all natural things are a analogous to
the snub in their nature; e.g. nose, eye, face, flesh, bone, and, in general,
animal; leaf, root, bark, and, in general, plant (for none of these can be
defined without reference to movement – they always have matter), it is clear
how we must seek and define the ‘what’ in the case of natural objects, and also
that it belongs to the student of nature to study even soul in a certain sense,
i.e. so much of it as is not independent of matter.
That physics, then, is a theoretical science,
is plain from these considerations. Mathematics also, however, is theoretical;
but whether its objects are immovable and separable from matter, is not at
present clear; still, it is clear that some mathematical theorems consider them
qua immovable and qua separable from matter. But if there is something which is
eternal and immovable and separable, clearly the knowledge of it belongs to a
theoretical science, – not, however, to physics (for physics deals with certain
movable things) nor to mathematics, but to a science prior to both. For physics
deals with things which exist separately but are not immovable, and some parts
of mathematics deal with things which are immovable but presumably do not exist
separately, but as embodied in matter; while the first science deals with things
which both exist separately and are immovable. Now all causes must be eternal,
but especially these; for they are the causes that operate on so much of the
divine as appears to us. There must, then, be three theoretical philosophies,
mathematics, physics, and what we may call theology, since it is obvious that if
the divine is present anywhere, it is present in things of this sort. And the
highest science must deal with the highest genus. Thus, while the theoretical
sciences are more to be desired than the other sciences, this is more to be
desired than the other theoretical sciences. For one might raise the question
whether first philosophy is universal, or deals with one genus, i.e. some one
kind of being; for not even the mathematical sciences are all alike in this
respect, – geometry and astronomy deal with a certain particular kind of thing,
while universal mathematics applies alike to all. We answer that if there is no
substance other than those which are formed by nature, natural science will be
the first science; but if there is an immovable substance, the science of this
must be prior and must be first philosophy, and universal in this way, because
it is first. And it will belong to this to consider being qua being – both what
it is and the attributes which belong to it qua being.
2
But since the unqualified term ‘being’ has
several meanings, of which one was seen’ to be the accidental, and another the
true (‘non-being’ being the false), while besides these there are the figures of
predication (e.g. the ‘what’, quality, quantity, place, time, and any similar
meanings which ‘being’ may have), and again besides all these there is that
which ‘is’ potentially or actually: – since ‘being’ has many meanings, we must
say regarding the accidental, that there can be no scientific treatment of it.
This is confirmed by the fact that no science practical, productive, or
theoretical troubles itself about it. For on the one hand he who produces a
house does not produce all the attributes that come into being along with the
house; for these are innumerable; the house that has been made may quite well be
pleasant for some people, hurtful for some, and useful to others, and different
– to put it shortly from all things that are; and the science of building does
not aim at producing any of these attributes. And in the same way the geometer
does not consider the attributes which attach thus to figures, nor whether
‘triangle’ is different from ‘triangle whose angles are equal to two right
angles’. – And this happens naturally enough; for the accidental is practically
a mere name. And so Plato was in a sense not wrong in ranking sophistic as
dealing with that which is not. For the arguments of the sophists deal, we may
say, above all with the accidental; e.g. the question whether ‘musical’ and
‘lettered’ are different or the same, and whether ‘musical Coriscus’ and
‘Coriscus’ are the same, and whether ‘everything which is, but is not eternal,
has come to be’, with the paradoxical conclusion that if one who was musical has
come to be lettered, he must also have been lettered and have come to be
musical, and all the other arguments of this sort; the accidental is obviously
akin to non-being. And this is clear also from arguments such as the following:
things which are in another sense come into being and pass out of being by a
process, but things which are accidentally do not. But still we must, as far as
we can, say further, regarding the accidental, what its nature is and from what
cause it proceeds; for it will perhaps at the same time become clear why there
is no science of it.
Since, among things which are, some are always
in the same state and are of necessity (not necessity in the sense of compulsion
but that which we assert of things because they cannot be otherwise), and some
are not of necessity nor always, but for the most part, this is the principle
and this the cause of the existence of the accidental; for that which is neither
always nor for the most part, we call accidental. For instance, if in the
dog-days there is wintry and cold weather, we say this is an accident, but not
if there is sultry heat, because the latter is always or for the most part so,
but not the former. And it is an accident that a man is pale (for this is
neither always nor for the most part so), but it is not by accident that he is
an animal. And that the builder produces health is an accident, because it is
the nature not of the builder but of the doctor to do this, – but the builder
happened to be a doctor. Again, a confectioner, aiming at giving pleasure, may
make something wholesome, but not in virtue of the confectioner’s art; and
therefore we say ‘it was an accident’, and while there is a sense in which he
makes it, in the unqualified sense he does not. For to other things answer
faculties productive of them, but to accidental results there corresponds no
determinate art nor faculty; for of things which are or come to be by accident,
the cause also is accidental. Therefore, since not all things either are or come
to be of necessity and always, but, the majority of things are for the most
part, the accidental must exist; for instance a pale man is not always nor for
the most part musical, but since this sometimes happens, it must be accidental
(if not, everything will be of necessity). The matter, therefore, which is
capable of being otherwise than as it usually is, must be the cause of the
accidental. And we must take as our starting-point the question whether there is
nothing that is neither always nor for the most part. Surely this is impossible.
There is, then, besides these something which is fortuitous and accidental. But
while the usual exists, can nothing be said to be always, or are there eternal
things? This must be considered later,’ but that there is no science of the
accidental is obvious; for all science is either of that which is always or of
that which is for the most part. (For how else is one to learn or to teach
another? The thing must be determined as occurring either always or for the most
part, e.g. that honey-water is useful for a patient in a fever is true for the
most part.) But that which is contrary to the usual law science will be unable
to state, i.e. when the thing does not happen, e.g.’on the day of new moon’; for
even that which happens on the day of new moon happens then either always or for
the most part; but the accidental is contrary to such laws. We have stated,
then, what the accidental is, and from what cause it arises, and that there is
no science which deals with it.
3
That there are principles and causes which are
generable and destructible without ever being in course of being generated or
destroyed, is obvious. For otherwise all things will be of necessity, since that
which is being generated or destroyed must have a cause which is not
accidentally its cause. Will A exist or not? It will if B happens; and if not,
not. And B will exist if C happens. And thus if time is constantly subtracted
from a limited extent of time, one will obviously come to the present. This man,
then, will die by violence, if he goes out; and he will do this if he gets
thirsty; and he will get thirsty if something else happens; and thus we shall
come to that which is now present, or to some past event. For instance, he will
go out if he gets thirsty; and he will get thirsty if he is eating pungent food;
and this is either the case or not; so that he will of necessity die, or of
necessity not die. And similarly if one jumps over to past events, the same
account will hold good; for this – I mean the past condition – is already
present in something. Everything, therefore, that will be, will be of necessity;
e.g. it is necessary that he who lives shall one day die; for already some
condition has come into existence, e.g. the presence of contraries in the same
body. But whether he is to die by disease or by violence is not yet determined,
but depends on the happening of something else. Clearly then the process goes
back to a certain starting-point, but this no longer points to something
further. This then will be the starting-point for the fortuitous, and will have
nothing else as cause of its coming to be. But to what sort of starting-point
and what sort of cause we thus refer the fortuitous – whether to matter or to
the purpose or to the motive power, must be carefully
considered.
4
Let us dismiss accidental being; for we have
sufficiently determined its nature. But since that which is in the sense of
being true, or is not in the sense of being false, depends on combination and
separation, and truth and falsity together depend on the allocation of a pair of
contradictory judgements (for the true judgement affirms where the subject and
predicate really are combined, and denies where they are separated, while the
false judgement has the opposite of this allocation; it is another question, how
it happens that we think things together or apart; by ‘together’ and ‘apart’ I
mean thinking them so that there is no succession in the thoughts but they
become a unity); for falsity and truth are not in things – it is not as if the
good were true, and the bad were in itself false – but in thought; while with
regard to simple concepts and ‘whats’ falsity and truth do not exist even in
thought – this being so, we must consider later what has to be discussed with
regard to that which is or is not in this sense. But since the combination and
the separation are in thought and not in the things, and that which is in this
sense is a different sort of ‘being’ from the things that are in the full sense
(for the thought attaches or removes either the subject’s ‘what’ or its having a
certain quality or quantity or something else), that which is accidentally and
that which is in the sense of being true must be dismissed. For the cause of the
former is indeterminate, and that of the latter is some affection of the
thought, and both are related to the remaining genus of being, and do not
indicate the existence of any separate class of being. Therefore let these be
dismissed, and let us consider the causes and the principles of being itself,
qua being. (It was clear in our discussion of the various meanings of terms,
that ‘being’ has several meanings.)
1
There are several senses in which a thing may
be said to ‘be’, as we pointed out previously in our book on the various senses
of words;’ for in one sense the ‘being’ meant is ‘what a thing is’ or a ‘this’,
and in another sense it means a quality or quantity or one of the other things
that are predicated as these are. While ‘being’ has all these senses, obviously
that which ‘is’ primarily is the ‘what’, which indicates the substance of the
thing. For when we say of what quality a thing is, we say that it is good or
bad, not that it is three cubits long or that it is a man; but when we say what
it is, we do not say ‘white’ or ‘hot’ or ‘three cubits long’, but ‘a man’ or ‘a
‘god’. And all other things are said to be because they are, some of them,
quantities of that which is in this primary sense, others qualities of it,
others affections of it, and others some other determination of it. And so one
might even raise the question whether the words ‘to walk’, ‘to be healthy’, ‘to
sit’ imply that each of these things is existent, and similarly in any other
case of this sort; for none of them is either self-subsistent or capable of
being separated from substance, but rather, if anything, it is that which walks
or sits or is healthy that is an existent thing. Now these are seen to be more
real because there is something definite which underlies them (i.e. the
substance or individual), which is implied in such a predicate; for we never use
the word ‘good’ or ‘sitting’ without implying this. Clearly then it is in virtue
of this category that each of the others also is. Therefore that which is
primarily, i.e. not in a qualified sense but without qualification, must be
substance.
Now there are several senses in which a thing
is said to be first; yet substance is first in every sense – (1) in definition,
(2) in order of knowledge, (3) in time. For (3) of the other categories none can
exist independently, but only substance. And (1) in definition also this is
first; for in the definition of each term the definition of its substance must
be present. And (2) we think we know each thing most fully, when we know what it
is, e.g. what man is or what fire is, rather than when we know its quality, its
quantity, or its place; since we know each of these predicates also, only when
we know what the quantity or the quality is.
And indeed the question which was raised of old
and is raised now and always, and is always the subject of doubt, viz. what
being is, is just the question, what is substance? For it is this that some
assert to be one, others more than one, and that some assert to be limited in
number, others unlimited. And so we also must consider chiefly and primarily and
almost exclusively what that is which is in this sense.
2
Substance is thought to belong most obviously
to bodies; and so we say that not only animals and plants and their parts are
substances, but also natural bodies such as fire and water and earth and
everything of the sort, and all things that are either parts of these or
composed of these (either of parts or of the whole bodies), e.g. the physical
universe and its parts, stars and moon and sun. But whether these alone are
substances, or there are also others, or only some of these, or others as well,
or none of these but only some other things, are substances, must be considered.
Some think the limits of body, i.e. surface, line, point, and unit, are
substances, and more so than body or the solid.
Further, some do not think there is anything
substantial besides sensible things, but others think there are eternal
substances which are more in number and more real; e.g. Plato posited two kinds
of substance – the Forms and objects of mathematics – as well as a third kind,
viz. the substance of sensible bodies. And Speusippus made still more kinds of
substance, beginning with the One, and assuming principles for each kind of
substance, one for numbers, another for spatial magnitudes, and then another for
the soul; and by going on in this way he multiplies the kinds of substance. And
some say Forms and numbers have the same nature, and the other things come after
them – lines and planes – until we come to the substance of the material
universe and to sensible bodies.
Regarding these matters, then, we must inquire
which of the common statements are right and which are not right, and what
substances there are, and whether there are or are not any besides sensible
substances, and how sensible substances exist, and whether there is a substance
capable of separate existence (and if so why and how) or no such substance,
apart from sensible substances; and we must first sketch the nature of
substance.
3
The word ‘substance’ is applied, if not in more
senses, still at least to four main objects; for both the essence and the
universal and the genus, are thought to be the substance of each thing, and
fourthly the substratum. Now the substratum is that of which everything else is
predicated, while it is itself not predicated of anything else. And so we must
first determine the nature of this; for that which underlies a thing primarily
is thought to be in the truest sense its substance. And in one sense matter is
said to be of the nature of substratum, in another, shape, and in a third, the
compound of these. (By the matter I mean, for instance, the bronze, by the shape
the pattern of its form, and by the compound of these the statue, the concrete
whole.) Therefore if the form is prior to the matter and more real, it will be
prior also to the compound of both, for the same reason.
We have now outlined the nature of substance,
showing that it is that which is not predicated of a stratum, but of which all
else is predicated. But we must not merely state the matter thus; for this is
not enough. The statement itself is obscure, and further, on this view, matter
becomes substance. For if this is not substance, it baffles us to say what else
is. When all else is stripped off evidently nothing but matter remains. For
while the rest are affections, products, and potencies of bodies, length,
breadth, and depth are quantities and not substances (for a quantity is not a
substance), but the substance is rather that to which these belong primarily.
But when length and breadth and depth are taken away we see nothing left unless
there is something that is bounded by these; so that to those who consider the
question thus matter alone must seem to be substance. By matter I mean that
which in itself is neither a particular thing nor of a certain quantity nor
assigned to any other of the categories by which being is determined. For there
is something of which each of these is predicated, whose being is different from
that of each of the predicates (for the predicates other than substance are
predicated of substance, while substance is predicated of matter). Therefore the
ultimate substratum is of itself neither a particular thing nor of a particular
quantity nor otherwise positively characterized; nor yet is it the negations of
these, for negations also will belong to it only by
accident.
If we adopt this point of view, then, it
follows that matter is substance. But this is impossible; for both separability
and ‘thisness’ are thought to belong chiefly to substance. And so form and the
compound of form and matter would be thought to be substance, rather than
matter. The substance compounded of both, i.e. of matter and shape, may be
dismissed; for it is posterior and its nature is obvious. And matter also is in
a sense manifest. But we must inquire into the third kind of substance; for this
is the most perplexing.
Some of the sensible substances are generally
admitted to be substances, so that we must look first among these. For it is an
advantage to advance to that which is more knowable. For learning proceeds for
all in this way – through that which is less knowable by nature to that which is
more knowable; and just as in conduct our task is to start from what is good for
each and make what is without qualification good good for each, so it is our
task to start from what is more knowable to oneself and make what is knowable by
nature knowable to oneself. Now what is knowable and primary for particular sets
of people is often knowable to a very small extent, and has little or nothing of
reality. But yet one must start from that which is barely knowable but knowable
to oneself, and try to know what is knowable without qualification, passing, as
has been said, by way of those very things which one does
know.
4
Since at the start we distinguished the various
marks by which we determine substance, and one of these was thought to be the
essence, we must investigate this. And first let us make some linguistic remarks
about it. The essence of each thing is what it is said to be propter se. For
being you is not being musical, since you are not by your very nature musical.
What, then, you are by your very nature is your essence.
Nor yet is the whole of this the essence of a
thing; not that which is propter se as white is to a surface, because being a
surface is not identical with being white. But again the combination of both –
‘being a white surface’ – is not the essence of surface, because ‘surface’
itself is added. The formula, therefore, in which the term itself is not present
but its meaning is expressed, this is the formula of the essence of each thing.
Therefore if to be a white surface is to be a smooth surface, to be white and to
be smooth are one and the same.
But since there are also compounds answering to
the other categories (for there is a substratum for each category, e.g. for
quality, quantity, time, place, and motion), we must inquire whether there is a
formula of the essence of each of them, i.e. whether to these compounds also
there belongs an essence, e.g. ‘white man’. Let the compound be denoted by
‘cloak’. What is the essence of cloak? But, it may be said, this also is not a
propter se expression. We reply that there are just two ways in which a
predicate may fail to be true of a subject propter se, and one of these results
from the addition, and the other from the omission, of a determinant. One kind
of predicate is not propter se because the term that is being defined is
combined with another determinant, e.g. if in defining the essence of white one
were to state the formula of white man; the other because in the subject another
determinant is combined with that which is expressed in the formula, e.g. if
‘cloak’ meant ‘white man’, and one were to define cloak as white; white man is
white indeed, but its essence is not to be white.
But is being-a-cloak an essence at all?
Probably not. For the essence is precisely what something is; but when an
attribute is asserted of a subject other than itself, the complex is not
precisely what some ‘this’ is, e.g. white man is not precisely what some ‘this’
is, since thisness belongs only to substances. Therefore there is an essence
only of those things whose formula is a definition. But we have a definition not
where we have a word and a formula identical in meaning (for in that case all
formulae or sets of words would be definitions; for there will be some name for
any set of words whatever, so that even the Iliad will be a definition), but
where there is a formula of something primary; and primary things are those
which do not imply the predication of one element in them of another element.
Nothing, then, which is not a species of a genus will have an essence – only
species will have it, for these are thought to imply not merely that the subject
participates in the attribute and has it as an affection, or has it by accident;
but for ever thing else as well, if it has a name, there be a formula of its
meaning – viz. that this attribute belongs to this subject; or instead of a
simple formula we shall be able to give a more accurate one; but there will be
no definition nor essence.
Or has ‘definition’, like ‘what a thing is’,
several meanings? ‘What a thing is’ in one sense means substance and the ‘this’,
in another one or other of the predicates, quantity, quality, and the like. For
as ‘is’ belongs to all things, not however in the same sense, but to one sort of
thing primarily and to others in a secondary way, so too ‘what a thing is’
belongs in the simple sense to substance, but in a limited sense to the other
categories. For even of a quality we might ask what it is, so that quality also
is a ‘what a thing is’, – not in the simple sense, however, but just as, in the
case of that which is not, some say, emphasizing the linguistic form, that that
is which is not is-not is simply, but is non-existent; so too with
quality.
We must no doubt inquire how we should express
ourselves on each point, but certainly not more than how the facts actually
stand. And so now also, since it is evident what language we use, essence will
belong, just as ‘what a thing is’ does, primarily and in the simple sense to
substance, and in a secondary way to the other categories also, – not essence in
the simple sense, but the essence of a quality or of a quantity. For it must be
either by an equivocation that we say these are, or by adding to and taking from
the meaning of ‘are’ (in the way in which that which is not known may be said to
be known), – the truth being that we use the word neither ambiguously nor in the
same sense, but just as we apply the word ‘medical’ by virtue of a reference to
one and the same thing, not meaning one and the same thing, nor yet speaking
ambiguously; for a patient and an operation and an instrument are called medical
neither by an ambiguity nor with a single meaning, but with reference to a
common end. But it does not matter at all in which of the two ways one likes to
describe the facts; this is evident, that definition and essence in the primary
and simple sense belong to substances. Still they belong to other things as
well, only not in the primary sense. For if we suppose this it does not follow
that there is a definition of every word which means the same as any formula; it
must mean the same as a particular kind of formula; and this condition is
satisfied if it is a formula of something which is one, not by continuity like
the Iliad or the things that are one by being bound together, but in one of the
main senses of ‘one’, which answer to the senses of ‘is’; now ‘that which is’ in
one sense denotes a ‘this’, in another a quantity, in another a quality. And so
there can be a formula or definition even of white man, but not in the sense in
which there is a definition either of white or of a
substance.
5
It is a difficult question, if one denies that
a formula with an added determinant is a definition, whether any of the terms
that are not simple but coupled will be definable. For we must explain them by
adding a determinant. E.g. there is the nose, and concavity, and snubness, which
is compounded out of the two by the presence of the one in the other, and it is
not by accident that the nose has the attribute either of concavity or of
snubness, but in virtue of its nature; nor do they attach to it as whiteness
does to Callias, or to man (because Callias, who happens to be a man, is white),
but as ‘male’ attaches to animal and ‘equal’ to quantity, and as all so-called
‘attributes propter se’ attach to their subjects. And such attributes are those
in which is involved either the formula or the name of the subject of the
particular attribute, and which cannot be explained without this; e.g. white can
be explained apart from man, but not female apart from animal. Therefore there
is either no essence and definition of any of these things, or if there is, it
is in another sense, as we have said.
But there is also a second difficulty about
them. For if snub nose and concave nose are the same thing, snub and concave
will be the thing; but if snub and concave are not the same (because it is
impossible to speak of snubness apart from the thing of which it is an attribute
propter se, for snubness is concavity-in-a-nose), either it is impossible to say
‘snub nose’ or the same thing will have been said twice, concave-nose nose; for
snub nose will be concave-nose nose. And so it is absurd that such things should
have an essence; if they have, there will be an infinite regress; for in
snub-nose nose yet another ‘nose’ will be involved.
Clearly, then, only substance is definable. For
if the other categories also are definable, it must be by addition of a
determinant, e.g. the qualitative is defined thus, and so is the odd, for it
cannot be defined apart from number; nor can female be defined apart from
animal. (When I say ‘by addition’ I mean the expressions in which it turns out
that we are saying the same thing twice, as in these instances.) And if this is
true, coupled terms also, like ‘odd number’, will not be definable (but this
escapes our notice because our formulae are not accurate.). But if these also
are definable, either it is in some other way or, as we definition and essence
must be said to have more than one sense. Therefore in one sense nothing will
have a definition and nothing will have an essence, except substances, but in
another sense other things will have them. Clearly, then, definition is the
formula of the essence, and essence belongs to substances either alone or
chiefly and primarily and in the unqualified sense.
6
We must inquire whether each thing and its
essence are the same or different. This is of some use for the inquiry
concerning substance; for each thing is thought to be not different from its
substance, and the essence is said to be the substance of each
thing.
Now in the case of accidental unities the two
would be generally thought to be different, e.g. white man would be thought to
be different from the essence of white man. For if they are the same, the
essence of man and that of white man are also the same; for a man and a white
man are the same thing, as people say, so that the essence of white man and that
of man would be also the same. But perhaps it does not follow that the essence
of accidental unities should be the same as that of the simple terms. For the
extreme terms are not in the same way identical with the middle term. But
perhaps this might be thought to follow, that the extreme terms, the accidents,
should turn out to be the same, e.g. the essence of white and that of musical;
but this is not actually thought to be the case.
But in the case of so-called self-subsistent
things, is a thing necessarily the same as its essence? E.g. if there are some
substances which have no other substances nor entities prior to them –
substances such as some assert the Ideas to be? – If the essence of good is to
be different from good-itself, and the essence of animal from animal-itself, and
the essence of being from being-itself, there will, firstly, be other substances
and entities and Ideas besides those which are asserted, and, secondly, these
others will be prior substances, if essence is substance. And if the posterior
substances and the prior are severed from each other, (a) there will be no
knowledge of the former, and (b) the latter will have no being. (By ‘severed’ I
mean, if the good-itself has not the essence of good, and the latter has not the
property of being good.) For (a) there is knowledge of each thing only when we
know its essence. And (b) the case is the same for other things as for the good;
so that if the essence of good is not good, neither is the essence of reality
real, nor the essence of unity one. And all essences alike exist or none of them
does; so that if the essence of reality is not real, neither is any of the
others. Again, that to which the essence of good does not belong is not good. –
The good, then, must be one with the essence of good, and the beautiful with the
essence of beauty, and so with all things which do not depend on something else
but are self-subsistent and primary. For it is enough if they are this, even if
they are not Forms; or rather, perhaps, even if they are Forms. (At the same
time it is clear that if there are Ideas such as some people say there are, it
will not be substratum that is substance; for these must be substances, but not
predicable of a substratum; for if they were they would exist only by being
participated in.)
Each thing itself, then, and its essence are
one and the same in no merely accidental way, as is evident both from the
preceding arguments and because to know each thing, at least, is just to know
its essence, so that even by the exhibition of instances it becomes clear that
both must be one.
(But of an accidental term, e.g.’the musical’
or ‘the white’, since it has two meanings, it is not true to say that it itself
is identical with its essence; for both that to which the accidental quality
belongs, and the accidental quality, are white, so that in a sense the accident
and its essence are the same, and in a sense they are not; for the essence of
white is not the same as the man or the white man, but it is the same as the
attribute white.)
The absurdity of the separation would appear
also if one were to assign a name to each of the essences; for there would be
yet another essence besides the original one, e.g. to the essence of horse there
will belong a second essence. Yet why should not some things be their essences
from the start, since essence is substance? But indeed not only are a thing and
its essence one, but the formula of them is also the same, as is clear even from
what has been said; for it is not by accident that the essence of one, and the
one, are one. Further, if they are to be different, the process will go on to
infinity; for we shall have (1) the essence of one, and (2) the one, so that to
terms of the former kind the same argument will be
applicable.
Clearly, then, each primary and self-subsistent
thing is one and the same as its essence. The sophistical objections to this
position, and the question whether Socrates and to be Socrates are the same
thing, are obviously answered by the same solution; for there is no difference
either in the standpoint from which the question would be asked, or in that from
which one could answer it successfully. We have explained, then, in what sense
each thing is the same as its essence and in what sense it is
not.
7
Of things that come to be, some come to be by
nature, some by art, some spontaneously. Now everything that comes to be comes
to be by the agency of something and from something and comes to be something.
And the something which I say it comes to be may be found in any category; it
may come to be either a ‘this’ or of some size or of some quality or
somewhere.
Now natural comings to be are the comings to be
of those things which come to be by nature; and that out of which they come to
be is what we call matter; and that by which they come to be is something which
exists naturally; and the something which they come to be is a man or a plant or
one of the things of this kind, which we say are substances if anything is – all
things produced either by nature or by art have matter; for each of them is
capable both of being and of not being, and this capacity is the matter in each
– and, in general, both that from which they are produced is nature, and the
type according to which they are produced is nature (for that which is produced,
e.g. a plant or an animal, has a nature), and so is that by which they are
produced – the so-called ‘formal’ nature, which is specifically the same (though
this is in another individual); for man begets man.
Thus, then, are natural products produced; all
other productions are called ‘makings’. And all makings proceed either from art
or from a faculty or from thought. Some of them happen also spontaneously or by
luck just as natural products sometimes do; for there also the same things
sometimes are produced without seed as well as from seed. Concerning these
cases, then, we must inquire later, but from art proceed the things of which the
form is in the soul of the artist. (By form I mean the essence of each thing and
its primary substance.) For even contraries have in a sense the same form; for
the substance of a privation is the opposite substance, e.g. health is the
substance of disease (for disease is the absence of health); and health is the
formula in the soul or the knowledge of it. The healthy subject is produced as
the result of the following train of thought: – since this is health, if the
subject is to be healthy this must first be present, e.g. a uniform state of
body, and if this is to be present, there must be heat; and the physician goes
on thinking thus until he reduces the matter to a final something which he
himself can produce. Then the process from this point onward, i.e. the process
towards health, is called a ‘making’. Therefore it follows that in a sense
health comes from health and house from house, that with matter from that
without matter; for the medical art and the building art are the form of health
and of the house, and when I speak of substance without matter I mean the
essence.
Of the productions or processes one part is
called thinking and the other making, – that which proceeds from the
starting-point and the form is thinking, and that which proceeds from the final
step of the thinking is making. And each of the other, intermediate, things is
produced in the same way. I mean, for instance, if the subject is to be healthy
his bodily state must be made uniform. What then does being made uniform imply?
This or that. And this depends on his being made warm. What does this imply?
Something else. And this something is present potentially; and what is present
potentially is already in the physician’s power.
The active principle then and the starting
point for the process of becoming healthy is, if it happens by art, the form in
the soul, and if spontaneously, it is that, whatever it is, which starts the
making, for the man who makes by art, as in healing the starting-point is
perhaps the production of warmth (and this the physician produces by rubbing).
Warmth in the body, then, is either a part of health or is followed (either
directly or through several intermediate steps) by something similar which is a
part of health; and this, viz. that which produces the part of health, is the
limiting-point – and so too with a house (the stones are the limiting-point
here) and in all other cases. Therefore, as the saying goes, it is impossible
that anything should be produced if there were nothing existing before.
Obviously then some part of the result will pre-exist of necessity; for the
matter is a part; for this is present in the process and it is this that becomes
something. But is the matter an element even in the formula? We certainly
describe in both ways what brazen circles are; we describe both the matter by
saying it is brass, and the form by saying that it is such and such a figure;
and figure is the proximate genus in which it is placed. The brazen circle,
then, has its matter in its formula.
As for that out of which as matter they are
produced, some things are said, when they have been produced, to be not that but
‘thaten’; e.g. the statue is not gold but golden. And a healthy man is not said
to be that from which he has come. The reason is that though a thing comes both
from its privation and from its substratum, which we call its matter (e.g. what
becomes healthy is both a man and an invalid), it is said to come rather from
its privation (e.g. it is from an invalid rather than from a man that a healthy
subject is produced). And so the healthy subject is not said to he an invalid,
but to be a man, and the man is said to be healthy. But as for the things whose
privation is obscure and nameless, e.g. in brass the privation of a particular
shape or in bricks and timber the privation of arrangement as a house, the thing
is thought to be produced from these materials, as in the former case the
healthy man is produced from an invalid. And so, as there also a thing is not
said to be that from which it comes, here the statue is not said to be wood but
is said by a verbal change to be wooden, not brass but brazen, not gold but
golden, and the house is said to be not bricks but bricken (though we should not
say without qualification, if we looked at the matter carefully, even that a
statue is produced from wood or a house from bricks, because coming to be
implies change in that from which a thing comes to be, and not permanence). It
is for this reason, then, that we use this way of
speaking.
8
Since anything which is produced is produced by
something (and this I call the starting-point of the production), and from
something (and let this be taken to be not the privation but the matter; for the
meaning we attach to this has already been explained), and since something is
produced (and this is either a sphere or a circle or whatever else it may chance
to be), just as we do not make the substratum (the brass), so we do not make the
sphere, except incidentally, because the brazen sphere is a sphere and we make
the forme. For to make a ‘this’ is to make a ‘this’ out of the substratum in the
full sense of the word. (I mean that to make the brass round is not to make the
round or the sphere, but something else, i.e. to produce this form in something
different from itself. For if we make the form, we must make it out of something
else; for this was assumed. E.g. we make a brazen sphere; and that in the sense
that out of this, which is brass, we make this other, which is a sphere.) If,
then, we also make the substratum itself, clearly we shall make it in the same
way, and the processes of making will regress to infinity. Obviously then the
form also, or whatever we ought to call the shape present in the sensible thing,
is not produced, nor is there any production of it, nor is the essence produced;
for this is that which is made to be in something else either by art or by
nature or by some faculty. But that there is a brazen sphere, this we make. For
we make it out of brass and the sphere; we bring the form into this particular
matter, and the result is a brazen sphere. But if the essence of sphere in
general is to be produced, something must be produced out of something. For the
product will always have to be divisible, and one part must be this and another
that; I mean the one must be matter and the other form. If, then, a sphere is
‘the figure whose circumference is at all points equidistant from the centre’,
part of this will be the medium in which the thing made will be, and part will
be in that medium, and the whole will be the thing produced, which corresponds
to the brazen sphere. It is obvious, then, from what has been said, that that
which is spoken of as form or substance is not produced, but the concrete thing
which gets its name from this is produced, and that in everything which is
generated matter is present, and one part of the thing is matter and the other
form.
Is there, then, a sphere apart from the
individual spheres or a house apart from the bricks? Rather we may say that no
‘this’ would ever have been coming to be, if this had been so, but that the
‘form’ means the ‘such’, and is not a ‘this’ – a definite thing; but the artist
makes, or the father begets, a ‘such’ out of a ‘this’; and when it has been
begotten, it is a ‘this such’. And the whole ‘this’, Callias or Socrates, is
analogous to ‘this brazen sphere’, but man and animal to ‘brazen sphere’ in
general. Obviously, then, the cause which consists of the Forms (taken in the
sense in which some maintain the existence of the Forms, i.e. if they are
something apart from the individuals) is useless, at least with regard to
comings-to-be and to substances; and the Forms need not, for this reason at
least, be self-subsistent substances. In some cases indeed it is even obvious
that the begetter is of the same kind as the begotten (not, however, the same
nor one in number, but in form), i.e. in the case of natural products (for man
begets man), unless something happens contrary to nature, e.g. the production of
a mule by a horse. (And even these cases are similar; for that which would be
found to be common to horse and ass, the genus next above them, has not received
a name, but it would doubtless be both in fact something like a mule.)
Obviously, therefore, it is quite unnecessary to set up a Form as a pattern (for
we should have looked for Forms in these cases if in any; for these are
substances if anything is so); the begetter is adequate to the making of the
product and to the causing of the form in the matter. And when we have the
whole, such and such a form in this flesh and in these bones, this is Callias or
Socrates; and they are different in virtue of their matter (for that is
different), but the same in form; for their form is
indivisible.
9
The question might be raised, why some things
are produced spontaneously as well as by art, e.g. health, while others are not,
e.g. a house. The reason is that in some cases the matter which governs the
production in the making and producing of any work of art, and in which a part
of the product is present, – some matter is such as to be set in motion by
itself and some is not of this nature, and of the former kind some can move
itself in the particular way required, while other matter is incapable of this;
for many things can be set in motion by themselves but not in some particular
way, e.g. that of dancing. The things, then, whose matter is of this sort, e.g.
stones, cannot be moved in the particular way required, except by something
else, but in another way they can move themselves – and so it is with fire.
Therefore some things will not exist apart from some one who has the art of
making them, while others will; for motion will be started by these things which
have not the art but can themselves be moved by other things which have not the
art or with a motion starting from a part of the product.
And it is clear also from what has been said
that in a sense every product of art is produced from a thing which shares its
name (as natural products are produced), or from a part of itself which shares
its name (e.g. the house is produced from a house, qua produced by reason; for
the art of building is the form of the house), or from something which contains
a art of it, – if we exclude things produced by accident; for the cause of the
thing’s producing the product directly per se is a part of the product. The heat
in the movement caused heat in the body, and this is either health, or a part of
health, or is followed by a part of health or by health itself. And so it is
said to cause health, because it causes that to which health attaches as a
consequence.
Therefore, as in syllogisms, substance is the
starting-point of everything. It is from ‘what a thing is’ that syllogisms
start; and from it also we now find processes of production to
start.
Things which are formed by nature are in the
same case as these products of art. For the seed is productive in the same way
as the things that work by art; for it has the form potentially, and that from
which the seed comes has in a sense the same name as the offspring only in a
sense, for we must not expect parent and offspring always to have exactly the
same name, as in the production of ‘human being’ from ‘human’ for a ‘woman’ also
can be produced by a ‘man’ – unless the offspring be an imperfect form; which is
the reason why the parent of a mule is not a mule. The natural things which
(like the artificial objects previously considered) can be produced
spontaneously are those whose matter can be moved even by itself in the way in
which the seed usually moves it; those things which have not such matter cannot
be produced except from the parent animals themselves.
But not only regarding substance does our
argument prove that its form does not come to be, but the argument applies to
all the primary classes alike, i.e. quantity, quality, and the other categories.
For as the brazen sphere comes to be, but not the sphere nor the brass, and so
too in the case of brass itself, if it comes to be, it is its concrete unity
that comes to be (for the matter and the form must always exist before), so is
it both in the case of substance and in that of quality and quantity and the
other categories likewise; for the quality does not come to be, but the wood of
that quality, and the quantity does not come to be, but the wood or the animal
of that size. But we may learn from these instances a peculiarity of substance,
that there must exist beforehand in complete reality another substance which
produces it, e.g. an animal if an animal is produced; but it is not necessary
that a quality or quantity should pre-exist otherwise than
potentially.
10
Since a definition is a formula, and every
formula has parts, and as the formula is to the thing, so is the part of the
formula to the part of the thing, the question is already being asked whether
the formula of the parts must be present in the formula of the whole or not. For
in some cases the formulae of the parts are seen to be present, and in some not.
The formula of the circle does not include that of the segments, but that of the
syllable includes that of the letters; yet the circle is divided into segments
as the syllable is into letters. – And further if the parts are prior to the
whole, and the acute angle is a part of the right angle and the finger a part of
the animal, the acute angle will be prior to the right angle and finger to the
man. But the latter are thought to be prior; for in formula the parts are
explained by reference to them, and in respect also of the power of existing
apart from each other the wholes are prior to the parts.
Perhaps we should rather say that ‘part’ is
used in several senses. One of these is ‘that which measures another thing in
respect of quantity’. But let this sense be set aside; let us inquire about the
parts of which substance consists. If then matter is one thing, form another,
the compound of these a third, and both the matter and the form and the compound
are substance even the matter is in a sense called part of a thing, while in a
sense it is not, but only the elements of which the formula of the form
consists. E.g. of concavity flesh (for this is the matter in which it is
produced) is not a part, but of snubness it is a part; and the bronze is a part
of the concrete statue, but not of the statue when this is spoken of in the
sense of the form. (For the form, or the thing as having form, should be said to
be the thing, but the material element by itself must never be said to be so.)
And so the formula of the circle does not include that of the segments, but the
formula of the syllable includes that of the letters; for the letters are parts
of the formula of the form, and not matter, but the segments are parts in the
sense of matter on which the form supervenes; yet they are nearer the form than
the bronze is when roundness is produced in bronze. But in a sense not even
every kind of letter will be present in the formula of the syllable, e.g.
particular waxen letters or the letters as movements in the air; for in these
also we have already something that is part of the syllable only in the sense
that it is its perceptible matter. For even if the line when divided passes away
into its halves, or the man into bones and muscles and flesh, it does not follow
that they are composed of these as parts of their essence, but rather as matter;
and these are parts of the concrete thing, but not also of the form, i.e. of
that to which the formula refers; wherefore also they are not present in the
formulae. In one kind of formula, then, the formula of such parts will be
present, but in another it must not be present, where the formula does not refer
to the concrete object. For it is for this reason that some things have as their
constituent principles parts into which they pass away, while some have not.
Those things which are the form and the matter taken together, e.g. the snub, or
the bronze circle, pass away into these materials, and the matter is a part of
them; but those things which do not involve matter but are without matter, and
whose formulae are formulae of the form only, do not pass away, – either not at
all or at any rate not in this way. Therefore these materials are principles and
parts of the concrete things, while of the form they are neither parts nor
principles. And therefore the clay statue is resolved into clay and the ball
into bronze and Callias into flesh and bones, and again the circle into its
segments; for there is a sense of ‘circle’ in which involves matter. For
‘circle’ is used ambiguously, meaning both the circle, unqualified, and the
individual circle, because there is no name peculiar to the
individuals.
The truth has indeed now been stated, but still
let us state it yet more clearly, taking up the question again. The parts of the
formula, into which the formula is divided, are prior to it, either all or some
of them. The formula of the right angle, however, does not include the formula
of the acute, but the formula of the acute includes that of the right angle; for
he who defines the acute uses the right angle; for the acute is ‘less than a
right angle’. The circle and the semicircle also are in a like relation; for the
semicircle is defined by the circle; and so is the finger by the whole body, for
a finger is ‘such and such a part of a man’. Therefore the parts which are of
the nature of matter, and into which as its matter a thing is divided, are
posterior; but those which are of the nature of parts of the formula, and of the
substance according to its formula, are prior, either all or some of them. And
since the soul of animals (for this is the substance of a living being) is their
substance according to the formula, i.e. the form and the essence of a body of a
certain kind (at least we shall define each part, if we define it well, not
without reference to its function, and this cannot belong to it without
perception), so that the parts of soul are prior, either all or some of them, to
the concrete ‘animal’, and so too with each individual animal; and the body and
parts are posterior to this, the essential substance, and it is not the
substance but the concrete thing that is divided into these parts as its matter:
– this being so, to the concrete thing these are in a sense prior, but in a
sense they are not. For they cannot even exist if severed from the whole; for it
is not a finger in any and every state that is the finger of a living thing, but
a dead finger is a finger only in name. Some parts are neither prior nor
posterior to the whole, i.e. those which are dominant and in which the formula,
i.e. the essential substance, is immediately present, e.g. perhaps the heart or
the brain; for it does not matter in the least which of the two has this
quality. But man and horse and terms which are thus applied to individuals, but
universally, are not substance but something composed of this particular formula
and this particular matter treated as universal; and as regards the individual,
Socrates already includes in him ultimate individual matter; and similarly in
all other cases. ‘A part’ may be a part either of the form (i.e. of the
essence), or of the compound of the form and the matter, or of the matter
itself. But only the parts of the form are parts of the formula, and the formula
is of the universal; for ‘being a circle’ is the same as the circle, and ‘being
a soul’ the same as the soul. But when we come to the concrete thing, e.g. this
circle, i.e. one of the individual circles, whether perceptible or intelligible
(I mean by intelligible circles the mathematical, and by perceptible circles
those of bronze and of wood), – of these there is no definition, but they are
known by the aid of intuitive thinking or of perception; and when they pass out
of this complete realization it is not clear whether they exist or not; but they
are always stated and recognized by means of the universal formula. But matter
is unknowable in itself. And some matter is perceptible and some intelligible,
perceptible matter being for instance bronze and wood and all matter that is
changeable, and intelligible matter being that which is present in perceptible
things not qua perceptible, i.e. the objects of
mathematics.
We have stated, then, how matters stand with
regard to whole and part, and their priority and posteriority. But when any one
asks whether the right angle and the circle and the animal are prior, or the
things into which they are divided and of which they consist, i.e. the parts, we
must meet the inquiry by saying that the question cannot be answered simply. For
if even bare soul is the animal or the living thing, or the soul of each
individual is the individual itself, and ‘being a circle’ is the circle, and
‘being a right angle’ and the essence of the right angle is the right angle,
then the whole in one sense must be called posterior to the art in one sense,
i.e. to the parts included in the formula and to the parts of the individual
right angle (for both the material right angle which is made of bronze, and that
which is formed by individual lines, are posterior to their parts); while the
immaterial right angle is posterior to the parts included in the formula, but
prior to those included in the particular instance, and the question must not be
answered simply. If, however, the soul is something different and is not
identical with the animal, even so some parts must, as we have maintained, be
called prior and others must not.
11
Another question is naturally raised, viz. what
sort of parts belong to the form and what sort not to the form, but to the
concrete thing. Yet if this is not plain it is not possible to define any thing;
for definition is of the universal and of the form. If then it is not evident
what sort of parts are of the nature of matter and what sort are not, neither
will the formula of the thing be evident. In the case of things which are found
to occur in specifically different materials, as a circle may exist in bronze or
stone or wood, it seems plain that these, the bronze or the stone, are no part
of the essence of the circle, since it is found apart from them. Of things which
are not seen to exist apart, there is no reason why the same may not be true,
just as if all circles that had ever been seen were of bronze; for none the less
the bronze would be no part of the form; but it is hard to eliminate it in
thought. E.g. the form of man is always found in flesh and bones and parts of
this kind; are these then also parts of the form and the formula? No, they are
matter; but because man is not found also in other matters we are unable to
perform the abstraction.
Since this is thought to be possible, but it is
not clear when it is the case, some people already raise the question even in
the case of the circle and the triangle, thinking that it is not right to define
these by reference to lines and to the continuous, but that all these are to the
circle or the triangle as flesh and bones are to man, and bronze or stone to the
statue; and they reduce all things to numbers, and they say the formula of
‘line’ is that of ‘two’. And of those who assert the Ideas some make ‘two’ the
line-itself, and others make it the Form of the line; for in some cases they say
the Form and that of which it is the Form are the same, e.g. ‘two’ and the Form
of two; but in the case of ‘line’ they say this is no longer
so.
It follows then that there is one Form for many
things whose form is evidently different (a conclusion which confronted the
Pythagoreans also); and it is possible to make one thing the Form-itself of all,
and to hold that the others are not Forms; but thus all things will be
one.
We have pointed out, then, that the question of
definitions contains some difficulty, and why this is so. And so to reduce all
things thus to Forms and to eliminate the matter is useless labour; for some
things surely are a particular form in a particular matter, or particular things
in a particular state. And the comparison which Socrates the younger used to
make in the case of ‘animal’ is not sound; for it leads away from the truth, and
makes one suppose that man can possibly exist without his parts, as the circle
can without the bronze. But the case is not similar; for an animal is something
perceptible, and it is not possible to define it without reference to movement –
nor, therefore, without reference to the parts’ being in a certain state. For it
is not a hand in any and every state that is a part of man, but only when it can
fulfil its work, and therefore only when it is alive; if it is not alive it is
not a part.
Regarding the objects of mathematics, why are
the formulae of the parts not parts of the formulae of the wholes; e.g. why are
not the semicircles included in the formula of the circle? It cannot be said,
‘because these parts are perceptible things’; for they are not. But perhaps this
makes no difference; for even some things which are not perceptible must have
matter; indeed there is some matter in everything which is not an essence and a
bare form but a ‘this’. The semicircles, then, will not be parts of the
universal circle, but will be parts of the individual circles, as has been said
before; for while one kind of matter is perceptible, there is another which is
intelligible.
It is clear also that the soul is the primary
substance and the body is matter, and man or animal is the compound of both
taken universally; and ‘Socrates’ or ‘Coriscus’, if even the soul of Socrates
may be called Socrates, has two meanings (for some mean by such a term the soul,
and others mean the concrete thing), but if ‘Socrates’ or ‘Coriscus’ means
simply this particular soul and this particular body, the individual is
analogous to the universal in its composition.
Whether there is, apart from the matter of such
substances, another kind of matter, and one should look for some substance other
than these, e.g. numbers or something of the sort, must be considered later. For
it is for the sake of this that we are trying to determine the nature of
perceptible substances as well, since in a sense the inquiry about perceptible
substances is the work of physics, i.e. of second philosophy; for the physicist
must come to know not only about the matter, but also about the substance
expressed in the formula, and even more than about the other. And in the case of
definitions, how the elements in the formula are parts of the definition, and
why the definition is one formula (for clearly the thing is one, but in virtue
of what is the thing one, although it has parts?), – this must be considered
later.
What the essence is and in what sense it is
independent, has been stated universally in a way which is true of every case,
and also why the formula of the essence of some things contains the parts of the
thing defined, while that of others does not. And we have stated that in the
formula of the substance the material parts will not be present (for they are
not even parts of the substance in that sense, but of the concrete substance;
but of this there is in a sense a formula, and in a sense there is not; for
there is no formula of it with its matter, for this is indefinite, but there is
a formula of it with reference to its primary substance – e.g. in the case of
man the formula of the soul – , for the substance is the indwelling form, from
which and the matter the so-called concrete substance is derived; e.g. concavity
is a form of this sort, for from this and the nose arise ‘snub nose’ and
‘snubness’); but in the concrete substance, e.g. a snub nose or Callias, the
matter also will be present. And we have stated that the essence and the thing
itself are in some cases the same; ie. in the case of primary substances, e.g.
curvature and the essence of curvature if this is primary. (By a ‘primary’
substance I mean one which does not imply the presence of something in something
else, i.e. in something that underlies it which acts as matter.) But things
which are of the nature of matter, or of wholes that include matter, are not the
same as their essences, nor are accidental unities like that of ‘Socrates’ and
‘musical’; for these are the same only by accident.
12
Now let us treat first of definition, in so far
as we have not treated of it in the Analytics; for the problem stated in them is
useful for our inquiries concerning substance. I mean this problem: – wherein
can consist the unity of that, the formula of which we call a definition, as for
instance, in the case of man, ‘two-footed animal’; for let this be the formula
of man. Why, then, is this one, and not many, viz. ‘animal’ and ‘two-footed’?
For in the case of ‘man’ and ‘pale’ there is a plurality when one term does not
belong to the other, but a unity when it does belong and the subject, man, has a
certain attribute; for then a unity is produced and we have ‘the pale man’. In
the present case, on the other hand, one does not share in the other; the genus
is not thought to share in its differentiae (for then the same thing would share
in contraries; for the differentiae by which the genus is divided are contrary).
And even if the genus does share in them, the same argument applies, since the
differentiae present in man are many, e.g. endowed with feet, two-footed,
featherless. Why are these one and not many? Not because they are present in one
thing; for on this principle a unity can be made out of all the attributes of a
thing. But surely all the attributes in the definition must be one; for the
definition is a single formula and a formula of substance, so that it must be a
formula of some one thing; for substance means a ‘one’ and a ‘this’, as we
maintain.
We must first inquire about definitions reached
by the method of divisions. There is nothing in the definition except the
first-named and the differentiae. The other genera are the first genus and along
with this the differentiae that are taken with it, e.g. the first may be
‘animal’, the next ‘animal which is two-footed’, and again ‘animal which is
two-footed and featherless’, and similarly if the definition includes more
terms. And in general it makes no difference whether it includes many or few
terms, – nor, therefore, whether it includes few or simply two; and of the two
the one is differentia and the other genus; e.g. in ‘two-footed animal’ ‘animal’
is genus, and the other is differentia.
If then the genus absolutely does not exist
apart from the species-of-a-genus, or if it exists but exists as matter (for the
voice is genus and matter, but its differentiae make the species, i.e. the
letters, out of it), clearly the definition is the formula which comprises the
differentiae.
But it is also necessary that the division be
by the differentia of the diferentia; e.g. ‘endowed with feet’ is a differentia
of ‘animal’; again the differentia of ‘animal endowed with feet’ must be of it
qua endowed with feet. Therefore we must not say, if we are to speak rightly,
that of that which is endowed with feet one part has feathers and one is
featherless (if we do this we do it through incapacity); we must divide it only
into cloven-footed and not cloven; for these are differentiae in the foot;
cloven-footedness is a form of footedness. And the process wants always to go on
so till it reaches the species that contain no differences. And then there will
be as many kinds of foot as there are differentiae, and the kinds of animals
endowed with feet will be equal in number to the differentiae. If then this is
so, clearly the last differentia will be the substance of the thing and its
definition, since it is not right to state the same things more than once in our
definitions; for it is superfluous. And this does happen; for when we say
‘animal endowed with feet and two-footed’ we have said nothing other than
‘animal having feet, having two feet’; and if we divide this by the proper
division, we shall be saying the same thing more than once – as many times as
there are differentiae.
If then a differentia of a differentia be taken
at each step, one differentia – the last – will be the form and the substance;
but if we divide according to accidental qualities, e.g. if we were to divide
that which is endowed with feet into the white and the black, there will be as
many differentiae as there are cuts. Therefore it is plain that the definition
is the formula which contains the differentiae, or, according to the right
method, the last of these. This would be evident, if we were to change the order
of such definitions, e.g. of that of man, saying ‘animal which is two-footed and
endowed with feet’; for ‘endowed with feet’ is superfluous when ‘two-footed’ has
been said. But there is no order in the substance; for how are we to think the
one element posterior and the other prior? Regarding the definitions, then,
which are reached by the method of divisions, let this suffice as our first
attempt at stating their nature.
13
Let us return to the subject of our inquiry,
which is substance. As the substratum and the essence and the compound of these
are called substance, so also is the universal. About two of these we have
spoken; both about the essence and about the substratum, of which we have said
that it underlies in two senses, either being a ‘this’ – which is the way in
which an animal underlies its attributes – or as the matter underlies the
complete reality. The universal also is thought by some to be in the fullest
sense a cause, and a principle; therefore let us attack the discussion of this
point also. For it seems impossible that any universal term should be the name
of a substance. For firstly the substance of each thing is that which is
peculiar to it, which does not belong to anything else; but the universal is
common, since that is called universal which is such as to belong to more than
one thing. Of which individual then will this be the substance? Either of all or
of none; but it cannot be the substance of all. And if it is to be the substance
of one, this one will be the others also; for things whose substance is one and
whose essence is one are themselves also one.
Further, substance means that which is not
predicable of a subject, but the universal is predicable of some subject
always.
But perhaps the universal, while it cannot be
substance in the way in which the essence is so, can be present in this; e.g.
‘animal’ can be present in ‘man’ and ‘horse’. Then clearly it is a formula of
the essence. And it makes no difference even if it is not a formula of
everything that is in the substance; for none the less the universal will be the
substance of something, as ‘man’ is the substance of the individual man in whom
it is present, so that the same result will follow once more; for the universal,
e.g. ‘animal’, will be the substance of that in which it is present as something
peculiar to it. And further it is impossible and absurd that the ‘this’, i.e.
the substance, if it consists of parts, should not consist of substances nor of
what is a ‘this’, but of quality; for that which is not substance, i.e. the
quality, will then be prior to substance and to the ‘this’. Which is impossible;
for neither in formula nor in time nor in coming to be can the modifications be
prior to the substance; for then they will also be separable from it. Further,
Socrates will contain a substance present in a substance, so that this will be
the substance of two things. And in general it follows, if man and such things
are substance, that none of the elements in their formulae is the substance of
anything, nor does it exist apart from the species or in anything else; I mean,
for instance, that no ‘animal’ exists apart from the particular kinds of animal,
nor does any other of the elements present in formulae exist
apart.
If, then, we view the matter from these
standpoints, it is plain that no universal attribute is a substance, and this is
plain also from the fact that no common predicate indicates a ‘this’, but rather
a ‘such’. If not, many difficulties follow and especially the ‘third
man’.
The conclusion is evident also from the
following consideration. A substance cannot consist of substances present in it
in complete reality; for things that are thus in complete reality two are never
in complete reality one, though if they are potentially two, they can be one
(e.g. the double line consists of two halves – potentially; for the complete
realization of the halves divides them from one another); therefore if the
substance is one, it will not consist of substances present in it and present in
this way, which Democritus describes rightly; he says one thing cannot be made
out of two nor two out of one; for he identifies substances with his indivisible
magnitudes. It is clear therefore that the same will hold good of number, if
number is a synthesis of units, as is said by some; for two is either not one,
or there is no unit present in it in complete reality. But our result involves a
difficulty. If no substance can consist of universals because a universal
indicates a ‘such’, not a ‘this’, and if no substance can be composed of
substances existing in complete reality, every substance would be incomposite,
so that there would not even be a formula of any substance. But it is thought by
all and was stated long ago that it is either only, or primarily, substance that
can defined; yet now it seems that not even substance can. There cannot, then,
be a definition of anything; or in a sense there can be, and in a sense there
cannot. And what we are saying will be plainer from what
follows.
14
It is clear also from these very facts what
consequence confronts those who say the Ideas are substances capable of separate
existence, and at the same time make the Form consist of the genus and the
differentiae. For if the Forms exist and ‘animal’ is present in ‘man’ and
‘horse’, it is either one and the same in number, or different. (In formula it
is clearly one; for he who states the formula will go through the formula in
either case.) If then there is a ‘man-in-himself’ who is a ‘this’ and exists
apart, the parts also of which he consists, e.g. ‘animal’ and ‘two-footed’, must
indicate ‘thises’, and be capable of separate existence, and substances;
therefore ‘animal’, as well as ‘man’, must be of this
sort.
Now (1) if the ‘animal’ in ‘the horse’ and in
‘man’ is one and the same, as you are with yourself, (a) how will the one in
things that exist apart be one, and how will this ‘animal’ escape being divided
even from itself?
Further, (b) if it is to share in ‘two-footed’
and ‘many-footed’, an impossible conclusion follows; for contrary attributes
will belong at the same time to it although it is one and a ‘this’. If it is not
to share in them, what is the relation implied when one says the animal is
two-footed or possessed of feet? But perhaps the two things are ‘put together’
and are ‘in contact’, or are ‘mixed’. Yet all these expressions are
absurd.
But (2) suppose the Form to be different in
each species. Then there will be practically an infinite number of things whose
substance is animal’; for it is not by accident that ‘man’ has ‘animal’ for one
of its elements. Further, many things will be ‘animal-itself’. For (i) the
‘animal’ in each species will be the substance of the species; for it is after
nothing else that the species is called; if it were, that other would be an
element in ‘man’, i.e. would be the genus of man. And further, (ii) all the
elements of which ‘man’ is composed will be Ideas. None of them, then, will be
the Idea of one thing and the substance of another; this is impossible. The
‘animal’, then, present in each species of animals will be animal-itself.
Further, from what is this ‘animal’ in each species derived, and how will it be
derived from animal-itself? Or how can this ‘animal’, whose essence is simply
animality, exist apart from animal-itself?
Further, (3)in the case of sensible things both
these consequences and others still more absurd follow. If, then, these
consequences are impossible, clearly there are not Forms of sensible things in
the sense in which some maintain their existence.
15
Since substance is of two kinds, the concrete
thing and the formula (I mean that one kind of substance is the formula taken
with the matter, while another kind is the formula in its generality),
substances in the former sense are capable of destruction (for they are capable
also of generation), but there is no destruction of the formula in the sense
that it is ever in course of being destroyed (for there is no generation of it
either; the being of house is not generated, but only the being of this house),
but without generation and destruction formulae are and are not; for it has been
shown that no one begets nor makes these. For this reason, also, there is
neither definition of nor demonstration about sensible individual substances,
because they have matter whose nature is such that they are capable both of
being and of not being; for which reason all the individual instances of them
are destructible. If then demonstration is of necessary truths and definition is
a scientific process, and if, just as knowledge cannot be sometimes knowledge
and sometimes ignorance, but the state which varies thus is opinion, so too
demonstration and definition cannot vary thus, but it is opinion that deals with
that which can be otherwise than as it is, clearly there can neither be
definition of nor demonstration about sensible individuals. For perishing things
are obscure to those who have the relevant knowledge, when they have passed from
our perception; and though the formulae remain in the soul unchanged, there will
no longer be either definition or demonstration. And so when one of the
definition-mongers defines any individual, he must recognize that his definition
may always be overthrown; for it is not possible to define such
things.
Nor is it possible to define any Idea. For the
Idea is, as its supporters say, an individual, and can exist apart; and the
formula must consist of words; and he who defines must not invent a word (for it
would be unknown), but the established words are common to all the members of a
class; these then must apply to something besides the thing defined; e.g. if one
were defining you, he would say ‘an animal which is lean’ or ‘pale’, or
something else which will apply also to some one other than you. If any one were
to say that perhaps all the attributes taken apart may belong to many subjects,
but together they belong only to this one, we must reply first that they belong
also to both the elements; e.g. ‘two-footed animal’ belongs to animal and to the
two-footed. (And in the case of eternal entities this is even necessary, since
the elements are prior to and parts of the compound; nay more, they can also
exist apart, if ‘man’ can exist apart. For either neither or both can. If, then,
neither can, the genus will not exist apart from the various species; but if it
does, the differentia will also.) Secondly, we must reply that ‘animal’ and
‘two-footed’ are prior in being to ‘two-footed animal’; and things which are
prior to others are not destroyed when the others are.
Again, if the Ideas consist of Ideas (as they
must, since elements are simpler than the compound), it will be further
necessary that the elements also of which the Idea consists, e.g. ‘animal’ and
‘two-footed’, should be predicated of many subjects. If not, how will they come
to be known? For there will then be an Idea which cannot be predicated of more
subjects than one. But this is not thought possible – every Idea is thought to
be capable of being shared.
As has been said, then, the impossibility of
defining individuals escapes notice in the case of eternal things, especially
those which are unique, like the sun or the moon. For people err not only by
adding attributes whose removal the sun would survive, e.g. ‘going round the
earth’ or ‘night-hidden’ (for from their view it follows that if it stands still
or is visible, it will no longer be the sun; but it is strange if this is so;
for ‘the sun’ means a certain substance); but also by the mention of attributes
which can belong to another subject; e.g. if another thing with the stated
attributes comes into existence, clearly it will be a sun; the formula therefore
is general. But the sun was supposed to be an individual, like Cleon or
Socrates. After all, why does not one of the supporters of the Ideas produce a
definition of an Idea? It would become clear, if they tried, that what has now
been said is true.
16
Evidently even of the things that are thought
to be substances, most are only potencies, – both the parts of animals (for none
of them exists separately; and when they are separated, then too they exist, all
of them, merely as matter) and earth and fire and air; for none of them is a
unity, but as it were a mere heap, till they are worked up and some unity is
made out of them. One might most readily suppose the parts of living things and
the parts of the soul nearly related to them to turn out to be both, i.e.
existent in complete reality as well as in potency, because they have sources of
movement in something in their joints; for which reason some animals live when
divided. Yet all the parts must exist only potentially, when they are one and
continuous by nature, – not by force or by growing into one, for such a
phenomenon is an abnormality.
Since the term ‘unity’ is used like the term
‘being’, and the substance of that which is one is one, and things whose
substance is numerically one are numerically one, evidently neither unity nor
being can be the substance of things, just as being an element or a principle
cannot be the substance, but we ask what, then, the principle is, that we may
reduce the thing to something more knowable. Now of these concepts ‘being’ and
‘unity’ are more substantial than ‘principle’ or ‘element’ or ‘cause’, but not
even the former are substance, since in general nothing that is common is
substance; for substance does not belong to anything but to itself and to that
which has it, of which it is the substance. Further, that which is one cannot be
in many places at the same time, but that which is common is present in many
places at the same time; so that clearly no universal exists apart from its
individuals.
But those who say the Forms exist, in one
respect are right, in giving the Forms separate existence, if they are
substances; but in another respect they are not right, because they say the one
over many is a Form. The reason for their doing this is that they cannot declare
what are the substances of this sort, the imperishable substances which exist
apart from the individual and sensible substances. They make them, then, the
same in kind as the perishable things (for this kind of substance we know) –
’man-himself’ and ‘horse-itself’, adding to the sensible things the word
‘itself’. Yet even if we had not seen the stars, none the less, I suppose, would
they have been eternal substances apart from those which we knew; so that now
also if we do not know what non-sensible substances there are, yet it is
doubtless necessary that there should he some. – Clearly, then, no universal
term is the name of a substance, and no substance is composed of
substances.
17
Let us state what, i.e. what kind of thing,
substance should be said to be, taking once more another starting-point; for
perhaps from this we shall get a clear view also of that substance which exists
apart from sensible substances. Since, then, substance is a principle and a
cause, let us pursue it from this starting-point. The ‘why’ is always sought in
this form – ’why does one thing attach to some other?’ For to inquire why the
musical man is a musical man, is either to inquire – as we have said why the man
is musical, or it is something else. Now ‘why a thing is itself’ is a
meaningless inquiry (for (to give meaning to the question ‘why’) the fact or the
existence of the thing must already be evident – e.g. that the moon is eclipsed
– but the fact that a thing is itself is the single reason and the single cause
to be given in answer to all such questions as why the man is man, or the
musician musical’, unless one were to answer ‘because each thing is inseparable
from itself, and its being one just meant this’; this, however, is common to all
things and is a short and easy way with the question). But we can inquire why
man is an animal of such and such a nature. This, then, is plain, that we are
not inquiring why he who is a man is a man. We are inquiring, then, why
something is predicable of something (that it is predicable must be clear; for
if not, the inquiry is an inquiry into nothing). E.g. why does it thunder? This
is the same as ‘why is sound produced in the clouds?’ Thus the inquiry is about
the predication of one thing of another. And why are these things, i.e. bricks
and stones, a house? Plainly we are seeking the cause. And this is the essence
(to speak abstractly), which in some cases is the end, e.g. perhaps in the case
of a house or a bed, and in some cases is the first mover; for this also is a
cause. But while the efficient cause is sought in the case of genesis and
destruction, the final cause is sought in the case of being
also.
The object of the inquiry is most easily
overlooked where one term is not expressly predicated of another (e.g. when we
inquire ‘what man is’), because we do not distinguish and do not say definitely
that certain elements make up a certain whole. But we must articulate our
meaning before we begin to inquire; if not, the inquiry is on the border-line
between being a search for something and a search for nothing. Since we must
have the existence of the thing as something given, clearly the question is why
the matter is some definite thing; e.g. why are these materials a house? Because
that which was the essence of a house is present. And why is this individual
thing, or this body having this form, a man? Therefore what we seek is the
cause, i.e. the form, by reason of which the matter is some definite thing; and
this is the substance of the thing. Evidently, then, in the case of simple terms
no inquiry nor teaching is possible; our attitude towards such things is other
than that of inquiry.
Since that which is compounded out of something
so that the whole is one, not like a heap but like a syllable – now the syllable
is not its elements, ba is not the same as b and a, nor is flesh fire and earth
(for when these are separated the wholes, i.e. the flesh and the syllable, no
longer exist, but the elements of the syllable exist, and so do fire and earth);
the syllable, then, is something – not only its elements (the vowel and the
consonant) but also something else, and the flesh is not only fire and earth or
the hot and the cold, but also something else: – if, then, that something must
itself be either an element or composed of elements, (1) if it is an element the
same argument will again apply; for flesh will consist of this and fire and
earth and something still further, so that the process will go on to infinity.
But (2) if it is a compound, clearly it will be a compound not of one but of
more than one (or else that one will be the thing itself), so that again in this
case we can use the same argument as in the case of flesh or of the syllable.
But it would seem that this ‘other’ is something, and not an element, and that
it is the cause which makes this thing flesh and that a syllable. And similarly
in all other cases. And this is the substance of each thing (for this is the
primary cause of its being); and since, while some things are not substances, as
many as are substances are formed in accordance with a nature of their own and
by a process of nature, their substance would seem to be this kind of ‘nature’,
which is not an element but a principle. An element, on the other hand, is that
into which a thing is divided and which is present in it as matter; e.g. a and b
are the elements of the syllable.
1
We must reckon up the results arising from what has been said, and compute the sum of them, and put the finishing touch to our inquiry. We have said that the causes, principles, and elements of substances are the object of our search. And some substances are recognized by every one, but some have been advocated by particular schools. Those generally recognized are the natural substances, i.e. fire, earth, water, air, &c., the simple bodies; second plants and their parts, and animals and the parts of animals; and finally the physical universe and its parts; while some particular schools say that Forms and the objects of mathematics are substances. But there are arguments which lead to the conclusion that there are other substances, the essence and the substratum. Again, in another way the genus seems more substantial than the various spccies, and the universal than the particulars. And with the universal and the genus the Ideas are connected; it is in virtue of the same argument that they are thought to be substances. And since the essence is substance, and the definition is a formula of the essence, for this reason we have discussed definition and essential predication. Since the definition is a formula, and a formula has parts, we had to consider also with respect to the notion of ‘part’, what are parts of the substance and what are not, and whether the parts of the substance are also parts of the definition. Further, too, neither the universal nor the genus is a substance; we must inquire later into the Ideas and the objects of mathematics; for some say these are substances as well as the sensible substances.
But now let us resume the discussion of the
generally recognized substances. These are the sensible substances, and sensible
substances all have matter. The substratum is substance, and this is in one
sense the matter (and by matter I mean that which, not being a ‘this’ actually,
is potentially a ‘this’), and in another sense the formula or shape (that which
being a ‘this’ can be separately formulated), and thirdly the complex of these
two, which alone is generated and destroyed, and is, without qualification,
capable of separate existence; for of substances completely expressible in a
formula some are separable and some are separable and some are
not.
But clearly matter also is substance; for in
all the opposite changes that occur there is something which underlies the
changes, e.g. in respect of place that which is now here and again elsewhere,
and in respect of increase that which is now of one size and again less or
greater, and in respect of alteration that which is now healthy and again
diseased; and similarly in respect of substance there is something that is now
being generated and again being destroyed, and now underlies the process as a
‘this’ and again underlies it in respect of a privation of positive character.
And in this change the others are involved. But in either one or two of the
others this is not involved; for it is not necessary if a thing has matter for
change of place that it should also have matter for generation and
destruction.
The difference between becoming in the full
sense and becoming in a qualified sense has been stated in our physical
works.
2
Since the substance which exists as underlying
and as matter is generally recognized, and this that which exists potentially,
it remains for us to say what is the substance, in the sense of actuality, of
sensible things. Democritus seems to think there are three kinds of difference
between things; the underlying body, the matter, is one and the same, but they
differ either in rhythm, i.e. shape, or in turning, i.e. position, or in
inter-contact, i.e. order. But evidently there are many differences; for
instance, some things are characterized by the mode of composition of their
matter, e.g. the things formed by blending, such as honey-water; and others by
being bound together, e.g. bundle; and others by being glued together, e.g. a
book; and others by being nailed together, e.g. a casket; and others in more
than one of these ways; and others by position, e.g. threshold and lintel (for
these differ by being placed in a certain way); and others by time, e.g. dinner
and breakfast; and others by place, e.g. the winds; and others by the affections
proper to sensible things, e.g. hardness and softness, density and rarity,
dryness and wetness; and some things by some of these qualities, others by them
all, and in general some by excess and some by defect. Clearly, then, the word
‘is’ has just as many meanings; a thing is a threshold because it lies in such
and such a position, and its being means its lying in that position, while being
ice means having been solidified in such and such a way. And the being of some
things will be defined by all these qualities, because some parts of them are
mixed, others are blended, others are bound together, others are solidified, and
others use the other differentiae; e.g. the hand or the foot requires such
complex definition. We must grasp, then, the kinds of differentiae (for these
will be the principles of the being of things), e.g. the things characterized by
the more and the less, or by the dense and the rare, and by other such
qualities; for all these are forms of excess and defect. And anything that is
characterized by shape or by smoothness and roughness is characterized by the
straight and the curved. And for other things their being will mean their being
mixed, and their not being will mean the opposite.
It is clear, then, from these facts that, since
its substance is the cause of each thing’s being, we must seek in these
differentiae what is the cause of the being of each of these things. Now none of
these differentiae is substance, even when coupled with matter, yet it is what
is analogous to substance in each case; and as in substances that which is
predicated of the matter is the actuality itself, in all other definitions also
it is what most resembles full actuality. E.g. if we had to define a threshold,
we should say ‘wood or stone in such and such a position’, and a house we should
define as ‘bricks and timbers in such and such a position’,(or a purpose may
exist as well in some cases), and if we had to define ice we should say ‘water
frozen or solidified in such and such a way’, and harmony is ‘such and such a
blending of high and low’; and similarly in all other
cases.
Obviously, then, the actuality or the formula
is different when the matter is different; for in some cases it is the
composition, in others the mixing, and in others some other of the attributes we
have named. And so, of the people who go in for defining, those who define a
house as stones, bricks, and timbers are speaking of the potential house, for
these are the matter; but those who propose ‘a receptacle to shelter chattels
and living beings’, or something of the sort, speak of the actuality. Those who
combine both of these speak of the third kind of substance, which is composed of
matter and form (for the formula that gives the differentiae seems to be an
account of the form or actuality, while that which gives the components is
rather an account of the matter); and the same is true of the kind of
definitions which Archytas used to accept; they are accounts of the combined
form and matter. E.g. what is still weather? Absence of motion in a large
expanse of air; air is the matter, and absence of motion is the actuality and
substance. What is a calm? Smoothness of sea; the material substratum is the
sea, and the actuality or shape is smoothness. It is obvious then, from what has
been said, what sensible substance is and how it exists – one kind of it as
matter, another as form or actuality, while the third kind is that which is
composed of these two.
3
We must not fail to notice that sometimes it is
not clear whether a name means the composite substance, or the actuality or
form, e.g. whether ‘house’ is a sign for the composite thing, ‘a covering
consisting of bricks and stones laid thus and thus’, or for the actuality or
form, ‘a covering’, and whether a line is ‘twoness in length’ or ‘twoness’, and
whether an animal is soul in a body’ or ‘a soul’; for soul is the substance or
actuality of some body. ‘Animal’ might even be applied to both, not as something
definable by one formula, but as related to a single thing. But this question,
while important for another purpose, is of no importance for the inquiry into
sensible substance; for the essence certainly attaches to the form and the
actuality. For ‘soul’ and ‘to be soul’ are the same, but ‘to be man’ and ‘man’
are not the same, unless even the bare soul is to be called man; and thus on one
interpretation the thing is the same as its essence, and on another it is
not.
If we examine we find that the syllable does
not consist of the letters + juxtaposition, nor is the house bricks +
juxtaposition. And this is right; for the juxtaposition or mixing does not
consist of those things of which it is the juxtaposition or mixing. And the same
is true in all other cases; e.g. if the threshold is characterized by its
position, the position is not constituted by the threshold, but rather the
latter is constituted by the former. Nor is man animal + biped, but there must
be something besides these, if these are matter, – something which is neither an
element in the whole nor a compound, but is the substance; but this people
eliminate, and state only the matter. If, then, this is the cause of the thing’s
being, and if the cause of its being is its substance, they will not be stating
the substance itself.
(This, then, must either be eternal or it must
be destructible without being ever in course of being destroyed, and must have
come to be without ever being in course of coming to be. But it has been proved
and explained elsewhere that no one makes or begets the form, but it is the
individual that is made, i.e. the complex of form and matter that is generated.
Whether the substances of destructible things can exist apart, is not yet at all
clear; except that obviously this is impossible in some cases – in the case of
things which cannot exist apart from the individual instances, e.g. house or
utensil. Perhaps, indeed, neither these things themselves, nor any of the other
things which are not formed by nature, are substances at all; for one might say
that the nature in natural objects is the only substance to be found in
destructible things.)
Therefore the difficulty which used to be
raised by the school of Antisthenes and other such uneducated people has a
certain timeliness. They said that the ‘what’ cannot be defined (for the
definition so called is a ‘long rigmarole’) but of what sort a thing, e.g.
silver, is, they thought it possible actually to explain, not saying what it is,
but that it is like tin. Therefore one kind of substance can be defined and
formulated, i.e. the composite kind, whether it be perceptible or intelligible;
but the primary parts of which this consists cannot be defined, since a
definitory formula predicates something of something, and one part of the
definition must play the part of matter and the other that of
form.
It is also obvious that, if substances are in a
sense numbers, they are so in this sense and not, as some say, as numbers of
units. For a definition is a sort of number; for (1) it is divisible, and into
indivisible parts (for definitory formulae are not infinite), and number also is
of this nature. And (2) as, when one of the parts of which a number consists has
been taken from or added to the number, it is no longer the same number, but a
different one, even if it is the very smallest part that has been taken away or
added, so the definition and the essence will no longer remain when anything has
been taken away or added. And (3) the number must be something in virtue of
which it is one, and this these thinkers cannot state, what makes it one, if it
is one (for either it is not one but a sort of heap, or if it is, we ought to
say what it is that makes one out of many); and the definition is one, but
similarly they cannot say what makes it one. And this is a natural result; for
the same reason is applicable, and substance is one in the sense which we have
explained, and not, as some say, by being a sort of unit or point; each is a
complete reality and a definite nature. And (4) as number does not admit of the
more and the less, neither does substance, in the sense of form, but if any
substance does, it is only the substance which involves matter. Let this, then,
suffice for an account of the generation and destruction of so-called substances
in what sense it is possible and in what sense impossible – and of the reduction
of things to number.
4
Regarding material substance we must not forget
that even if all things come from the same first cause or have the same things
for their first causes, and if the same matter serves as starting-point for
their generation, yet there is a matter proper to each, e.g. for phlegm the
sweet or the fat, and for bile the bitter, or something else; though perhaps
these come from the same original matter. And there come to be several matters
for the same thing, when the one matter is matter for the other; e.g. phlegm
comes from the fat and from the sweet, if the fat comes from the sweet; and it
comes from bile by analysis of the bile into its ultimate matter. For one thing
comes from another in two senses, either because it will be found at a later
stage, or because it is produced if the other is analysed into its original
constituents. When the matter is one, different things may be produced owing to
difference in the moving cause; e.g. from wood may be made both a chest and a
bed. But some different things must have their matter different; e.g. a saw
could not be made of wood, nor is this in the power of the moving cause; for it
could not make a saw of wool or of wood. But if, as a matter of fact, the same
thing can be made of different material, clearly the art, i.e. the moving
principle, is the same; for if both the matter and the moving cause were
different, the product would be so too.
When one inquires into the cause of something,
one should, since ‘causes’ are spoken of in several senses, state all the
possible causes. what is the material cause of man? Shall we say ‘the menstrual
fluid’? What is moving cause? Shall we say ‘the seed’? The formal cause? His
essence. The final cause? His end. But perhaps the latter two are the same. – It
is the proximate causes we must state. What is the material cause? We must name
not fire or earth, but the matter peculiar to the thing.
Regarding the substances that are natural and
generable, if the causes are really these and of this number and we have to
learn the causes, we must inquire thus, if we are to inquire rightly. But in the
case of natural but eternal substances another account must be given. For
perhaps some have no matter, or not matter of this sort but only such as can be
moved in respect of place. Nor does matter belong to those things which exist by
nature but are not substances; their substratum is the substance. E.g what is
the cause of eclipse? What is its matter? There is none; the moon is that which
suffers eclipse. What is the moving cause which extinguished the light? The
earth. The final cause perhaps does not exist. The formal principle is the
definitory formula, but this is obscure if it does not include the cause. E.g.
what is eclipse? Deprivation of light. But if we add ‘by the earth’s coming in
between’, this is the formula which includes the cause. In the case of sleep it
is not clear what it is that proximately has this affection. Shall we say that
it is the animal? Yes, but the animal in virtue of what, i.e. what is the
proximate subject? The heart or some other part. Next, by what is it produced?
Next, what is the affection – that of the proximate subject, not of the whole
animal? Shall we say that it is immobility of such and such a kind? Yes, but to
what process in the proximate subject is this due?
5
Since some things are and are not, without
coming to be and ceasing to be, e.g. points, if they can be said to be, and in
general forms (for it is not ‘white’ comes to be, but the wood comes to be
white, if everything that comes to be comes from something and comes to be
something), not all contraries can come from one another, but it is in different
senses that a pale man comes from a dark man, and pale comes from dark. Nor has
everything matter, but only those things which come to be and change into one
another. Those things which, without ever being in course of changing, are or
are not, have no matter.
There is difficulty in the question how the
matter of each thing is related to its contrary states. E.g. if the body is
potentially healthy, and disease is contrary to health, is it potentially both
healthy and diseased? And is water potentially wine and vinegar? We answer that
it is the matter of one in virtue of its positive state and its form, and of the
other in virtue of the privation of its positive state and the corruption of it
contrary to its nature. It is also hard to say why wine is not said to be the
matter of vinegar nor potentially vinegar (though vinegar is produced from it),
and why a living man is not said to be potentially dead. In fact they are not,
but the corruptions in question are accidental, and it is the matter of the
animal that is itself in virtue of its corruption the potency and matter of a
corpse, and it is water that is the matter of vinegar. For the corpse comes from
the animal, and vinegar from wine, as night from day. And all the things which
change thus into one another must go back to their matter; e.g. if from a corpse
is produced an animal, the corpse first goes back to its matter, and only then
becomes an animal; and vinegar first goes back to water, and only then becomes
wine.
6
To return to the difficulty which has been
stated with respect both to definitions and to numbers, what is the cause of
their unity? In the case of all things which have several parts and in which the
totality is not, as it were, a mere heap, but the whole is something beside the
parts, there is a cause; for even in bodies contact is the cause of unity in
some cases, and in others viscosity or some other such quality. And a definition
is a set of words which is one not by being connected together, like the Iliad,
but by dealing with one object. – What then, is it that makes man one; why is he
one and not many, e.g. animal + biped, especially if there are, as some say, an
animal-itself and a biped-itself? Why are not those Forms themselves the man, so
that men would exist by participation not in man, nor in one Form, but in two,
animal and biped, and in general man would be not one but more than one thing,
animal and biped?
Clearly, then, if people proceed thus in their
usual manner of definition and speech, they cannot explain and solve the
difficulty. But if, as we say, one element is matter and another is form, and
one is potentially and the other actually, the question will no longer be
thought a difficulty. For this difficulty is the same as would arise if ‘round
bronze’ were the definition of ‘cloak’; for this word would be a sign of the
definitory formula, so that the question is, what is the cause of the unity of
‘round’ and ‘bronze’? The difficulty disappears, because the one is matter, the
other form. What, then, causes this – that which was potentially to be actually
– except, in the case of things which are generated, the agent? For there is no
other cause of the potential sphere’s becoming actually a sphere, but this was
the essence of either. Of matter some is intelligible, some perceptible, and in
a formula there is always an element of matter as well as one of actuality; e.g.
the circle is ‘a plane figure’. But of the things which have no matter, either
intelligible or perceptible, each is by its nature essentially a kind of unity,
as it is essentially a kind of being – individual substance, quality, or
quantity (and so neither ‘existent’ nor ‘one’ is present in their definitions),
and the essence of each of them is by its very nature a kind of unity as it is a
kind of being – and so none of these has any reason outside itself, for being
one, nor for being a kind of being; for each is by its nature a kind of being
and a kind of unity, not as being in the genus ‘being’ or ‘one’ nor in the sense
that being and unity can exist apart from particulars.
Owing to the difficulty about unity some speak
of ‘participation’, and raise the question, what is the cause of participation
and what is it to participate; and others speak of ‘communion’, as Lycophron
says knowledge is a communion of knowing with the soul; and others say life is a
‘composition’ or ‘connexion’ of soul with body. Yet the same account applies to
all cases; for being healthy, too, will on this showing be either a ‘communion’
or a ‘connexion’ or a ‘composition’ of soul and health, and the fact that the
bronze is a triangle will be a ‘composition’ of bronze and triangle, and the
fact that a thing is white will be a ‘composition’ of surface and whiteness. The
reason is that people look for a unifying formula, and a difference, between
potency and complete reality. But, as has been said, the proximate matter and
the form are one and the same thing, the one potentially, and the other
actually. Therefore it is like asking what in general is the cause of unity and
of a thing’s being one; for each thing is a unity, and the potential and the
actual are somehow one. Therefore there is no other cause here unless there is
something which caused the movement from potency into actuality. And all things
which have no matter are without qualification essentially
unities.
1
We have treated of that which is primarily and to which all the other categories of being are referred – i.e. of substance. For it is in virtue of the concept of substance that the others also are said to be – quantity and quality and the like; for all will be found to involve the concept of substance, as we said in the first part of our work. And since ‘being’ is in one way divided into individual thing, quality, and quantity, and is in another way distinguished in respect of potency and complete reality, and of function, let us now add a discussion of potency and complete reality. And first let us explain potency in the strictest sense, which is, however, not the most useful for our present purpose. For potency and actuality extend beyond the cases that involve a reference to motion. But when we have spoken of this first kind, we shall in our discussions of actuality’ explain the other kinds of potency as well.
We have pointed out elsewhere that ‘potency’
and the word ‘can’ have several senses. Of these we may neglect all the
potencies that are so called by an equivocation. For some are called so by
analogy, as in geometry we say one thing is or is not a ‘power’ of another by
virtue of the presence or absence of some relation between them. But all
potencies that conform to the same type are originative sources of some kind,
and are called potencies in reference to one primary kind of potency, which is
an originative source of change in another thing or in the thing itself qua
other. For one kind is a potency of being acted on, i.e. the originative source,
in the very thing acted on, of its being passively changed by another thing or
by itself qua other; and another kind is a state of insusceptibility to change
for the worse and to destruction by another thing or by the thing itself qua
other by virtue of an originative source of change. In all these definitions is
implied the formula if potency in the primary sense. – And again these so-called
potencies are potencies either of merely acting or being acted on, or of acting
or being acted on well, so that even in the formulae of the latter the formulae
of the prior kinds of potency are somehow implied.
Obviously, then, in a sense the potency of
acting and of being acted on is one (for a thing may be ‘capable’ either because
it can itself be acted on or because something else can be acted on by it), but
in a sense the potencies are different. For the one is in the thing acted on; it
is because it contains a certain originative source, and because even the matter
is an originative source, that the thing acted on is acted on, and one thing by
one, another by another; for that which is oily can be burnt, and that which
yields in a particular way can be crushed; and similarly in all other cases. But
the other potency is in the agent, e.g. heat and the art of building are
present, one in that which can produce heat and the other in the man who can
build. And so, in so far as a thing is an organic unity, it cannot be acted on
by itself; for it is one and not two different things. And ‘impotence’and
‘impotent’ stand for the privation which is contrary to potency of this sort, so
that every potency belongs to the same subject and refers to the same process as
a corresponding impotence. Privation has several senses; for it means (1) that
which has not a certain quality and (2) that which might naturally have it but
has not it, either (a) in general or (b) when it might naturally have it, and
either (a) in some particular way, e.g. when it has not it completely, or (b)
when it has not it at all. And in certain cases if things which naturally have a
quality lose it by violence, we say they have suffered
privation.
2
Since some such originative sources are present
in soulless things, and others in things possessed of soul, and in soul, and in
the rational part of the soul, clearly some potencies will, be non-rational and
some will be non-rational and some will be accompanied by a rational formula.
This is why all arts, i.e. all productive forms of knowledge, are potencies;
they are originative sources of change in another thing or in the artist himself
considered as other.
And each of those which are accompanied by a
rational formula is alike capable of contrary effects, but one non-rational
power produces one effect; e.g. the hot is capable only of heating, but the
medical art can produce both disease and health. The reason is that science is a
rational formula, and the same rational formula explains a thing and its
privation, only not in the same way; and in a sense it applies to both, but in a
sense it applies rather to the positive fact. Therefore such sciences must deal
with contraries, but with one in virtue of their own nature and with the other
not in virtue of their nature; for the rational formula applies to one object in
virtue of that object’s nature, and to the other, in a sense, accidentally. For
it is by denial and removal that it exhibits the contrary; for the contrary is
the primary privation, and this is the removal of the positive term. Now since
contraries do not occur in the same thing, but science is a potency which
depends on the possession of a rational formula, and the soul possesses an
originative source of movement; therefore, while the wholesome produces only
health and the calorific only heat and the frigorific only cold, the scientific
man produces both the contrary effects. For the rational formula is one which
applies to both, though not in the same way, and it is in a soul which possesses
an originative source of movement; so that the soul will start both processes
from the same originative source, having linked them up with the same thing. And
so the things whose potency is according to a rational formula act contrariwise
to the things whose potency is non-rational; for the products of the former are
included under one originative source, the rational
formula.
It is obvious also that the potency of merely
doing a thing or having it done to one is implied in that of doing it or having
it done well, but the latter is not always implied in the former: for he who
does a thing well must also do it, but he who does it merely need not also do it
well.
3
There are some who say, as the Megaric school
does, that a thing ‘can’ act only when it is acting, and when it is not acting
it ‘cannot’ act, e.g. that he who is not building cannot build, but only he who
is building, when he is building; and so in all other cases. It is not hard to
see the absurdities that attend this view.
For it is clear that on this view a man will
not be a builder unless he is building (for to be a builder is to be able to
build), and so with the other arts. If, then, it is impossible to have such arts
if one has not at some time learnt and acquired them, and it is then impossible
not to have them if one has not sometime lost them (either by forgetfulness or
by some accident or by time; for it cannot be by the destruction of the object,
for that lasts for ever), a man will not have the art when he has ceased to use
it, and yet he may immediately build again; how then will he have got the art?
And similarly with regard to lifeless things; nothing will be either cold or hot
or sweet or perceptible at all if people are not perceiving it; so that the
upholders of this view will have to maintain the doctrine of Protagoras. But,
indeed, nothing will even have perception if it is not perceiving, i.e.
exercising its perception. If, then, that is blind which has not sight though it
would naturally have it, when it would naturally have it and when it still
exists, the same people will be blind many times in the day – and deaf
too.
Again, if that which is deprived of potency is
incapable, that which is not happening will be incapable of happening; but he
who says of that which is incapable of happening either that it is or that it
will be will say what is untrue; for this is what incapacity meant. Therefore
these views do away with both movement and becoming. For that which stands will
always stand, and that which sits will always sit, since if it is sitting it
will not get up; for that which, as we are told, cannot get up will be incapable
of getting up. But we cannot say this, so that evidently potency and actuality
are different (but these views make potency and actuality the same, and so it is
no small thing they are seeking to annihilate), so that it is possible that a
thing may be capable of being and not he, and capable of not being and yet he,
and similarly with the other kinds of predicate; it may be capable of walking
and yet not walk, or capable of not walking and yet walk. And a thing is capable
of doing something if there will be nothing impossible in its having the
actuality of that of which it is said to have the capacity. I mean, for
instance, if a thing is capable of sitting and it is open to it to sit, there
will be nothing impossible in its actually sitting; and similarly if it is
capable of being moved or moving, or of standing or making to stand, or of being
or coming to be, or of not being or not coming to be.
The word ‘actuality’, which we connect with
‘complete reality’, has, in the main, been extended from movements to other
things; for actuality in the strict sense is thought to be identical with
movement. And so people do not assign movement to non-existent things, though
they do assign some other predicates. E.g. they say that non-existent things are
objects of thought and desire, but not that they are moved; and this because,
while ex hypothesi they do not actually exist, they would have to exist actually
if they were moved. For of non-existent things some exist potentially; but they
do not exist, because they do not exist in complete
reality.
4
If what we have described is identical with the
capable or convertible with it, evidently it cannot be true to say ‘this is
capable of being but will not be’, which would imply that the things incapable
of being would on this showing vanish. Suppose, for instance, that a man – one
who did not take account of that which is incapable of being – were to say that
the diagonal of the square is capable of being measured but will not be
measured, because a thing may well be capable of being or coming to be, and yet
not be or be about to be. But from the premisses this necessarily follows, that
if we actually supposed that which is not, but is capable of being, to be or to
have come to be, there will be nothing impossible in this; but the result will
be impossible, for the measuring of the diagonal is impossible. For the false
and the impossible are not the same; that you are standing now is false, but
that you should be standing is not impossible.
At the same time it is clear that if, when A is
real, B must be real, then, when A is possible, B also must be possible. For if
B need not be possible, there is nothing to prevent its not being possible. Now
let A be supposed possible. Then, when A was possible, we agreed that nothing
impossible followed if A were supposed to be real; and then B must of course be
real. But we supposed B to be impossible. Let it be impossible then. If, then, B
is impossible, A also must be so. But the first was supposed impossible;
therefore the second also is impossible. If, then, A is possible, B also will be
possible, if they were so related that if A,is real, B must be real. If, then, A
and B being thus related, B is not possible on this condition, and B will not be
related as was supposed. And if when A is possible, B must be possible, then if
A is real, B also must be real. For to say that B must be possible, if A is
possible, means this, that if A is real both at the time when and in the way in
which it was supposed capable of being real, B also must then and in that way be
real.
5
As all potencies are either innate, like the
senses, or come by practice, like the power of playing the flute, or by
learning, like artistic power, those which come by practice or by rational
formula we must acquire by previous exercise but this is not necessary with
those which are not of this nature and which imply
passivity.
Since that which is ‘capable’ is capable of
something and at some time in some way (with all the other qualifications which
must be present in the definition), and since some things can produce change
according to a rational formula and their potencies involve such a formula,
while other things are nonrational and their potencies are non-rational, and the
former potencies must be in a living thing, while the latter can be both in the
living and in the lifeless; as regards potencies of the latter kind, when the
agent and the patient meet in the way appropriate to the potency in question,
the one must act and the other be acted on, but with the former kind of potency
this is not necessary. For the nonrational potencies are all productive of one
effect each, but the rational produce contrary effects, so that if they produced
their effects necessarily they would produce contrary effects at the same time;
but this is impossible. There must, then, be something else that decides; I mean
by this, desire or will. For whichever of two things the animal desires
decisively, it will do, when it is present, and meets the passive object, in the
way appropriate to the potency in question. Therefore everything which has a
rational potency, when it desires that for which it has a potency and in the
circumstances in which it has the potency, must do this. And it has the potency
in question when the passive object is present and is in a certain state; if not
it will not be able to act. (To add the qualification ‘if nothing external
prevents it’ is not further necessary; for it has the potency on the terms on
which this is a potency of acting, and it is this not in all circumstances but
on certain conditions, among which will be the exclusion of external hindrances;
for these are barred by some of the positive qualifications.) And so even if one
has a rational wish, or an appetite, to do two things or contrary things at the
same time, one will not do them; for it is not on these terms that one has the
potency for them, nor is it a potency of doing both at the same time, since one
will do the things which it is a potency of doing, on the terms on which one has
the potency.
6
Since we have treated of the kind of potency
which is related to movement, let us discuss actuality – what, and what kind of
thing, actuality is. For in the course of our analysis it will also become
clear, with regard to the potential, that we not only ascribe potency to that
whose nature it is to move something else, or to be moved by something else,
either without qualification or in some particular way, but also use the word in
another sense, which is the reason of the inquiry in the course of which we have
discussed these previous senses also. Actuality, then, is the existence of a
thing not in the way which we express by ‘potentially’; we say that potentially,
for instance, a statue of Hermes is in the block of wood and the half-line is in
the whole, because it might be separated out, and we call even the man who is
not studying a man of science, if he is capable of studying; the thing that
stands in contrast to each of these exists actually. Our meaning can be seen in
the particular cases by induction, and we must not seek a definition of
everything but be content to grasp the analogy, that it is as that which is
building is to that which is capable of building, and the waking to the
sleeping, and that which is seeing to that which has its eyes shut but has
sight, and that which has been shaped out of the matter to the matter, and that
which has been wrought up to the unwrought. Let actuality be defined by one
member of this antithesis, and the potential by the other. But all things are
not said in the same sense to exist actually, but only by analogy – as A is in B
or to B, C is in D or to D; for some are as movement to potency, and the others
as substance to some sort of matter.
But also the infinite and the void and all
similar things are said to exist potentially and actually in a different sense
from that which applies to many other things, e.g. to that which sees or walks
or is seen. For of the latter class these predicates can at some time be also
truly asserted without qualification; for the seen is so called sometimes
because it is being seen, sometimes because it is capable of being seen. But the
infinite does not exist potentially in the sense that it will ever actually have
separate existence; it exists potentially only for knowledge. For the fact that
the process of dividing never comes to an end ensures that this activity exists
potentially, but not that the infinite exists separately.
Since of the actions which have a limit none is
an end but all are relative to the end, e.g. the removing of fat, or
fat-removal, and the bodily parts themselves when one is making them thin are in
movement in this way (i.e. without being already that at which the movement
aims), this is not an action or at least not a complete one (for it is not an
end); but that movement in which the end is present is an action. E.g. at the
same time we are seeing and have seen, are understanding and have understood,
are thinking and have thought (while it is not true that at the same time we are
learning and have learnt, or are being cured and have been cured). At the same
time we are living well and have lived well, and are happy and have been happy.
If not, the process would have had sometime to cease, as the process of making
thin ceases: but, as things are, it does not cease; we are living and have
lived. Of these processes, then, we must call the one set movements, and the
other actualities. For every movement is incomplete – making thin, learning,
walking, building; these are movements, and incomplete at that. For it is not
true that at the same time a thing is walking and has walked, or is building and
has built, or is coming to be and has come to be, or is being moved and has been
moved, but what is being moved is different from what has been moved, and what
is moving from what has moved. But it is the same thing that at the same time
has seen and is seeing, seeing, or is thinking and has thought. The latter sort
of process, then, I call an actuality, and the former a
movement.
7
What, and what kind of thing, the actual is,
may be taken as explained by these and similar considerations. But we must
distinguish when a thing exists potentially and when it does not; for it is not
at any and every time. E.g. is earth potentially a man? No – but rather when it
has already become seed, and perhaps not even then. It is just as it is with
being healed; not everything can be healed by the medical art or by luck, but
there is a certain kind of thing which is capable of it, and only this is
potentially healthy. And (1) the delimiting mark of that which as a result of
thought comes to exist in complete reality from having existed potentially is
that if the agent has willed it it comes to pass if nothing external hinders,
while the condition on the other side – viz. in that which is healed – is that
nothing in it hinders the result. It is on similar terms that we have what is
potentially a house; if nothing in the thing acted on – i.e. in the matter –
prevents it from becoming a house, and if there is nothing which must be added
or taken away or changed, this is potentially a house; and the same is true of
all other things the source of whose becoming is external. And (2) in the cases
in which the source of the becoming is in the very thing which comes to be, a
thing is potentially all those things which it will be of itself if nothing
external hinders it. E.g. the seed is not yet potentially a man; for it must be
deposited in something other than itself and undergo a change. But when through
its own motive principle it has already got such and such attributes, in this
state it is already potentially a man; while in the former state it needs
another motive principle, just as earth is not yet potentially a statue (for it
must first change in order to become brass.)
It seems that when we call a thing not
something else but ‘thaten’ – e.g. a casket is not ‘wood’ but ‘wooden’, and wood
is not ‘earth’ but ‘earthen’, and again earth will illustrate our point if it is
similarly not something else but ‘thaten’ – that other thing is always
potentially (in the full sense of that word) the thing which comes after it in
this series. E.g. a casket is not ‘earthen’ nor ‘earth’, but ‘wooden’; for this
is potentially a casket and this is the matter of a casket, wood in general of a
casket in general, and this particular wood of this particular casket. And if
there is a first thing, which is no longer, in reference to something else,
called ‘thaten’, this is prime matter; e.g. if earth is ‘airy’ and air is not
‘fire’ but ‘fiery’, fire is prime matter, which is not a ‘this’. For the subject
or substratum is differentiated by being a ‘this’ or not being one; i.e. the
substratum of modifications is, e.g. a man, i.e. a body and a soul, while the
modification is ‘musical’ or ‘pale’. (The subject is called, when music comes to
be present in it, not ‘music’ but ‘musical’, and the man is not ‘paleness’ but
‘pale’, and not ‘ambulation’ or ‘movement’ but ‘walking’ or ‘moving’, – which is
akin to the ‘thaten’.) Wherever this is so, then, the ultimate subject is a
substance; but when this is not so but the predicate is a form and a ‘this’, the
ultimate subject is matter and material substance. And it is only right that
‘thaten’ should be used with reference both to the matter and to the accidents;
for both are indeterminates.
We have stated, then, when a thing is to be
said to exist potentially and when it is not.
8
From our discussion of the various senses of
‘prior’, it is clear that actuality is prior to potency. And I mean by potency
not only that definite kind which is said to be a principle of change in another
thing or in the thing itself regarded as other, but in general every principle
of movement or of rest. For nature also is in the same genus as potency; for it
is a principle of movement – not, however, in something else but in the thing
itself qua itself. To all such potency, then, actuality is prior both in formula
and in substantiality; and in time it is prior in one sense, and in another
not.
(1) Clearly it is prior in formula; for that
which is in the primary sense potential is potential because it is possible for
it to become active; e.g. I mean by ‘capable of building’ that which can build,
and by ‘capable of seeing’ that which can see, and by ‘visible’ that which can
be seen. And the same account applies to all other cases, so that the formula
and the knowledge of the one must precede the knowledge of the
other.
(2) In time it is prior in this sense: the
actual which is identical in species though not in number with a potentially
existing thing is to it. I mean that to this particular man who now exists
actually and to the corn and to the seeing subject the matter and the seed and
that which is capable of seeing, which are potentially a man and corn and
seeing, but not yet actually so, are prior in time; but prior in time to these
are other actually existing things, from which they were produced. For from the
potentially existing the actually existing is always produced by an actually
existing thing, e.g. man from man, musician by musician; there is always a first
mover, and the mover already exists actually. We have said in our account of
substance that everything that is produced is something produced from something
and by something, and that the same in species as it.
This is why it is thought impossible to be a
builder if one has built nothing or a harper if one has never played the harp;
for he who learns to play the harp learns to play it by playing it, and all
other learners do similarly. And thence arose the sophistical quibble, that one
who does not possess a science will be doing that which is the object of the
science; for he who is learning it does not possess it. But since, of that which
is coming to be, some part must have come to be, and, of that which, in general,
is changing, some part must have changed (this is shown in the treatise on
movement), he who is learning must, it would seem, possess some part of the
science. But here too, then, it is clear that actuality is in this sense also,
viz. in order of generation and of time, prior to potency.
But (3) it is also prior in substantiality;
firstly, (a) because the things that are posterior in becoming are prior in form
and in substantiality (e.g. man is prior to boy and human being to seed; for the
one already has its form, and the other has not), and because everything that
comes to be moves towards a principle, i.e. an end (for that for the sake of
which a thing is, is its principle, and the becoming is for the sake of the
end), and the actuality is the end, and it is for the sake of this that the
potency is acquired. For animals do not see in order that they may have sight,
but they have sight that they may see. And similarly men have the art of
building that they may build, and theoretical science that they may theorize;
but they do not theorize that they may have theoretical science, except those
who are learning by practice; and these do not theorize except in a limited
sense, or because they have no need to theorize. Further, matter exists in a
potential state, just because it may come to its form; and when it exists
actually, then it is in its form. And the same holds good in all cases, even
those in which the end is a movement. And so, as teachers think they have
achieved their end when they have exhibited the pupil at work, nature does
likewise. For if this is not the case, we shall have Pauson’s Hermes over again,
since it will be hard to say about the knowledge, as about the figure in the
picture, whether it is within or without. For the action is the end, and the
actuality is the action. And so even the word ‘actuality’ is derived from
‘action’, and points to the complete reality.
And while in some cases the exercise is the
ultimate thing (e.g. in sight the ultimate thing is seeing, and no other product
besides this results from sight), but from some things a product follows (e.g.
from the art of building there results a house as well as the act of building),
yet none the less the act is in the former case the end and in the latter more
of an end than the potency is. For the act of building is realized in the thing
that is being built, and comes to be, and is, at the same time as the
house.
Where, then, the result is something apart from
the exercise, the actuality is in the thing that is being made, e.g. the act of
building is in the thing that is being built and that of weaving in the thing
that is being woven, and similarly in all other cases, and in general the
movement is in the thing that is being moved; but where there is no product
apart from the actuality, the actuality is present in the agents, e.g. the act
of seeing is in the seeing subject and that of theorizing in the theorizing
subject and the life is in the soul (and therefore well-being also; for it is a
certain kind of life).
Obviously, therefore, the substance or form is
actuality. According to this argument, then, it is obvious that actuality is
prior in substantial being to potency; and as we have said, one actuality always
precedes another in time right back to the actuality of the eternal prime
mover.
But (b) actuality is prior in a stricter sense
also; for eternal things are prior in substance to perishable things, and no
eternal thing exists potentially. The reason is this. Every potency is at one
and the same time a potency of the opposite; for, while that which is not
capable of being present in a subject cannot be present, everything that is
capable of being may possibly not be actual. That, then, which is capable of
being may either be or not be; the same thing, then, is capable both of being
and of not being. And that which is capable of not being may possibly not be;
and that which may possibly not be is perishable, either in the full sense, or
in the precise sense in which it is said that it possibly may not be, i.e. in
respect either of place or of quantity or quality; ‘in the full sense’ means ‘in
respect of substance’. Nothing, then, which is in the full sense imperishable is
in the full sense potentially existent (though there is nothing to prevent its
being so in some respect, e.g. potentially of a certain quality or in a certain
place); all imperishable things, then, exist actually. Nor can anything which is
of necessity exist potentially; yet these things are primary; for if these did
not exist, nothing would exist. Nor does eternal movement, if there be such,
exist potentially; and, if there is an eternal mobile, it is not in motion in
virtue of a potentiality, except in respect of ‘whence’ and ‘whither’ (there is
nothing to prevent its having matter which makes it capable of movement in
various directions). And so the sun and the stars and the whole heaven are ever
active, and there is no fear that they may sometime stand still, as the natural
philosophers fear they may. Nor do they tire in this activity; for movement is
not for them, as it is for perishable things, connected with the potentiality
for opposites, so that the continuity of the movement should be laborious; for
it is that kind of substance which is matter and potency, not actuality, that
causes this.
Imperishable things are imitated by those that
are involved in change, e.g. earth and fire. For these also are ever active; for
they have their movement of themselves and in themselves. But the other
potencies, according to our previous discussion, are all potencies for
opposites; for that which can move another in this way can also move it not in
this way, i.e. if it acts according to a rational formula; and the same
non-rational potencies will produce opposite results by their presence or
absence.
If, then, there are any entities or substances
such as the dialecticians say the Ideas are, there must be something much more
scientific than science-itself and something more mobile than movement-itself;
for these will be more of the nature of actualities, while science-itself and
movement-itself are potencies for these.
Obviously, then, actuality is prior both to
potency and to every principle of change.
9
That the actuality is also better and more
valuable than the good potency is evident from the following argument.
Everything of which we say that it can do something, is alike capable of
contraries, e.g. that of which we say that it can be well is the same as that
which can be ill, and has both potencies at once; for the same potency is a
potency of health and illness, of rest and motion, of building and throwing
down, of being built and being thrown down. The capacity for contraries, then,
is present at the same time; but contraries cannot be present at the same time,
and the actualities also cannot be present at the same time, e.g. health and
illness. Therefore, while the good must be one of them, the capacity is both
alike, or neither; the actuality, then, is better. Also in the case of bad
things the end or actuality must be worse than the potency; for that which ‘can’
is both contraries alike. Clearly, then, the bad does not exist apart from bad
things; for the bad is in its nature posterior to the potency. And therefore we
may also say that in the things which are from the beginning, i.e. in eternal
things, there is nothing bad, nothing defective, nothing perverted (for
perversion is something bad).
It is an activity also that geometrical
constructions are discovered; for we find them by dividing. If the figures had
been already divided, the constructions would have been obvious; but as it is
they are present only potentially. Why are the angles of the triangle equal to
two right angles? Because the angles about one point are equal to two right
angles. If, then, the line parallel to the side had been already drawn upwards,
the reason would have been evident to any one as soon as he saw the figure. Why
is the angle in a semicircle in all cases a right angle? If three lines are
equal the two which form the base, and the perpendicular from the centre – the
conclusion is evident at a glance to one who knows the former proposition.
Obviously, therefore, the potentially existing constructions are discovered by
being brought to actuality; the reason is that the geometer’s thinking is an
actuality; so that the potency proceeds from an actuality; and therefore it is
by making constructions that people come to know them (though the single
actuality is later in generation than the corresponding potency). (See
diagram.)
10
The terms ‘being’ and ‘non-being’ are employed
firstly with reference to the categories, and secondly with reference to the
potency or actuality of these or their non-potency or nonactuality, and thirdly
in the sense of true and false. This depends, on the side of the objects, on
their being combined or separated, so that he who thinks the separated to be
separated and the combined to be combined has the truth, while he whose thought
is in a state contrary to that of the objects is in error. This being so, when
is what is called truth or falsity present, and when is it not? We must consider
what we mean by these terms. It is not because we think truly that you are pale,
that you are pale, but because you are pale we who say this have the truth. If,
then, some things are always combined and cannot be separated, and others are
always separated and cannot be combined, while others are capable either of
combination or of separation, ‘being’ is being combined and one, and ‘not being’
is being not combined but more than one. Regarding contingent facts, then, the
same opinion or the same statement comes to be false and true, and it is
possible for it to be at one time correct and at another erroneous; but
regarding things that cannot be otherwise opinions are not at one time true and
at another false, but the same opinions are always true or always
false.
But with regard to incomposites, what is being
or not being, and truth or falsity? A thing of this sort is not composite, so as
to ‘be’ when it is compounded, and not to ‘be’ if it is separated, like ‘that
the wood is white’ or ‘that the diagonal is incommensurable’; nor will truth and
falsity be still present in the same way as in the previous cases. In fact, as
truth is not the same in these cases, so also being is not the same; but (a)
truth or falsity is as follows – contact and assertion are truth (assertion not
being the same as affirmation), and ignorance is non-contact. For it is not
possible to be in error regarding the question what a thing is, save in an
accidental sense; and the same holds good regarding non-composite substances
(for it is not possible to be in error about them). And they all exist actually,
not potentially; for otherwise they would have come to be and ceased to be; but,
as it is, being itself does not come to be (nor cease to be); for if it had done
so it would have had to come out of something. About the things, then, which are
essences and actualities, it is not possible to be in error, but only to know
them or not to know them. But we do inquire what they are, viz. whether they are
of such and such a nature or not.
(b) As regards the ‘being’ that answers to
truth and the ‘non-being’ that answers to falsity, in one case there is truth if
the subject and the attribute are really combined, and falsity if they are not
combined; in the other case, if the object is existent it exists in a particular
way, and if it does not exist in this way does not exist at all. And truth means
knowing these objects, and falsity does not exist, nor error, but only ignorance
– and not an ignorance which is like blindness; for blindness is akin to a total
absence of the faculty of thinking.
It is evident also that about unchangeable
things there can be no error in respect of time, if we assume them to be
unchangeable. E.g. if we suppose that the triangle does not change, we shall not
suppose that at one time its angles are equal to two right angles while at
another time they are not (for that would imply change). It is possible,
however, to suppose that one member of such a class has a certain attribute and
another has not; e.g. while we may suppose that no even number is prime, we may
suppose that some are and some are not. But regarding a numerically single
number not even this form of error is possible; for we cannot in this case
suppose that one instance has an attribute and another has not, but whether our
judgement be true or false, it is implied that the fact is
eternal.
1
We have said previously, in our distinction of the various meanings of words, that ‘one’ has several meanings; the things that are directly and of their own nature and not accidentally called one may be summarized under four heads, though the word is used in more senses. (1) There is the continuous, either in general, or especially that which is continuous by nature and not by contact nor by being together; and of these, that has more unity and is prior, whose movement is more indivisible and simpler. (2) That which is a whole and has a certain shape and form is one in a still higher degree; and especially if a thing is of this sort by nature, and not by force like the things which are unified by glue or nails or by being tied together, i.e. if it has in itself the cause of its continuity. A thing is of this sort because its movement is one and indivisible in place and time; so that evidently if a thing has by nature a principle of movement that is of the first kind (i.e. local movement) and the first in that kind (i.e. circular movement), this is in the primary sense one extended thing. Some things, then, are one in this way, qua continuous or whole, and the other things that are one are those whose definition is one. Of this sort are the things the thought of which is one, i.e. those the thought of which is indivisible; and it is indivisible if the thing is indivisible in kind or in number. (3) In number, then, the individual is indivisible, and (4) in kind, that which in intelligibility and in knowledge is indivisible, so that that which causes substances to be one must be one in the primary sense. ‘One’, then, has all these meanings – the naturally continuous and the whole, and the individual and the universal. And all these are one because in some cases the movement, in others the thought or the definition is indivisible.
But it must be observed that the questions,
what sort of things are said to be one, and what it is to be one and what is the
definition of it, should not be assumed to be the same. ‘One’ has all these
meanings, and each of the things to which one of these kinds of unity belongs
will be one; but ‘to be one’ will sometimes mean being one of these things, and
sometimes being something else which is even nearer to the meaning of the word
‘one’ while these other things approximate to its application. This is also true
of ‘element’ or ‘cause’, if one had both to specify the things of which it is
predicable and to render the definition of the word. For in a sense fire is an
element (and doubtless also ‘the indefinite’ or something else of the sort is by
its own nature the element), but in a sense it is not; for it is not the same
thing to be fire and to be an element, but while as a particular thing with a
nature of its own fire is an element, the name ‘element’ means that it has this
attribute, that there is something which is made of it as a primary constituent.
And so with ‘cause’ and ‘one’ and all such terms. For this reason, too, ‘to be
one’ means ‘to be indivisible, being essentially one means a «this» and capable
of being isolated either in place, or in form or thought’; or perhaps ‘to be
whole and indivisible’; but it means especially ‘to be the first measure of a
kind’, and most strictly of quantity; for it is from this that it has been
extended to the other categories. For measure is that by which quantity is
known; and quantity qua quantity is known either by a ‘one’ or by a number, and
all number is known by a ‘one’. Therefore all quantity qua quantity is known by
the one, and that by which quantities are primarily known is the one itself; and
so the one is the starting-point of number qua number. And hence in the other
classes too ‘measure’ means that by which each is first known, and the measure
of each is a unit – in length, in breadth, in depth, in weight, in speed. (The
words ‘weight’ and ‘speed’ are common to both contraries; for each of them has
two meanings – ‘weight’ means both that which has any amount of gravity and that
which has an excess of gravity, and ‘speed’ both that which has any amount of
movement and that which has an excess of movement; for even the slow has a
certain speed and the comparatively light a certain
weight.)
In all these, then, the measure and
starting-point is something one and indivisible, since even in lines we treat as
indivisible the line a foot long. For everywhere we seek as the measure
something one and indivisible; and this is that which is simple either in
quality or in quantity. Now where it is thought impossible to take away or to
add, there the measure is exact (hence that of number is most exact; for we
posit the unit as indivisible in every respect); but in all other cases we
imitate this sort of measure. For in the case of a furlong or a talent or of
anything comparatively large any addition or subtraction might more easily
escape our notice than in the case of something smaller; so that the first thing
from which, as far as our perception goes, nothing can be subtracted, all men
make the measure, whether of liquids or of solids, whether of weight or of size;
and they think they know the quantity when they know it by means of this
measure. And indeed they know movement too by the simple movement and the
quickest; for this occupies least time. And so in astronomy a ‘one’ of this sort
is the starting-point and measure (for they assume the movement of the heavens
to be uniform and the quickest, and judge the others by reference to it), and in
music the quarter-tone (because it is the least interval), and in speech the
letter. And all these are ones in this sense – not that ‘one’ is something
predicable in the same sense of all of these, but in the sense we have
mentioned.
But the measure is not always one in number –
sometimes there are several; e.g. the quarter-tones (not to the ear, but as
determined by the ratios) are two, and the articulate sounds by which we measure
are more than one, and the diagonal of the square and its side are measured by
two quantities, and all spatial magnitudes reveal similar varieties of unit.
Thus, then, the one is the measure of all things, because we come to know the
elements in the substance by dividing the things either in respect of quantity
or in respect of kind. And the one is indivisible just because the first of each
class of things is indivisible. But it is not in the same way that every ‘one’
is indivisible e.g. a foot and a unit; the latter is indivisible in every
respect, while the former must be placed among things which are undivided to
perception, as has been said already – only to perception, for doubtless every
continuous thing is divisible.
The measure is always homogeneous with the
thing measured; the measure of spatial magnitudes is a spatial magnitude, and in
particular that of length is a length, that of breadth a breadth, that of
articulate sound an articulate sound, that of weight a weight, that of units a
unit. (For we must state the matter so, and not say that the measure of numbers
is a number; we ought indeed to say this if we were to use the corresponding
form of words, but the claim does not really correspond – it is as if one
claimed that the measure of units is units and not a unit; number is a plurality
of units.)
Knowledge, also, and perception, we call the
measure of things for the same reason, because we come to know something by them
– while as a matter of fact they are measured rather than measure other things.
But it is with us as if some one else measured us and we came to know how big we
are by seeing that he applied the cubit-measure to such and such a fraction of
us. But Protagoras says ‘man is the measure of all things’, as if he had said
‘the man who knows’ or ‘the man who perceives’; and these because they have
respectively knowledge and perception, which we say are the measures of objects.
Such thinkers are saying nothing, then, while they appear to be saying something
remarkable.
Evidently, then, unity in the strictest sense,
if we define it according to the meaning of the word, is a measure, and most
properly of quantity, and secondly of quality. And some things will be one if
they are indivisible in quantity, and others if they are indivisible in quality;
and so that which is one is indivisible, either absolutely or qua
one.
2
With regard to the substance and nature of the
one we must ask in which of two ways it exists. This is the very question that
we reviewed in our discussion of problems, viz. what the one is and how we must
conceive of it, whether we must take the one itself as being a substance (as
both the Pythagoreans say in earlier and Plato in later times), or there is,
rather, an underlying nature and the one should be described more intelligibly
and more in the manner of the physical philosophers, of whom one says the one is
love, another says it is air, and another the indefinite.
If, then, no universal can be a substance, as
has been said our discussion of substance and being, and if being itself cannot
be a substance in the sense of a one apart from the many (for it is common to
the many), but is only a predicate, clearly unity also cannot be a substance;
for being and unity are the most universal of all predicates. Therefore, on the
one hand, genera are not certain entities and substances separable from other
things; and on the other hand the one cannot be a genus, for the same reasons
for which being and substance cannot be genera.
Further, the position must be similar in all
the kinds of unity. Now ‘unity’ has just as many meanings as ‘being’; so that
since in the sphere of qualities the one is something definite – some particular
kind of thing – and similarly in the sphere of quantities, clearly we must in
every category ask what the one is, as we must ask what the existent is, since
it is not enough to say that its nature is just to be one or existent. But in
colours the one is a colour, e.g. white, and then the other colours are observed
to be produced out of this and black, and black is the privation of white, as
darkness of light. Therefore if all existent things were colours, existent
things would have been a number, indeed, but of what? Clearly of colours; and
the ‘one’ would have been a particular ‘one’, i.e. white. And similarly if all
existing things were tunes, they would have been a number, but a number of
quarter-tones, and their essence would not have been number; and the one would
have been something whose substance was not to be one but to be the
quarter-tone. And similarly if all existent things had been articulate sounds,
they would have been a number of letters, and the one would have been a vowel.
And if all existent things were rectilinear figures, they would have been a
number of figures, and the one would have been the triangle. And the same
argument applies to all other classes. Since, therefore, while there are numbers
and a one both in affections and in qualities and in quantities and in movement,
in all cases the number is a number of particular things and the one is one
something, and its substance is not just to be one, the same must be true of
substances also; for it is true of all cases alike.
That the one, then, in every class is a
definite thing, and in no case is its nature just this, unity, is evident; but
as in colours the one-itself which we must seek is one colour, so too in
substance the one-itself is one substance. That in a sense unity means the same
as being is clear from the facts that its meanings correspond to the categories
one to one, and it is not comprised within any category (e.g. it is comprised
neither in ‘what a thing is’ nor in quality, but is related to them just as
being is); that in ‘one man’ nothing more is predicated than in ‘man’ (just as
being is nothing apart from substance or quality or quantity); and that to be
one is just to be a particular thing.
3
The one and the many are opposed in several
ways, of which one is the opposition of the one and plurality as indivisible and
divisible; for that which is either divided or divisible is called a plurality,
and that which is indivisible or not divided is called one. Now since opposition
is of four kinds, and one of these two terms is privative in meaning, they must
be contraries, and neither contradictory nor correlative in meaning. And the one
derives its name and its explanation from its contrary, the indivisible from the
divisible, because plurality and the divisible is more perceptible than the
indivisible, so that in definition plurality is prior to the indivisible,
because of the conditions of perception.
To the one belong, as we indicated graphically
in our distinction of the contraries, the same and the like and the equal, and
to plurality belong the other and the unlike and the unequal. ‘The same’ has
several meanings; (1) we sometimes mean ‘the same numerically’; again, (2) we
call a thing the same if it is one both in definition and in number, e.g. you
are one with yourself both in form and in matter; and again, (3) if the
definition of its primary essence is one; e.g. equal straight lines are the
same, and so are equal and equal-angled quadrilaterals; there are many such, but
in these equality constitutes unity.
Things are like if, not being absolutely the
same, nor without difference in respect of their concrete substance, they are
the same in form; e.g. the larger square is like the smaller, and unequal
straight lines are like; they are like, but not absolutely the same. Other
things are like, if, having the same form, and being things in which difference
of degree is possible, they have no difference of degree. Other things, if they
have a quality that is in form one and same – e.g. whiteness – in a greater or
less degree, are called like because their form is one. Other things are called
like if the qualities they have in common are more numerous than those in which
they differ – either the qualities in general or the prominent qualities; e.g.
tin is like silver, qua white, and gold is like fire, qua yellow and
red.
Evidently, then, ‘other’ and ‘unlike’ also have
several meanings. And the other in one sense is the opposite of the same (so
that everything is either the same as or other than everything else). In another
sense things are other unless both their matter and their definition are one (so
that you are other than your neighbour). The other in the third sense is
exemplified in the objects of mathematics. ‘Other or the same’ can therefore be
predicated of everything with regard to everything else – but only if the things
are one and existent, for ‘other’ is not the contradictory of ‘the same’; which
is why it is not predicated of non-existent things (while ‘not the same’ is so
predicated). It is predicated of all existing things; for everything that is
existent and one is by its very nature either one or not one with anything
else.
The other, then, and the same are thus opposed.
But difference is not the same as otherness. For the other and that which it is
other than need not be other in some definite respect (for everything that is
existent is either other or the same), but that which is different is different
from some particular thing in some particular respect, so that there must be
something identical whereby they differ. And this identical thing is genus or
species; for everything that differs differs either in genus or in species, in
genus if the things have not their matter in common and are not generated out of
each other (i.e. if they belong to different figures of predication), and in
species if they have the same genus (‘genus’ meaning that identical thing which
is essentially predicated of both the different things).
Contraries are different, and contrariety is a
kind of difference. That we are right in this supposition is shown by induction.
For all of these too are seen to be different; they are not merely other, but
some are other in genus, and others are in the same line of predication, and
therefore in the same genus, and the same in genus. We have distinguished
elsewhere what sort of things are the same or other in
genus.
4
Since things which differ may differ from one
another more or less, there is also a greatest difference, and this I call
contrariety. That contrariety is the greatest difference is made clear by
induction. For things which differ in genus have no way to one another, but are
too far distant and are not comparable; and for things that differ in species
the extremes from which generation takes place are the contraries, and the
distance between extremes – and therefore that between the contraries – is the
greatest.
But surely that which is greatest in each class
is complete. For that is greatest which cannot be exceeded, and that is complete
beyond which nothing can be found. For the complete difference marks the end of
a series (just as the other things which are called complete are so called
because they have attained an end), and beyond the end there is nothing; for in
everything it is the extreme and includes all else, and therefore there is
nothing beyond the end, and the complete needs nothing further. From this, then,
it is clear that contrariety is complete difference; and as contraries are so
called in several senses, their modes of completeness will answer to the various
modes of contrariety which attach to the contraries.
This being so, it is clear that one thing have
more than one contrary (for neither can there be anything more extreme than the
extreme, nor can there be more than two extremes for the one interval), and, to
put the matter generally, this is clear if contrariety is a difference, and if
difference, and therefore also the complete difference, must be between two
things.
And the other commonly accepted definitions of
contraries are also necessarily true. For not only is (1) the complete
difference the greatest difference (for we can get no difference beyond it of
things differing either in genus or in species; for it has been shown that there
is no ‘difference’ between anything and the things outside its genus, and among
the things which differ in species the complete difference is the greatest); but
also (2) the things in the same genus which differ most are contrary (for the
complete difference is the greatest difference between species of the same
genus); and (3) the things in the same receptive material which differ most are
contrary (for the matter is the same for contraries); and (4) of the things
which fall under the same faculty the most different are contrary (for one
science deals with one class of things, and in these the complete difference is
the greatest).
The primary contrariety is that between
positive state and privation – not every privation, however (for ‘privation’ has
several meanings), but that which is complete. And the other contraries must be
called so with reference to these, some because they possess these, others
because they produce or tend to produce them, others because they are
acquisitions or losses of these or of other contraries. Now if the kinds of
opposition are contradiction and privation and contrariety and relation, and of
these the first is contradiction, and contradiction admits of no intermediate,
while contraries admit of one, clearly contradiction and contrariety are not the
same. But privation is a kind of contradiction; for what suffers privation,
either in general or in some determinate way, either that which is quite
incapable of having some attribute or that which, being of such a nature as to
have it, has it not; here we have already a variety of meanings, which have been
distinguished elsewhere. Privation, therefore, is a contradiction or incapacity
which is determinate or taken along with the receptive material. This is the
reason why, while contradiction does not admit of an intermediate, privation
sometimes does; for everything is equal or not equal, but not everything is
equal or unequal, or if it is, it is only within the sphere of that which is
receptive of equality. If, then, the comings-to-be which happen to the matter
start from the contraries, and proceed either from the form and the possession
of the form or from a privation of the form or shape, clearly all contrariety
must be privation, but presumably not all privation is contrariety (the reason
being that that has suffered privation may have suffered it in several ways);
for it is only the extremes from which changes proceed that are
contraries.
And this is obvious also by induction. For
every contrariety involves, as one of its terms, a privation, but not all cases
are alike; inequality is the privation of equality and unlikeness of likeness,
and on the other hand vice is the privation of virtue. But the cases differ in a
way already described; in one case we mean simply that the thing has suffered
privation, in another case that it has done so either at a certain time or in a
certain part (e.g. at a certain age or in the dominant part), or throughout.
This is why in some cases there is a mean (there are men who are neither good
nor bad), and in others there is not (a number must be either odd or even).
Further, some contraries have their subject defined, others have not. Therefore
it is evident that one of the contraries is always privative; but it is enough
if this is true of the first – i.e. the generic – contraries, e.g. the one and
the many; for the others can be reduced to these.
5
Since one thing has one contrary, we might
raise the question how the one is opposed to the many, and the equal to the
great and the small. For if we used the word ‘whether’ only in an antithesis
such as ‘whether it is white or black’, or ‘whether it is white or not white’
(we do not ask ‘whether it is a man or white’), unless we are proceeding on a
prior assumption and asking something such as ‘whether it was Cleon or Socrates
that came’ as this is not a necessary disjunction in any class of things; yet
even this is an extension from the case of opposites; for opposites alone cannot
be present together; and we assume this incompatibility here too in asking which
of the two came; for if they might both have come, the question would have been
absurd; but if they might, even so this falls just as much into an antithesis,
that of the ‘one or many’, i.e. ‘whether both came or one of the two’: – if,
then, the question ‘whether’ is always concerned with opposites, and we can ask
‘whether it is greater or less or equal’, what is the opposition of the equal to
the other two? It is not contrary either to one alone or to both; for why should
it be contrary to the greater rather than to the less? Further, the equal is
contrary to the unequal. Therefore if it is contrary to the greater and the
less, it will be contrary to more things than one. But if the unequal means the
same as both the greater and the less together, the equal will be opposite to
both (and the difficulty supports those who say the unequal is a ‘two’), but it
follows that one thing is contrary to two others, which is impossible. Again,
the equal is evidently intermediate between the great and the small, but no
contrariety is either observed to be intermediate, or, from its definition, can
be so; for it would not be complete if it were intermediate between any two
things, but rather it always has something intermediate between its own
terms.
It remains, then, that it is opposed either as
negation or as privation. It cannot be the negation or privation of one of the
two; for why of the great rather than of the small? It is, then, the privative
negation of both. This is why ‘whether’ is said with reference to both, not to
one of the two (e.g. ‘whether it is greater or equal’ or ‘whether it is equal or
less’); there are always three cases. But it is not a necessary privation; for
not everything which is not greater or less is equal, but only the things which
are of such a nature as to have these attributes.
The equal, then, is that which is neither great
nor small but is naturally fitted to be either great or small; and it is opposed
to both as a privative negation (and therefore is also intermediate). And that
which is neither good nor bad is opposed to both, but has no name; for each of
these has several meanings and the recipient subject is not one; but that which
is neither white nor black has more claim to unity. Yet even this has not one
name, though the colours of which this negation is privatively predicated are in
a way limited; for they must be either grey or yellow or something else of the
kind. Therefore it is an incorrect criticism that is passed by those who think
that all such phrases are used in the same way, so that that which is neither a
shoe nor a hand would be intermediate between a shoe and a hand, since that
which is neither good nor bad is intermediate between the good and the bad – as
if there must be an intermediate in all cases. But this does not necessarily
follow. For the one phrase is a joint denial of opposites between which there is
an intermediate and a certain natural interval; but between the other two there
is no ‘difference’; for the things, the denials of which are combined, belong to
different classes, so that the substratum is not one.
6
We might raise similar questions about the one
and the many. For if the many are absolutely opposed to the one, certain
impossible results follow. One will then be few, whether few be treated here as
singular or plural; for the many are opposed also to the few. Further, two will
be many, since the double is multiple and ‘double’ derives its meaning from
‘two’; therefore one will be few; for what is that in comparison with which two
are many, except one, which must therefore be few? For there is nothing fewer.
Further, if the much and the little are in plurality what the long and the short
are in length, and whatever is much is also many, and the many are much (unless,
indeed, there is a difference in the case of an easily-bounded continuum), the
little (or few) will be a plurality. Therefore one is a plurality if it is few;
and this it must be, if two are many. But perhaps, while the ‘many’ are in a
sense said to be also ‘much’, it is with a difference; e.g. water is much but
not many. But ‘many’ is applied to the things that are divisible; in the one
sense it means a plurality which is excessive either absolutely or relatively
(while ‘few’ is similarly a plurality which is deficient), and in another sense
it means number, in which sense alone it is opposed to the one. For we say ‘one
or many’, just as if one were to say ‘one and ones’ or ‘white thing and white
things’, or to compare the things that have been measured with the measure. It
is in this sense also that multiples are so called. For each number is said to
be many because it consists of ones and because each number is measurable by
one; and it is ‘many’ as that which is opposed to one, not to the few. In this
sense, then, even two is many – not, however, in the sense of a plurality which
is excessive either relatively or absolutely; it is the first plurality. But
without qualification two is few; for it is first plurality which is deficient
(for this reason Anaxagoras was not right in leaving the subject with the
statement that ‘all things were together, boundless both in plurality and in
smallness’ – where for ‘and in smallness’ he should have said ‘and in fewness’;
for they could not have been boundless in fewness), since it is not one, as some
say, but two, that make a few.
The one is opposed then to the many in numbers
as measure to thing measurable; and these are opposed as are the relatives which
are not from their very nature relatives. We have distinguished elsewhere the
two senses in which relatives are so called: – (1) as contraries; (2) as
knowledge to thing known, a term being called relative because another is
relative to it. There is nothing to prevent one from being fewer than something,
e.g. than two; for if one is fewer, it is not therefore few. Plurality is as it
were the class to which number belongs; for number is plurality measurable by
one, and one and number are in a sense opposed, not as contrary, but as we have
said some relative terms are opposed; for inasmuch as one is measure and the
other measurable, they are opposed. This is why not everything that is one is a
number; i.e. if the thing is indivisible it is not a number. But though
knowledge is similarly spoken of as relative to the knowable, the relation does
not work out similarly; for while knowledge might be thought to be the measure,
and the knowable the thing measured, the fact that all knowledge is knowable,
but not all that is knowable is knowledge, because in a sense knowledge is
measured by the knowable. – Plurality is contrary neither to the few (the many
being contrary to this as excessive plurality to plurality exceeded), nor to the
one in every sense; but in the one sense these are contrary, as has been said,
because the former is divisible and the latter indivisible, while in another
sense they are relative as knowledge is to knowable, if plurality is number and
the one is a measure.
7
Since contraries admit of an intermediate and
in some cases have it, intermediates must be composed of the contraries. For (1)
all intermediates are in the same genus as the things between which they stand.
For we call those things intermediates, into which that which changes must
change first; e.g. if we were to pass from the highest string to the lowest by
the smallest intervals, we should come sooner to the intermediate notes, and in
colours if we were to pass from white to black, we should come sooner to crimson
and grey than to black; and similarly in all other cases. But to change from one
genus to another genus is not possible except in an incidental way, as from
colour to figure. Intermediates, then, must be in the same genus both as one
another and as the things they stand between.
But (2) all intermediates stand between
opposites of some kind; for only between these can change take place in virtue
of their own nature (so that an intermediate is impossible between things which
are not opposite; for then there would be change which was not from one opposite
towards the other). Of opposites, contradictories admit of no middle term; for
this is what contradiction is – an opposition, one or other side of which must
attach to anything whatever, i.e. which has no intermediate. Of other opposites,
some are relative, others privative, others contrary. Of relative terms, those
which are not contrary have no intermediate; the reason is that they are not in
the same genus. For what intermediate could there be between knowledge and
knowable? But between great and small there is one.
(3) If intermediates are in the same genus, as
has been shown, and stand between contraries, they must be composed of these
contraries. For either there will be a genus including the contraries or there
will be none. And if (a) there is to be a genus in such a way that it is
something prior to the contraries, the differentiae which constituted the
contrary species-of-a-genus will be contraries prior to the species; for species
are composed of the genus and the differentiae. (E.g. if white and black are
contraries, and one is a piercing colour and the other a compressing colour,
these differentiae – ‘piercing’ and ‘compressing’ – are prior; so that these are
prior contraries of one another.) But, again, the species which differ
contrariwise are the more truly contrary species. And the other.species, i.e.
the intermediates, must be composed of their genus and their differentiae. (E.g.
all colours which are between white and black must be said to be composed of the
genus, i.e. colour, and certain differentiae. But these differentiae will not be
the primary contraries; otherwise every colour would be either white or black.
They are different, then, from the primary contraries; and therefore they will
be between the primary contraries; the primary differentiae are ‘piercing’ and
‘compressing’.)
Therefore it is (b) with regard to these
contraries which do not fall within a genus that we must first ask of what their
intermediates are composed. (For things which are in the same genus must be
composed of terms in which the genus is not an element, or else be themselves
incomposite.) Now contraries do not involve one another in their composition,
and are therefore first principles; but the intermediates are either all
incomposite, or none of them. But there is something compounded out of the
contraries, so that there can be a change from a contrary to it sooner than to
the other contrary; for it will have less of the quality in question than the
one contrary and more than the other. This also, then, will come between the
contraries. All the other intermediates also, therefore, are composite; for that
which has more of a quality than one thing and less than another is compounded
somehow out of the things than which it is said to have more and less
respectively of the quality. And since there are no other things prior to the
contraries and homogeneous with the intermediates, all intermediates must be
compounded out of the contraries. Therefore also all the inferior classes, both
the contraries and their intermediates, will be compounded out of the primary
contraries. Clearly, then, intermediates are (1) all in the same genus and (2)
intermediate between contraries, and (3) all compounded out of the
contraries.
8
That which is other in species is other than
something in something, and this must belong to both; e.g. if it is an animal
other in species, both are animals. The things, then, which are other in species
must be in the same genus. For by genus I mean that one identical thing which is
predicated of both and is differentiated in no merely accidental way, whether
conceived as matter or otherwise. For not only must the common nature attach to
the different things, e.g. not only must both be animals, but this very
animality must also be different for each (e.g. in the one case equinity, in the
other humanity), and so this common nature is specifically different for each
from what it is for the other. One, then, will be in virtue of its own nature
one sort of animal, and the other another, e.g. one a horse and the other a man.
This difference, then, must be an otherness of the genus. For I give the name of
‘difference in the genus’ an otherness which makes the genus itself
other.
This, then, will be a contrariety (as can be
shown also by induction). For all things are divided by opposites, and it has
been proved that contraries are in the same genus. For contrariety was seen to
be complete difference; and all difference in species is a difference from
something in something; so that this is the same for both and is their genus.
(Hence also all contraries which are different in species and not in genus are
in the same line of predication, and other than one another in the highest
degree – for the difference is complete – , and cannot be present along with one
another.) The difference, then, is a contrariety.
This, then, is what it is to be ‘other in
species’ – to have a contrariety, being in the same genus and being indivisible
(and those things are the same in species which have no contrariety, being
indivisible); we say ‘being indivisible’, for in the process of division
contrarieties arise in the intermediate stages before we come to the
indivisibles. Evidently, therefore, with reference to that which is called the
genus, none of the species-of-a-genus is either the same as it or other than it
in species (and this is fitting; for the matter is indicated by negation, and
the genus is the matter of that of which it is called the genus, not in the
sense in which we speak of the genus or family of the Heraclidae, but in that in
which the genus is an element in a thing’s nature), nor is it so with reference
to things which are not in the same genus, but it will differ in genus from
them, and in species from things in the same genus. For a thing’s difference
from that from which it differs in species must be a contrariety; and this
belongs only to things in the same genus.
9
One might raise the question, why woman does
not differ from man in species, when female and male are contrary and their
difference is a contrariety; and why a female and a male animal are not
different in species, though this difference belongs to animal in virtue of its
own nature, and not as paleness or darkness does; both ‘female’ and ‘male’
belong to it qua animal. This question is almost the same as the other, why one
contrariety makes things different in species and another does not, e.g. ‘with
feet’ and ‘with wings’ do, but paleness and darkness do not. Perhaps it is
because the former are modifications peculiar to the genus, and the latter are
less so. And since one element is definition and one is matter, contrarieties
which are in the definition make a difference in species, but those which are in
the thing taken as including its matter do not make one. And so paleness in a
man, or darkness, does not make one, nor is there a difference in species
between the pale man and the dark man, not even if each of them be denoted by
one word. For man is here being considered on his material side, and matter does
not create a difference; for it does not make individual men species of man,
though the flesh and the bones of which this man and that man consist are other.
The concrete thing is other, but not other in species, because in the definition
there is no contrariety. This is the ultimate indivisible kind. Callias is
definition + matter, the pale man, then, is so also, because it is the
individual Callias that is pale; man, then, is pale only incidentally. Neither
do a brazen and a wooden circle, then, differ in species; and if a brazen
triangle and a wooden circle differ in species, it is not because of the matter,
but because there is a contrariety in the definition. But does the matter not
make things other in species, when it is other in a certain way, or is there a
sense in which it does? For why is this horse other than this man in species,
although their matter is included with their definitions? Doubtless because
there is a contrariety in the definition. For while there is a contrariety also
between pale man and dark horse, and it is a contrariety in species, it does not
depend on the paleness of the one and the darkness of the other, since even if
both had been pale, yet they would have been other in species. But male and
female, while they are modifications peculiar to ‘animal’, are so not in virtue
of its essence but in the matter, ie. the body. This is why the same seed
becomes female or male by being acted on in a certain way. We have stated, then,
what it is to be other in species, and why some things differ in species and
others do not.
10
Since contraries are other in form, and the
perishable and the imperishable are contraries (for privation is a determinate
incapacity), the perishable and the imperishable must be different in
kind.
Now so far we have spoken of the general terms
themselves, so that it might be thought not to be necessary that every
imperishable thing should be different from every perishable thing in form, just
as not every pale thing is different in form from every dark thing. For the same
thing can be both, and even at the same time if it is a universal (e.g. man can
be both pale and dark), and if it is an individual it can still be both; for the
same man can be, though not at the same time, pale and dark. Yet pale is
contrary to dark.
But while some contraries belong to certain
things by accident (e.g. both those now mentioned and many others), others
cannot, and among these are ‘perishable’ and ‘imperishable’. For nothing is by
accident perishable. For what is accidental is capable of not being present, but
perishableness is one of the attributes that belong of necessity to the things
to which they belong; or else one and the same thing may be perishable and
imperishable, if perishableness is capable of not belonging to it.
Perishableness then must either be the essence or be present in the essence of
each perishable thing. The same account holds good for imperishableness also;
for both are attributes which are present of necessity. The characteristics,
then, in respect of which and in direct consequence of which one thing is
perishable and another imperishable, are opposite, so that the things must be
different in kind.
Evidently, then, there cannot be Forms such as
some maintain, for then one man would be perishable and another imperishable.
Yet the Forms are said to be the same in form with the individuals and not
merely to have the same name; but things which differ in kind are farther apart
than those which differ in form.
1
That Wisdom is a science of first principles is evident from the introductory chapters, in which we have raised objections to the statements of others about the first principles; but one might ask the question whether Wisdom is to be conceived as one science or as several. If as one, it may be objected that one science always deals with contraries, but the first principles are not contrary. If it is not one, what sort of sciences are those with which it is to be identified?
Further, is it the business of one science, or
of more than one, to examine the first principles of demonstration? If of one,
why of this rather than of any other? If of more, what sort of sciences must
these be said to be?
Further, does Wisdom investigate all substances
or not? If not all, it is hard to say which; but if, being one, it investigates
them all, it is doubtful how the same science can embrace several
subject-matters.
Further, does it deal with substances only or
also with their attributes? If in the case of attributes demonstration is
possible, in that of substances it is not. But if the two sciences are
different, what is each of them and which is Wisdom? If we think of it as
demonstrative, the science of the attributes is Wisdom, but if as dealing with
what is primary, the science of substances claims the
tide.
But again the science we are looking for must
not be supposed to deal with the causes which have been mentioned in the
Physics. For (A) it does not deal with the final cause (for that is the nature
of the good, and this is found in the field of action and movement; and it is
the first mover – for that is the nature of the end – but in the case of things
unmovable there is nothing that moved them first), and (B) in general it is hard
to say whether perchance the science we are now looking for deals with
perceptible substances or not with them, but with certain others. If with
others, it must deal either with the Forms or with the objects of mathematics.
Now (a) evidently the Forms do not exist. (But it is hard to say, even if one
suppose them to exist, why in the world the same is not true of the other things
of which there are Forms, as of the objects of mathematics. I mean that these
thinkers place the objects of mathematics between the Forms and perceptible
things, as a kind of third set of things apart both from the Forms and from the
things in this world; but there is not a third man or horse besides the ideal
and the individuals. If on the other hand it is not as they say, with what sort
of things must the mathematician be supposed to deal? Certainly not with the
things in this world; for none of these is the sort of thing which the
mathematical sciences demand.) Nor (b) does the science which we are now seeking
treat of the objects of mathematics; for none of them can exist separately. But
again it does not deal with perceptible substances; for they are
perishable.
In general one might raise the question, to
what kind of science it belongs to discuss the difficulties about the matter of
the objects of mathematics. Neither to physics (because the whole inquiry of the
physicist is about the things that have in themselves a principle. of movement
and rest), nor yet to the science which inquires into demonstration and science;
for this is just the subject which it investigates. It remains then that it is
the philosophy which we have set before ourselves that treats of those
subjects.
One might discuss the question whether the
science we are seeking should be said to deal with the principles which are by
some called elements; all men suppose these to be present in composite things.
But it might be thought that the science we seek should treat rather of
universals; for every definition and every science is of universals and not of
infimae species, so that as far as this goes it would deal with the highest
genera. These would turn out to be being and unity; for these might most of all
be supposed to contain all things that are, and to be most like principles
because they are by nature; for if they perish all other things are destroyed
with them; for everything is and is one. But inasmuch as, if one is to suppose
them to be genera, they must be predicable of their differentiae, and no genus
is predicable of any of its differentiae, in this way it would seem that we
should not make them genera nor principles. Further, if the simpler is more of a
principle than the less simple, and the ultimate members of the genus are
simpler than the genera (for they are indivisible, but the genera are divided
into many and differing species), the species might seem to be the principles,
rather than the genera. But inasmuch as the species are involved in the
destruction of the genera, the genera are more like principles; for that which
involves another in its destruction is a principle of it. These and others of
the kind are the subjects that involve difficulties.
2
Further, must we suppose something apart from
individual things, or is it these that the science we are seeking treats of? But
these are infinite in number. Yet the things that are apart from the individuals
are genera or species; but the science we now seek treats of neither of these.
The reason why this is impossible has been stated. Indeed, it is in general hard
to say whether one must assume that there is a separable substance besides the
sensible substances (i.e. the substances in this world), or that these are the
real things and Wisdom is concerned with them. For we seem to seek another kind
of substance, and this is our problem, i.e. to see if there is something which
can exist apart by itself and belongs to no sensible thing. – Further, if there
is another substance apart from and corresponding to sensible substances, which
kinds of sensible substance must be supposed to have this corresponding to them?
Why should one suppose men or horses to have it, more than either the other
animals or even all lifeless things? On the other hand to set up other and
eternal substances equal in number to the sensible and perishable substances
would seem to fall beyond the bounds of probability. – But if the principle we
now seek is not separable from corporeal things, what has a better claim to the
name matter? This, however, does not exist in actuality, but exists in potency.
And it would seem rather that the form or shape is a more important principle
than this; but the form is perishable, so that there is no eternal substance at
all which can exist apart and independent. But this is paradoxical; for such a
principle and substance seems to exist and is sought by nearly all the most
refined thinkers as something that exists; for how is there to be order unless
there is something eternal and independent and permanent?
Further, if there is a substance or principle
of such a nature as that which we are now seeking, and if this is one for all
things, and the same for eternal and for perishable things, it is hard to say
why in the world, if there is the same principle, some of the things that fall
under the principle are eternal, and others are not eternal; this is
paradoxical. But if there is one principle of perishable and another of eternal
things, we shall be in a like difficulty if the principle of perishable things,
as well as that of eternal, is eternal; for why, if the principle is eternal,
are not the things that fall under the principle also eternal? But if it is
perishable another principle is involved to account for it, and another to
account for that, and this will go on to infinity.
If on the other hand we are to set up what are
thought to be the most unchangeable principles, being and unity, firstly, if
each of these does not indicate a ‘this’ or substance, how will they be
separable and independent? Yet we expect the eternal and primary principles to
be so. But if each of them does signify a ‘this’ or substance, all things that
are are substances; for being is predicated of all things (and unity also of
some); but that all things that are are substance is false. Further, how can
they be right who say that the first principle is unity and this is substance,
and generate number as the first product from unity and from matter, assert that
number is substance? How are we to think of ‘two’, and each of the other numbers
composed of units, as one? On this point neither do they say anything nor is it
easy to say anything. But if we are to suppose lines or what comes after these
(I mean the primary surfaces) to be principles, these at least are not separable
substances, but sections and divisions – the former of surfaces, the latter of
bodies (while points are sections and divisions of lines); and further they are
limits of these same things; and all these are in other things and none is
separable. Further, how are we to suppose that there is a substance of unity and
the point? Every substance comes into being by a gradual process, but a point
does not; for the point is a division.
A further difficulty is raised by the fact that
all knowledge is of universals and of the ‘such’, but substance is not a
universal, but is rather a ‘this’ – a separable thing, so that if there is
knowledge about the first principles, the question arises, how are we to suppose
the first principle to be substance?
Further, is there anything apart from the
concrete thing (by which I mean the matter and that which is joined with it), or
not? If not, we are met by the objection that all things that are in matter are
perishable. But if there is something, it must be the form or shape. Now it is
hard to determine in which cases this exists apart and in which it does not; for
in some cases the form is evidently not separable, e.g. in the case of a
house.
Further, are the principles the same in kind or
in number? If they are one in number, all things will be the
same.
3
Since the science of the philosopher treats of
being qua being universally and not in respect of a part of it, and ‘being’ has
many senses and is not used in one only, it follows that if the word is used
equivocally and in virtue of nothing common to its various uses, being does not
fall under one science (for the meanings of an equivocal term do not form one
genus); but if the word is used in virtue of something common, being will fall
under one science. The term seems to be used in the way we have mentioned, like
‘medical’ and ‘healthy’. For each of these also we use in many senses. Terms are
used in this way by virtue of some kind of reference, in the one case to medical
science, in the other to health, in others to something else, but in each case
to one identical concept. For a discussion and a knife are called medical
because the former proceeds from medical science, and the latter is useful to
it. And a thing is called healthy in a similar way; one thing because it is
indicative of health, another because it is productive of it. And the same is
true in the other cases. Everything that is, then, is said to ‘be’ in this same
way; each thing that is is said to ‘be’ because it is a modification of being
qua being or a permanent or a transient state or a movement of it, or something
else of the sort. And since everything that is may be referred to something
single and common, each of the contrarieties also may be referred to the first
differences and contrarieties of being, whether the first differences of being
are plurality and unity, or likeness and unlikeness, or some other differences;
let these be taken as already discussed. It makes no difference whether that
which is be referred to being or to unity. For even if they are not the same but
different, at least they are convertible; for that which is one is also somehow
being, and that which is being is one.
But since every pair of contraries falls to be
examined by one and the same science, and in each pair one term is the privative
of the other though one might regarding some contraries raise the question, how
they can be privately related, viz. those which have an intermediate, e.g.
unjust and just – in all such cases one must maintain that the privation is not
of the whole definition, but of the infima species. if the just man is ‘by
virtue of some permanent disposition obedient to the laws’, the unjust man will
not in every case have the whole definition denied of him, but may be merely ‘in
some respect deficient in obedience to the laws’, and in this respect the
privation will attach to him; and similarly in all other
cases.
As the mathematician investigates abstractions
(for before beginning his investigation he strips off all the sensible
qualities, e.g. weight and lightness, hardness and its contrary, and also heat
and cold and the other sensible contrarieties, and leaves only the quantitative
and continuous, sometimes in one, sometimes in two, sometimes in three
dimensions, and the attributes of these qua quantitative and continuous, and
does not consider them in any other respect, and examines the relative positions
of some and the attributes of these, and the commensurabilities and
incommensurabilities of others, and the ratios of others; but yet we posit one
and the same science of all these things – geometry) – the same is true with
regard to being. For the attributes of this in so far as it is being, and the
contrarieties in it qua being, it is the business of no other science than
philosophy to investigate; for to physics one would assign the study of things
not qua being, but rather qua sharing in movement; while dialectic and sophistic
deal with the attributes of things that are, but not of things qua being, and
not with being itself in so far as it is being; therefore it remains that it is
the philosopher who studies the things we have named, in so far as they are
being. Since all that is is to ‘be’ in virtue of something single and common,
though the term has many meanings, and contraries are in the same case (for they
are referred to the first contrarieties and differences of being), and things of
this sort can fall under one science, the difficulty we stated at the beginning
appears to be solved, – I mean the question how there can be a single science of
things which are many and different in genus.
4
Since even the mathematician uses the common
axioms only in a special application, it must be the business of first
philosophy to examine the principles of mathematics also. That when equals are
taken from equals the remainders are equal, is common to all quantities, but
mathematics studies a part of its proper matter which it has detached, e.g.
lines or angles or numbers or some other kind of quantity – not, however, qua
being but in so far as each of them is continuous in one or two or three
dimensions; but philosophy does not inquire about particular subjects in so far
as each of them has some attribute or other, but speculates about being, in so
far as each particular thing is. – Physics is in the same position as
mathematics; for physics studies the attributes and the principles of the things
that are, qua moving and not qua being (whereas the primary science, we have
said, deals with these, only in so far as the underlying subjects are existent,
and not in virtue of any other character); and so both physics and mathematics
must be classed as parts of Wisdom.
5
There is a principle in things, about which we
cannot be deceived, but must always, on the contrary recognize the truth, – viz.
that the same thing cannot at one and the same time be and not be, or admit any
other similar pair of opposites. About such matters there is no proof in the
full sense, though there is proof ad hominem. For it is not possible to infer
this truth itself from a more certain principle, yet this is necessary if there
is to be completed proof of it in the full sense. But he who wants to prove to
the asserter of opposites that he is wrong must get from him an admission which
shall be identical with the principle that the same thing cannot be and not be
at one and the same time, but shall not seem to be identical; for thus alone can
his thesis be demonstrated to the man who asserts that opposite statements can
be truly made about the same subject. Those, then, who are to join in argument
with one another must to some extent understand one another; for if this does
not happen how are they to join in argument with one another? Therefore every
word must be intelligible and indicate something, and not many things but only
one; and if it signifies more than one thing, it must be made plain to which of
these the word is being applied. He, then, who says ‘this is and is not’ denies
what he affirms, so that what the word signifies, he says it does not signify;
and this is impossible. Therefore if ‘this is’ signifies something, one cannot
truly assert its contradictory.
Further, if the word signifies something and
this is asserted truly, this connexion must be necessary; and it is not possible
that that which necessarily is should ever not be; it is not possible therefore
to make the opposed affirmations and negations truly of the same subject.
Further, if the affirmation is no more true than the negation, he who says ‘man’
will be no more right than he who says ‘not-man’. It would seem also that in
saying the man is not a horse one would be either more or not less right than in
saying he is not a man, so that one will also be right in saying that the same
person is a horse; for it was assumed to be possible to make opposite statements
equally truly. It follows then that the same person is a man and a horse, or any
other animal.
While, then, there is no proof of these things
in the full sense, there is a proof which may suffice against one who will make
these suppositions. And perhaps if one had questioned Heraclitus himself in this
way one might have forced him to confess that opposite statements can never be
true of the same subjects. But, as it is, he adopted this opinion without
understanding what his statement involves. But in any case if what is said by
him is true, not even this itself will be true – viz. that the same thing can at
one and the same time both be and not be. For as, when the statements are
separated, the affirmation is no more true than the negation, in the same way –
the combined and complex statement being like a single affirmation – the whole
taken as an affirmation will be no more true than the negation. Further, if it
is not possible to affirm anything truly, this itself will be false – the
assertion that there is no true affirmation. But if a true affirmation exists,
this appears to refute what is said by those who raise such objections and
utterly destroy rational discourse.
6
The saying of Protagoras is like the views we
have mentioned; he said that man is the measure of all things, meaning simply
that that which seems to each man also assuredly is. If this is so, it follows
that the same thing both is and is not, and is bad and good, and that the
contents of all other opposite statements are true, because often a particular
thing appears beautiful to some and the contrary of beautiful to others, and
that which appears to each man is the measure. This difficulty may be solved by
considering the source of this opinion. It seems to have arisen in some cases
from the doctrine of the natural philosophers, and in others from the fact that
all men have not the same views about the same things, but a particular thing
appears pleasant to some and the contrary of pleasant to
others.
That nothing comes to be out of that which is
not, but everything out of that which is, is a dogma common to nearly all the
natural philosophers. Since, then, white cannot come to be if the perfectly
white and in no respect not-white existed before, that which becomes white must
come from that which is not white; so that it must come to be out of that which
is not (so they argue), unless the same thing was at the beginning white and
not-white. But it is not hard to solve this difficulty; for we have said in our
works on physics in what sense things that come to be come to be from that which
is not, and in what sense from that which is.
But to attend equally to the opinions and the
fancies of disputing parties is childish; for clearly one of them must be
mistaken. And this is evident from what happens in respect of sensation; for the
same thing never appears sweet to some and the contrary of sweet to others,
unless in the one case the sense-organ which discriminates the aforesaid
flavours has been perverted and injured. And if this is so the one party must be
taken to be the measure, and the other must not. And say the same of good and
bad, and beautiful and ugly, and all other such qualities. For to maintain the
view we are opposing is just like maintaining that the things that appear to
people who put their finger under their eye and make the object appear two
instead of one must be two (because they appear to be of that number) and again
one (for to those who do not interfere with their eye the one object appears
one).
In general, it is absurd to make the fact that
the things of this earth are observed to change and never to remain in the same
state, the basis of our judgement about the truth. For in pursuing the truth one
must start from the things that are always in the same state and suffer no
change. Such are the heavenly bodies; for these do not appear to be now of one
nature and again of another, but are manifestly always the same and share in no
change.
Further, if there is movement, there is also
something moved, and everything is moved out of something and into something; it
follows that that that which is moved must first be in that out of which it is
to be moved, and then not be in it, and move into the other and come to be in
it, and that the contradictory statements are not true at the same time, as
these thinkers assert they are.
And if the things of this earth continuously
flow and move in respect of quantity – if one were to suppose this, although it
is not true – why should they not endure in respect of quality? For the
assertion of contradictory statements about the same thing seems to have arisen
largely from the belief that the quantity of bodies does not endure, which, our
opponents hold, justifies them in saying that the same thing both is and is not
four cubits long. But essence depends on quality, and this is of determinate
nature, though quantity is of indeterminate.
Further, when the doctor orders people to take
some particular food, why do they take it? In what respect is ‘this is bread’
truer than ‘this is not bread’? And so it would make no difference whether one
ate or not. But as a matter of fact they take the food which is ordered,
assuming that they know the truth about it and that it is bread. Yet they should
not, if there were no fixed constant nature in sensible things, but all natures
moved and flowed for ever.
Again, if we are always changing and never
remain the same, what wonder is it if to us, as to the sick, things never appear
the same? (For to them also, because they are not in the same condition as when
they were well, sensible qualities do not appear alike; yet, for all that, the
sensible things themselves need not share in any change, though they produce
different, and not identical, sensations in the sick. And the same must surely
happen to the healthy if the afore-said change takes place.) But if we do not
change but remain the same, there will be something that
endures.
As for those to whom the difficulties mentioned
are suggested by reasoning, it is not easy to solve the difficulties to their
satisfaction, unless they will posit something and no longer demand a reason for
it; for it is only thus that all reasoning and all proof is accomplished; if
they posit nothing, they destroy discussion and all reasoning. Therefore with
such men there is no reasoning. But as for those who are perplexed by the
traditional difficulties, it is easy to meet them and to dissipate the causes of
their perplexity. This is evident from what has been said.
It is manifest, therefore, from these arguments
that contradictory statements cannot be truly made about the same subject at one
time, nor can contrary statements, because every contrariety depends on
privation. This is evident if we reduce the definitions of contraries to their
principle.
Similarly, no intermediate between contraries
can be predicated of one and the same subject, of which one of the contraries is
predicated. If the subject is white we shall be wrong in saying it is neither
black nor white, for then it follows that it is and is not white; for the second
of the two terms we have put together is true of it, and this is the
contradictory of white.
We could not be right, then, in accepting the
views either of Heraclitus or of Anaxagoras. If we were, it would follow that
contraries would be predicated of the same subject; for when Anaxagoras says
that in everything there is a part of everything, he says nothing is sweet any
more than it is bitter, and so with any other pair of contraries, since in
everything everything is present not potentially only, but actually and
separately. And similarly all statements cannot be false nor all true, both
because of many other difficulties which might be adduced as arising from this
position, and because if all are false it will not be true to say even this, and
if all are true it will not be false to say all are false.
7
Every science seeks certain principles and
causes for each of its objects – e.g. medicine and gymnastics and each of the
other sciences, whether productive or mathematical. For each of these marks off
a certain class of things for itself and busies itself about this as about
something existing and real, – not however qua real; the science that does this
is another distinct from these. Of the sciences mentioned each gets somehow the
‘what’ in some class of things and tries to prove the other truths, with more or
less precision. Some get the ‘what’ through perception, others by hypothesis; so
that it is clear from an induction of this sort that there is no demonstration.
of the substance or ‘what’.
There is a science of nature, and evidently it
must be different both from practical and from productive science. For in the
case of productive science the principle of movement is in the producer and not
in the product, and is either an art or some other faculty. And similarly in
practical science the movement is not in the thing done, but rather in the
doers. But the science of the natural philosopher deals with the things that
have in themselves a principle of movement. It is clear from these facts, then,
that natural science must be neither practical nor productive, but theoretical
(for it must fall into some one of these classes). And since each of the
sciences must somehow know the ‘what’ and use this as a principle, we must not
fall to observe how the natural philosopher should define things and how he
should state the definition of the essence – whether as akin to ‘snub’ or rather
to ‘concave’. For of these the definition of ‘snub’ includes the matter of the
thing, but that of ‘concave’ is independent of the matter; for snubness is found
in a nose, so that we look for its definition without eliminating the nose, for
what is snub is a concave nose. Evidently then the definition of flesh also and
of the eye and of the other parts must always be stated without eliminating the
matter.
Since there is a science of being qua being and
capable of existing apart, we must consider whether this is to be regarded as
the same as physics or rather as different. Physics deals with the things that
have a principle of movement in themselves; mathematics is theoretical, and is a
science that deals with things that are at rest, but its subjects cannot exist
apart. Therefore about that which can exist apart and is unmovable there is a
science different from both of these, if there is a substance of this nature (I
mean separable and unmovable), as we shall try to prove there is. And if there
is such a kind of thing in the world, here must surely be the divine, and this
must be the first and most dominant principle. Evidently, then, there are three
kinds of theoretical sciences – physics, mathematics, theology. The class of
theoretical sciences is the best, and of these themselves the last named is
best; for it deals with the highest of existing things, and each science is
called better or worse in virtue of its proper object.
One might raise the question whether the
science of being qua being is to be regarded as universal or not. Each of the
mathematical sciences deals with some one determinate class of things, but
universal mathematics applies alike to all. Now if natural substances are the
first of existing things, physics must be the first of sciences; but if there is
another entity and substance, separable and unmovable, the knowledge of it must
be different and prior to physics and universal because it is
prior.
8
Since ‘being’ in general has several senses, of
which one is ‘being by accident’, we must consider first that which ‘is’ in this
sense. Evidently none of the traditional sciences busies itself about the
accidental. For neither does architecture consider what will happen to those who
are to use the house (e.g. whether they have a painful life in it or not), nor
does weaving, or shoemaking, or the confectioner’s art, do the like; but each of
these sciences considers only what is peculiar to it, i.e. its proper end. And
as for the argument that ‘when he who is musical becomes lettered he’ll be both
at once, not having been both before; and that which is, not always having been,
must have come to be; therefore he must have at once become musical and
lettered’, – this none of the recognized sciences considers, but only sophistic;
for this alone busies itself about the accidental, so that Plato is not far
wrong when he says that the sophist spends his time on
non-being.
That a science of the accidental is not even
possible will be evident if we try to see what the accidental really is. We say
that everything either is always and of necessity (necessity not in the sense of
violence, but that which we appeal to in demonstrations), or is for the most
part, or is neither for the most part, nor always and of necessity, but merely
as it chances; e.g. there might be cold in the dogdays, but this occurs neither
always and of necessity, nor for the most part, though it might happen
sometimes. The accidental, then, is what occurs, but not always nor of
necessity, nor for the most part. Now we have said what the accidental is, and
it is obvious why there is no science of such a thing; for all science is of
that which is always or for the most part, but the accidental is in neither of
these classes.
Evidently there are not causes and principles
of the accidental, of the same kind as there are of the essential; for if there
were, everything would be of necessity. If A is when B is, and B is when C is,
and if C exists not by chance but of necessity, that also of which C was cause
will exist of necessity, down to the last causatum as it is called (but this was
supposed to be accidental). Therefore all things will be of necessity, and
chance and the possibility of a thing’s either occurring or not occurring are
removed entirely from the range of events. And if the cause be supposed not to
exist but to be coming to be, the same results will follow; everything will
occur of necessity. For to-morrow’s eclipse will occur if A occurs, and A if B
occurs, and B if C occurs; and in this way if we subtract time from the limited
time between now and to-morrow we shall come sometime to the already existing
condition. Therefore since this exists, everything after this will occur of
necessity, so that all things occur of necessity.
As to that which ‘is’ in the sense of being
true or of being by accident, the former depends on a combination in thought and
is an affection of thought (which is the reason why it is the principles, not of
that which ‘is’ in this sense, but of that which is outside and can exist apart,
that are sought); and the latter is not necessary but indeterminate (I mean the
accidental); and of such a thing the causes are unordered and
indefinite.
Adaptation to an end is found in events that
happen by nature or as the result of thought. It is ‘luck’ when one of these
events happens by accident. For as a thing may exist, so it may be a cause,
either by its own nature or by accident. Luck is an accidental cause at work in
such events adapted to an end as are usually effected in accordance with
purpose. And so luck and thought are concerned with the same sphere; for purpose
cannot exist without thought. The causes from which lucky results might happen
are indeterminate; and so luck is obscure to human calculation and is a cause by
accident, but in the unqualified sense a cause of nothing. It is good or bad
luck when the result is good or evil; and prosperity or misfortune when the
scale of the results is large.
Since nothing accidental is prior to the
essential, neither are accidental causes prior. If, then, luck or spontaneity is
a cause of the material universe, reason and nature are causes before
it.
9
Some things are only actually, some
potentially, some potentially and actually, what they are, viz. in one case a
particular reality, in another, characterized by a particular quantity, or the
like. There is no movement apart from things; for change is always according to
the categories of being, and there is nothing common to these and in no one
category. But each of the categories belongs to all its subjects in either of
two ways (e.g. ‘this-ness’ – for one kind of it is ‘positive form’, and the
other is ‘privation’; and as regards quality one kind is ‘white’ and the other
‘black’, and as regards quantity one kind is ‘complete’ and the other
‘incomplete’, and as regards spatial movement one is ‘upwards’ and the other
‘downwards’, or one thing is ‘light’ and another ‘heavy’); so that there are as
many kinds of movement and change as of being. There being a distinction in each
class of things between the potential and the completely real, I call the
actuality of the potential as such, movement. That what we say is true, is plain
from the following facts. When the ‘buildable’, in so far as it is what we mean
by ‘buildable’, exists actually, it is being built, and this is the process of
building. Similarly with learning, healing, walking, leaping, ageing, ripening.
Movement takes when the complete reality itself exists, and neither earlier nor
later. The complete reality, then, of that which exists potentially, when it is
completely real and actual, not qua itself, but qua movable, is movement. By qua
I mean this: bronze is potentially a statue; but yet it is not the complete
reality of bronze qua bronze that is movement. For it is not the same thing to
be bronze and to be a certain potency. If it were absolutely the same in its
definition, the complete reality of bronze would have been a movement. But it is
not the same. (This is evident in the case of contraries; for to be capable of
being well and to be capable of being ill are not the same – for if they were,
being well and being ill would have been the same – it is that which underlies
and is healthy or diseased, whether it is moisture or blood, that is one and the
same.) And since it is not. the same, as colour and the visible are not the
same, it is the complete reality of the potential, and as potential, that is
movement. That it is this, and that movement takes place when the complete
reality itself exists, and neither earlier nor later, is evident. For each thing
is capable of being sometimes actual, sometimes not, e.g. the buildable qua
buildable; and the actuality of the buildable qua buildable is building. For the
actuality is either this – the act of building – or the house. But when the
house exists, it is no longer buildable; the buildable is what is being built.
The actuality, then, must be the act of building, and this is a movement. And
the same account applies to all other movements.
That what we have said is right is evident from
what all others say about movement, and from the fact that it is not easy to
define it otherwise. For firstly one cannot put it in any class. This is evident
from what people say. Some call it otherness and inequality and the unreal; none
of these, however, is necessarily moved, and further, change is not either to
these or from these any more than from their opposites. The reason why people
put movement in these classes is that it is thought to be something indefinite,
and the principles in one of the two ‘columns of contraries’ are indefinite
because they are privative, for none of them is either a ‘this’ or a ‘such’ or
in any of the other categories. And the reason why movement is thought to be
indefinite is that it cannot be classed either with the potency of things or
with their actuality; for neither that which is capable of being of a certain
quantity, nor that which is actually of a certain quantity, is of necessity
moved, and movement is thought to be an actuality, but incomplete; the reason is
that the potential, whose actuality it is, is incomplete. And therefore it is
hard to grasp what movement is; for it must be classed either under privation or
under potency or under absolute actuality, but evidently none of these is
possible. Therefore what remains is that it must be what we said – both
actuality and the actuality we have described – which is hard to detect but
capable of existing.
And evidently movement is in the movable; for
it is the complete realization of this by that which is capable of causing
movement. And the actuality of that which is capable of causing movement is no
other than that of the movable. For it must be the complete reality of both. For
while a thing is capable of causing movement because it can do this, it is a
mover because it is active; but it is on the movable that it is capable of
acting, so that the actuality of both is one, just as there is the same interval
from one to two as from two to one, and as the steep ascent and the steep
descent are one, but the being of them is not one; the case of the mover and the
moved is similar.
10
The infinite is either that which is incapable
of being traversed because it is not its nature to be traversed (this
corresponds to the sense in which the voice is ‘invisible’), or that which
admits only of incomplete traverse or scarcely admits of traverse, or that
which, though it naturally admits of traverse, is not traversed or limited;
further, a thing may be infinite in respect of addition or of subtraction, or
both. The infinite cannot be a separate, independent thing. For if it is neither
a spatial magnitude nor a plurality, but infinity itself is its substance and
not an accident of it, it will be indivisible; for the divisible is either
magnitude or plurality. But if indivisible, it is not infinite, except as the
voice is invisible; but people do not mean this, nor are we examining this sort
of infinite, but the infinite as untraversable. Further, how can an infinite
exist by itself, unless number and magnitude also exist by themselvess – since
infinity is an attribute of these? Further, if the infinite is an accident of
something else, it cannot be qua infinite an element in things, as the invisible
is not an element in speech, though the voice is invisible. And evidently the
infinite cannot exist actually. For then any part of it that might be taken
would be infinite (for ‘to be infinite’ and ‘the infinite’ are the same, if the
infinite is substance and not predicated of a subject). Therefore it is either
indivisible, or if it is partible, it is divisible into infinites; but the same
thing cannot be many infinites (as a part of air is air, so a part of the
infinite would be infinite, if the infinite is substance and a principle).
Therefore it must be impartible and indivisible. But the actually infinite
cannot be indivisible; for it must be of a certain quantity. Therefore infinity
belongs to its subject incidentally. But if so, then (as we have said) it cannot
be it that is a principle, but that of which it is an accident – the air or the
even number.
This inquiry is universal; but that the
infinite is not among sensible things, is evident from the following argument.
If the definition of a body is ‘that which is bounded by planes’, there cannot
be an infinite body either sensible or intelligible; nor a separate and infinite
number, for number or that which has a number is numerable. Concretely, the
truth is evident from the following argument. The infinite can neither be
composite nor simple. For (a) it cannot be a composite body, since the elements
are limited in multitude. For the contraries must be equal and no one of them
must be infinite; for if one of the two bodies falls at all short of the other
in potency, the finite will be destroyed by the infinite. And that each should
be infinite is impossible. For body is that which has extension in all
directions, and the infinite is the boundlessly extended, so that if the
infinite is a body it will be infinite in every direction. Nor (b) can the
infinite body be one and simple – neither, as some say, something apart from the
elements, from which they generate these (for there is no such body apart from
the elements; for everything can be resolved into that of which it consists, but
no such product of analysis is observed except the simple bodies), nor fire nor
any other of the elements. For apart from the question how any of them could be
infinite, the All, even if it is finite, cannot either be or become any one of
them, as Heraclitus says all things sometime become fire. The same argument
applies to this as to the One which the natural philosophers posit besides the
elements. For everything changes from contrary to contrary, e.g. from hot to
cold.
Further, a sensible body is somewhere, and
whole and part have the same proper place, e.g. the whole earth and part of the
earth. Therefore if (a) the infinite body is homogeneous, it will be unmovable
or it will be always moving. But this is impossible; for why should it rather
rest, or move, down, up, or anywhere, rather than anywhere else? E.g. if there
were a clod which were part of an infinite body, where will this move or rest?
The proper place of the body which is homogeneous with it is infinite. Will the
clod occupy the whole place, then? And how? (This is impossible.) What then is
its rest or its movement? It will either rest everywhere, and then it cannot
move; or it will move everywhere, and then it cannot be still. But (b) if the
All has unlike parts, the proper places of the parts are unlike also, and,
firstly, the body of the All is not one except by contact, and, secondly, the
parts will be either finite or infinite in variety of kind. Finite they cannot
be; for then those of one kind will be infinite in quantity and those of another
will not (if the All is infinite), e.g. fire or water would be infinite, but
such an infinite element would be destruction to the contrary elements. But if
the parts are infinite and simple, their places also are infinite and there will
be an infinite number of elements; and if this is impossible, and the places are
finite, the All also must be limited.
In general, there cannot be an infinite body
and also a proper place for bodies, if every sensible body has either weight or
lightness. For it must move either towards the middle or upwards, and the
infinite either the whole or the half of it – cannot do either; for how will you
divide it? Or how will part of the infinite be down and part up, or part extreme
and part middle? Further, every sensible body is in a place, and there are six
kinds of place, but these cannot exist in an infinite body. In general, if there
cannot be an infinite place, there cannot be an infinite body; (and there cannot
be an infinite place,) for that which is in a place is somewhere, and this means
either up or down or in one of the other directions, and each of these is a
limit.
The infinite is not the same in the sense that
it is a single thing whether exhibited in distance or in movement or in time,
but the posterior among these is called infinite in virtue of its relation to
the prior; i.e. a movement is called infinite in virtue of the distance covered
by the spatial movement or alteration or growth, and a time is called infinite
because of the movement which occupies it.
11
Of things which change, some change in an
accidental sense, like that in which ‘the musical’ may be said to walk, and
others are said, without qualification, to change, because something in them
changes, i.e. the things that change in parts; the body becomes healthy, because
the eye does. But there is something which is by its own nature moved directly,
and this is the essentially movable. The same distinction is found in the case
of the mover; for it causes movement either in an accidental sense or in respect
of a part of itself or essentially. There is something that directly causes
movement; and there is something that is moved, also the time in which it is
moved, and that from which and that into which it is moved. But the forms and
the affections and the place, which are the terminals of the movement of moving
things, are unmovable, e.g. knowledge or heat; it is not heat that is a
movement, but heating. Change which is not accidental is found not in all
things, but between contraries, and their intermediates, and between
contradictories. We may convince ourselves of this by
induction.
That which changes changes either from positive
into positive, or from negative into negative, or from positive into negative,
or from negative into positive. (By positive I mean that which is expressed by
an affirmative term.) Therefore there must be three changes; that from negative
into negative is not change, because (since the terms are neither contraries nor
contradictories) there is no opposition. The change from the negative into the
positive which is its contradictory is generation – absolute change absolute
generation, and partial change partial generation; and the change from positive
to negative is destruction – absolute change absolute destruction, and partial
change partial destruction. If, then, ‘that which is not’ has several senses,
and movement can attach neither to that which implies putting together or
separating, nor to that which implies potency and is opposed to that which is in
the full sense (true, the not-white or not-good can be moved incidentally, for
the not-white might be a man; but that which is not a particular thing at all
can in no wise be moved), that which is not cannot be moved (and if this is so,
generation cannot be movement; for that which is not is generated; for even if
we admit to the full that its generation is accidental, yet it is true to say
that ‘not-being’ is predicable of that which is generated absolutely). Similarly
rest cannot be long to that which is not. These consequences, then, turn out to
be awkward, and also this, that everything that is moved is in a place, but that
which is not is not in a place; for then it would be somewhere. Nor is
destruction movement; for the contrary of movement is rest, but the contrary of
destruction is generation. Since every movement is a change, and the kinds of
change are the three named above, and of these those in the way of generation
and destruction are not movements, and these are the changes from a thing to its
contradictory, it follows that only the change from positive into positive is
movement. And the positives are either contrary or intermediate (for even
privation must be regarded as contrary), and are expressed by an affirmative
term, e.g. ‘naked’ or ‘toothless’ or ‘black’.
12
If the categories are classified as substance,
quality, place, acting or being acted on, relation, quantity, there must be
three kinds of movement – of quality, of quantity, of place. There is no
movement in respect of substance (because there is nothing contrary to
substance), nor of relation (for it is possible that if one of two things in
relation changes, the relative term which was true of the other thing ceases to
be true, though this other does not change at all, – so that their movement is
accidental), nor of agent and patient, or mover and moved, because there is no
movement of movement nor generation of generation, nor, in general, change of
change. For there might be movement of movement in two senses; (1) movement
might be the subject moved, as a man is moved because he changes from pale to
dark, – so that on this showing movement, too, may be either heated or cooled or
change its place or increase. But this is impossible; for change is not a
subject. Or (2) some other subject might change from change into some other form
of existence (e.g. a man from disease into health). But this also is not
possible except incidentally. For every movement is change from something into
something. (And so are generation and destruction; only, these are changes into
things opposed in certain ways while the other, movement, is into things opposed
in another way.) A thing changes, then, at the same time from health into
illness, and from this change itself into another. Clearly, then, if it has
become ill, it will have changed into whatever may be the other change concerned
(though it may be at rest), and, further, into a determinate change each time;
and that new change will be from something definite into some other definite
thing; therefore it will be the opposite change, that of growing well. We answer
that this happens only incidentally; e.g. there is a change from the process of
recollection to that of forgetting, only because that to which the process
attaches is changing, now into a state of knowledge, now into one of
ignorance.
Further, the process will go on to infinity, if
there is to be change of change and coming to be of coming to be. What is true
of the later, then, must be true of the earlier; e.g. if the simple coming to be
was once coming to be, that which comes to be something was also once coming to
be; therefore that which simply comes to be something was not yet in existence,
but something which was coming to be coming to be something was already in
existence. And this was once coming to be, so that at that time it was not yet
coming to be something else. Now since of an infinite number of terms there is
not a first, the first in this series will not exist, and therefore no following
term exist. Nothing, then, can either come term wi to be or move or change.
Further, that which is capable of a movement is also capable of the contrary
movement and rest, and that which comes to be also ceases to be. Therefore that
which is coming to be is ceasing to be when it has come to be coming to be; for
it cannot cease to be as soon as it is coming to be coming to be, nor after it
has come to be; for that which is ceasing to be must be. Further, there must be
a matter underlying that which comes to be and changes. What will this be, then,
– what is it that becomes movement or becoming, as body or soul is that which
suffers alteration? And; again, what is it that they move into? For it must be
the movement or becoming of something from something into something. How, then,
can this condition be fulfilled? There can be no learning of learning, and
therefore no becoming of becoming. Since there is not movement either of
substance or of relation or of activity and passivity, it remains that movement
is in respect of quality and quantity and place; for each of these admits of
contrariety. By quality I mean not that which is in the substance (for even the
differentia is a quality), but the passive quality, in virtue of which a thing
is said to be acted on or to be incapable of being acted on. The immobile is
either that which is wholly incapable of being moved, or that which is moved
with difficulty in a long time or begins slowly, or that which is of a nature to
be moved and can be moved but is not moved when and where and as it would
naturally be moved. This alone among immobiles I describe as being at rest; for
rest is contrary to movement, so that it must be a privation in that which is
receptive of movement.
Things which are in one proximate place are
together in place, and things which are in different places are apart: things
whose extremes are together touch: that at which a changing thing, if it changes
continuously according to its nature, naturally arrives before it arrives at the
extreme into which it is changing, is between. That which is most distant in a
straight line is contrary in place. That is successive which is after the
beginning (the order being determined by position or form or in some other way)
and has nothing of the same class between it and that which it succeeds, e.g.
lines in the case of a line, units in that of a unit, or a house in that of a
house. (There is nothing to prevent a thing of some other class from being
between.) For the successive succeeds something and is something later; ‘one’
does not succeed ‘two’, nor the first day of the month the second. That which,
being successive, touches, is contiguous. (Since all change is between
opposites, and these are either contraries or contradictories, and there is no
middle term for contradictories, clearly that which is between is between
contraries.) The continuous is a species of the contiguous. I call two things
continuous when the limits of each, with which they touch and by which they are
kept together, become one and the same, so that plainly the continuous is found
in the things out of which a unity naturally arises in virtue of their contact.
And plainly the successive is the first of these concepts (for the successive
does not necessarily touch, but that which touches is successive; and if a thing
is continuous, it touches, but if it touches, it is not necessarily continuous;
and in things in which there is no touching, there is no organic unity);
therefore a point is not the same as a unit; for contact belongs to points, but
not to units, which have only succession; and there is something between two of
the former, but not between two of the latter.
1
The subject of our inquiry is substance; for the principles and the causes we are seeking are those of substances. For if the universe is of the nature of a whole, substance is its first part; and if it coheres merely by virtue of serial succession, on this view also substance is first, and is succeeded by quality, and then by quantity. At the same time these latter are not even being in the full sense, but are qualities and movements of it, – or else even the not-white and the not-straight would be being; at least we say even these are, e.g. ‘there is a not-white’. Further, none of the categories other than substance can exist apart. And the early philosophers also in practice testify to the primacy of substance; for it was of substance that they sought the principles and elements and causes. The thinkers of the present day tend to rank universals as substances (for genera are universals, and these they tend to describe as principles and substances, owing to the abstract nature of their inquiry); but the thinkers of old ranked particular things as substances, e.g. fire and earth, not what is common to both, body.
There are three kinds of substance – one that
is sensible (of which one subdivision is eternal and another is perishable; the
latter is recognized by all men, and includes e.g. plants and animals), of which
we must grasp the elements, whether one or many; and another that is immovable,
and this certain thinkers assert to be capable of existing apart, some dividing
it into two, others identifying the Forms and the objects of mathematics, and
others positing, of these two, only the objects of mathematics. The former two
kinds of substance are the subject of physics (for they imply movement); but the
third kind belongs to another science, if there is no principle common to it and
to the other kinds.
2
Sensible substance is changeable. Now if change
proceeds from opposites or from intermediates, and not from all opposites (for
the voice is not-white, but it does not therefore change to white), but from the
contrary, there must be something underlying which changes into the contrary
state; for the contraries do not change. Further, something persists, but the
contrary does not persist; there is, then, some third thing besides the
contraries, viz. the matter. Now since changes are of four kinds – either in
respect of the ‘what’ or of the quality or of the quantity or of the place, and
change in respect of ‘thisness’ is simple generation and destruction, and change
in quantity is increase and diminution, and change in respect of an affection is
alteration, and change of place is motion, changes will be from given states
into those contrary to them in these several respects. The matter, then, which
changes must be capable of both states. And since that which ‘is’ has two
senses, we must say that everything changes from that which is potentially to
that which is actually, e.g. from potentially white to actually white, and
similarly in the case of increase and diminution. Therefore not only can a thing
come to be, incidentally, out of that which is not, but also all things come to
be out of that which is, but is potentially, and is not actually. And this is
the ‘One’ of Anaxagoras; for instead of ‘all things were together’ – and the
‘Mixture’ of Empedocles and Anaximander and the account given by Democritus – it
is better to say ‘all things were together potentially but not actually’.
Therefore these thinkers seem to have had some notion of matter. Now all things
that change have matter, but different matter; and of eternal things those which
are not generable but are movable in space have matter – not matter for
generation, however, but for motion from one place to
another.
One might raise the question from what sort of
non-being generation proceeds; for ‘non-being’ has three senses. If, then, one
form of non-being exists potentially, still it is not by virtue of a
potentiality for any and every thing, but different things come from different
things; nor is it satisfactory to say that ‘all things were together’; for they
differ in their matter, since otherwise why did an infinity of things come to
be, and not one thing? For ‘reason’ is one, so that if matter also were one,
that must have come to be in actuality which the matter was in potency. The
causes and the principles, then, are three, two being the pair of contraries of
which one is definition and form and the other is privation, and the third being
the matter.
3
Note, next, that neither the matter nor the
form comes to be – and I mean the last matter and form. For everything that
changes is something and is changed by something and into something. That by
which it is changed is the immediate mover; that which is changed, the matter;
that into which it is changed, the form. The process, then, will go on to
infinity, if not only the bronze comes to be round but also the round or the
bronze comes to be; therefore there must be a stop.
Note, next, that each substance comes into
being out of something that shares its name. (Natural objects and other things
both rank as substances.) For things come into being either by art or by nature
or by luck or by spontaneity. Now art is a principle of movement in something
other than the thing moved, nature is a principle in the thing itself (for man
begets man), and the other causes are privations of these
two.
There are three kinds of substance – the
matter, which is a ‘this’ in appearance (for all things that are characterized
by contact and not, by organic unity are matter and substratum, e.g. fire,
flesh, head; for these are all matter, and the last matter is the matter of that
which is in the full sense substance); the nature, which is a ‘this’ or positive
state towards which movement takes place; and again, thirdly, the particular
substance which is composed of these two, e.g. Socrates or Callias. Now in some
cases the ‘this’ does not exist apart from the composite substance, e.g. the
form of house does not so exist, unless the art of building exists apart (nor is
there generation and destruction of these forms, but it is in another way that
the house apart from its matter, and health, and all ideals of art, exist and do
not exist); but if the ‘this’ exists apart from the concrete thing, it is only
in the case of natural objects. And so Plato was not far wrong when he said that
there are as many Forms as there are kinds of natural object (if there are Forms
distinct from the things of this earth). The moving causes exist as things
preceding the effects, but causes in the sense of definitions are simultaneous
with their effects. For when a man is healthy, then health also exists; and the
shape of a bronze sphere exists at the same time as the bronze sphere. (But we
must examine whether any form also survives afterwards. For in some cases there
is nothing to prevent this; e.g. the soul may be of this sort – not all soul but
the reason; for presumably it is impossible that all soul should survive.)
Evidently then there is no necessity, on this ground at least, for the existence
of the Ideas. For man is begotten by man, a given man by an individual father;
and similarly in the arts; for the medical art is the formal cause of
health.
4
The causes and the principles of different
things are in a sense different, but in a sense, if one speaks universally and
analogically, they are the same for all. For one might raise the question
whether the principles and elements are different or the same for substances and
for relative terms, and similarly in the case of each of the categories. But it
would be paradoxical if they were the same for all. For then from the same
elements will proceed relative terms and substances. What then will this common
element be? For (1) (a) there is nothing common to and distinct from substance
and the other categories, viz. those which are predicated; but an element is
prior to the things of which it is an element. But again (b) substance is not an
element in relative terms, nor is any of these an element in substance. Further,
(2) how can all things have the same elements? For none of the elements can be
the same as that which is composed of elements, e.g. b or a cannot be the same
as ba. (None, therefore, of the intelligibles, e.g. being or unity, is an
element; for these are predicable of each of the compounds as well.) None of the
elements, then, will be either a substance or a relative term; but it must be
one or other. All things, then, have not the same
elements.
Or, as we are wont to put it, in a sense they
have and in a sense they have not; e.g. perhaps the elements of perceptible
bodies are, as form, the hot, and in another sense the cold, which is the
privation; and, as matter, that which directly and of itself potentially has
these attributes; and substances comprise both these and the things composed of
these, of which these are the principles, or any unity which is produced out of
the hot and the cold, e.g. flesh or bone; for the product must be different from
the elements. These things then have the same elements and principles (though
specifically different things have specifically different elements); but all
things have not the same elements in this sense, but only analogically; i.e. one
might say that there are three principles – the form, the privation, and the
matter. But each of these is different for each class; e.g. in colour they are
white, black, and surface, and in day and night they are light, darkness, and
air.
Since not only the elements present in a thing
are causes, but also something external, i.e. the moving cause, clearly while
‘principle’ and ‘element’ are different both are causes, and ‘principle’ is
divided into these two kinds; and that which acts as producing movement or rest
is a principle and a substance. Therefore analogically there are three elements,
and four causes and principles; but the elements are different in different
things, and the proximate moving cause is different for different things.
Health, disease, body; the moving cause is the medical art. Form, disorder of a
particular kind, bricks; the moving cause is the building art. And since the
moving cause in the case of natural things is – for man, for instance, man, and
in the products of thought the form or its contrary, there will be in a sense
three causes, while in a sense there are four. For the medical art is in some
sense health, and the building art is the form of the house, and man begets man;
further, besides these there is that which as first of all things moves all
things.
5
Some things can exist apart and some cannot,
and it is the former that are substances. And therefore all things have the same
causes, because, without substances, modifications and movements do not exist.
Further, these causes will probably be soul and body, or reason and desire and
body.
And in yet another way, analogically identical
things are principles, i.e. actuality and potency; but these also are not only
different for different things but also apply in different ways to them. For in
some cases the same thing exists at one time actually and at another
potentially, e.g. wine or flesh or man does so. (And these too fall under the
above-named causes. For the form exists actually, if it can exist apart, and so
does the complex of form and matter, and the privation, e.g. darkness or
disease; but the matter exists potentially; for this is that which can become
qualified either by the form or by the privation.) But the distinction of
actuality and potentiality applies in another way to cases where the matter of
cause and of effect is not the same, in some of which cases the form is not the
same but different; e.g. the cause of man is (1) the elements in man (viz. fire
and earth as matter, and the peculiar form), and further (2) something else
outside, i.e. the father, and (3) besides these the sun and its oblique course,
which are neither matter nor form nor privation of man nor of the same species
with him, but moving causes.
Further, one must observe that some causes can
be expressed in universal terms, and some cannot. The proximate principles of
all things are the ‘this’ which is proximate in actuality, and another which is
proximate in potentiality. The universal causes, then, of which we spoke do not
exist. For it is the individual that is the originative principle of the
individuals. For while man is the originative principle of man universally,
there is no universal man, but Peleus is the originative principle of Achilles,
and your father of you, and this particular b of this particular ba, though b in
general is the originative principle of ba taken without
qualification.
Further, if the causes of substances are the
causes of all things, yet different things have different causes and elements,
as was said; the causes of things that are not in the same class, e.g. of
colours and sounds, of substances and quantities, are different except in an
analogical sense; and those of things in the same species are different, not in
species, but in the sense that the causes of different individuals are
different, your matter and form and moving cause being different from mine,
while in their universal definition they are the same. And if we inquire what
are the principles or elements of substances and relations and qualities –
whether they are the same or different – clearly when the names of the causes
are used in several senses the causes of each are the same, but when the senses
are distinguished the causes are not the same but different, except that in the
following senses the causes of all are the same. They are (1) the same or
analogous in this sense, that matter, form, privation, and the moving cause are
common to all things; and (2) the causes of substances may be treated as causes
of all things in this sense, that when substances are removed all things are
removed; further, (3) that which is first in respect of complete reality is the
cause of all things. But in another sense there are different first causes, viz.
all the contraries which are neither generic nor ambiguous terms; and, further,
the matters of different things are different. We have stated, then, what are
the principles of sensible things and how many they are, and in what sense they
are the same and in what sense different.
6
Since there were three kinds of substance, two
of them physical and one unmovable, regarding the latter we must assert that it
is necessary that there should be an eternal unmovable substance. For substances
are the first of existing things, and if they are all destructible, all things
are destructible. But it is impossible that movement should either have come
into being or cease to be (for it must always have existed), or that time
should. For there could not be a before and an after if time did not exist.
Movement also is continuous, then, in the sense in which time is; for time is
either the same thing as movement or an attribute of movement. And there is no
continuous movement except movement in place, and of this only that which is
circular is continuous.
But if there is something which is capable of
moving things or acting on them, but is not actually doing so, there will not
necessarily be movement; for that which has a potency need not exercise it.
Nothing, then, is gained even if we suppose eternal substances, as the believers
in the Forms do, unless there is to be in them some principle which can cause
change; nay, even this is not enough, nor is another substance besides the Forms
enough; for if it is not to act, there will be no movement. Further even if it
acts, this will not be enough, if its essence is potency; for there will not be
eternal movement, since that which is potentially may possibly not be. There
must, then, be such a principle, whose very essence is actuality. Further, then,
these substances must be without matter; for they must be eternal, if anything
is eternal. Therefore they must be actuality.
Yet there is a difficulty; for it is thought
that everything that acts is able to act, but that not everything that is able
to act acts, so that the potency is prior. But if this is so, nothing that is
need be; for it is possible for all things to be capable of existing but not yet
to exist.
Yet if we follow the theologians who generate
the world from night, or the natural philosophers who say that ‘all things were
together’, the same impossible result ensues. For how will there be movement, if
there is no actually existing cause? Wood will surely not move itself – the
carpenter’s art must act on it; nor will the menstrual blood nor the earth set
themselves in motion, but the seeds must act on the earth and the semen on the
menstrual blood.
This is why some suppose eternal actuality –
e.g. Leucippus and Plato; for they say there is always movement. But why and
what this movement is they do say, nor, if the world moves in this way or that,
do they tell us the cause of its doing so. Now nothing is moved at random, but
there must always be something present to move it; e.g. as a matter of fact a
thing moves in one way by nature, and in another by force or through the
influence of reason or something else. (Further, what sort of movement is
primary? This makes a vast difference.) But again for Plato, at least, it is not
permissible to name here that which he sometimes supposes to be the source of
movement – that which moves itself; for the soul is later, and coeval with the
heavens, according to his account. To suppose potency prior to actuality, then,
is in a sense right, and in a sense not; and we have specified these senses.
That actuality is prior is testified by Anaxagoras (for his ‘reason’ is
actuality) and by Empedocles in his doctrine of love and strife, and by those
who say that there is always movement, e.g. Leucippus. Therefore chaos or night
did not exist for an infinite time, but the same things have always existed
(either passing through a cycle of changes or obeying some other law), since
actuality is prior to potency. If, then, there is a constant cycle, something
must always remain, acting in the same way. And if there is to be generation and
destruction, there must be something else which is always acting in different
ways. This must, then, act in one way in virtue of itself, and in another in
virtue of something else – either of a third agent, therefore, or of the first.
Now it must be in virtue of the first. For otherwise this again causes the
motion both of the second agent and of the third. Therefore it is better to say
‘the first’. For it was the cause of eternal uniformity; and something else is
the cause of variety, and evidently both together are the cause of eternal
variety. This, accordingly, is the character which the motions actually exhibit.
What need then is there to seek for other principles?
7
Since (1) this is a possible account of the
matter, and (2) if it were not true, the world would have proceeded out of night
and ‘all things together’ and out of non-being, these difficulties may be taken
as solved. There is, then, something which is always moved with an unceasing
motion, which is motion in a circle; and this is plain not in theory only but in
fact. Therefore the first heaven must be eternal. There is therefore also
something which moves it. And since that which moves and is moved is
intermediate, there is something which moves without being moved, being eternal,
substance, and actuality. And the object of desire and the object of thought
move in this way; they move without being moved. The primary objects of desire
and of thought are the same. For the apparent good is the object of appetite,
and the real good is the primary object of rational wish. But desire is
consequent on opinion rather than opinion on desire; for the thinking is the
starting-point. And thought is moved by the object of thought, and one of the
two columns of opposites is in itself the object of thought; and in this,
substance is first, and in substance, that which is simple and exists actually.
(The one and the simple are not the same; for ‘one’ means a measure, but
‘simple’ means that the thing itself has a certain nature.) But the beautiful,
also, and that which is in itself desirable are in the same column; and the
first in any class is always best, or analogous to the
best.
That a final cause may exist among unchangeable
entities is shown by the distinction of its meanings. For the final cause is (a)
some being for whose good an action is done, and (b) something at which the
action aims; and of these the latter exists among unchangeable entities though
the former does not. The final cause, then, produces motion as being loved, but
all other things move by being moved. Now if something is moved it is capable of
being otherwise than as it is. Therefore if its actuality is the primary form of
spatial motion, then in so far as it is subject to change, in this respect it is
capable of being otherwise, – in place, even if not in substance. But since
there is something which moves while itself unmoved, existing actually, this can
in no way be otherwise than as it is. For motion in space is the first of the
kinds of change, and motion in a circle the first kind of spatial motion; and
this the first mover produces. The first mover, then, exists of necessity; and
in so far as it exists by necessity, its mode of being is good, and it is in
this sense a first principle. For the necessary has all these senses – that
which is necessary perforce because it is contrary to the natural impulse, that
without which the good is impossible, and that which cannot be otherwise but can
exist only in a single way.
On such a principle, then, depend the heavens
and the world of nature. And it is a life such as the best which we enjoy, and
enjoy for but a short time (for it is ever in this state, which we cannot be),
since its actuality is also pleasure. (And for this reason are waking,
perception, and thinking most pleasant, and hopes and memories are so on account
of these.) And thinking in itself deals with that which is best in itself, and
that which is thinking in the fullest sense with that which is best in the
fullest sense. And thought thinks on itself because it shares the nature of the
object of thought; for it becomes an object of thought in coming into contact
with and thinking its objects, so that thought and object of thought are the
same. For that which is capable of receiving the object of thought, i.e. the
essence, is thought. But it is active when it possesses this object. Therefore
the possession rather than the receptivity is the divine element which thought
seems to contain, and the act of contemplation is what is most pleasant and
best. If, then, God is always in that good state in which we sometimes are, this
compels our wonder; and if in a better this compels it yet more. And God is in a
better state. And life also belongs to God; for the actuality of thought is
life, and God is that actuality; and God’s self-dependent actuality is life most
good and eternal. We say therefore that God is a living being, eternal, most
good, so that life and duration continuous and eternal belong to God; for this
is God.
Those who suppose, as the Pythagoreans and
Speusippus do, that supreme beauty and goodness are not present in the
beginning, because the beginnings both of plants and of animals are causes, but
beauty and completeness are in the effects of these, are wrong in their opinion.
For the seed comes from other individuals which are prior and complete, and the
first thing is not seed but the complete being; e.g. we must say that before the
seed there is a man, – not the man produced from the seed, but another from whom
the seed comes.
It is clear then from what has been said that
there is a substance which is eternal and unmovable and separate from sensible
things. It has been shown also that this substance cannot have any magnitude,
but is without parts and indivisible (for it produces movement through infinite
time, but nothing finite has infinite power; and, while every magnitude is
either infinite or finite, it cannot, for the above reason, have finite
magnitude, and it cannot have infinite magnitude because there is no infinite
magnitude at all). But it has also been shown that it is impassive and
unalterable; for all the other changes are posterior to change of
place.
8
It is clear, then, why these things are as they
are. But we must not ignore the question whether we have to suppose one such
substance or more than one, and if the latter, how many; we must also mention,
regarding the opinions expressed by others, that they have said nothing about
the number of the substances that can even be clearly stated. For the theory of
Ideas has no special discussion of the subject; for those who speak of Ideas say
the Ideas are numbers, and they speak of numbers now as unlimited, now as
limited by the number 10; but as for the reason why there should be just so many
numbers, nothing is said with any demonstrative exactness. We however must
discuss the subject, starting from the presuppositions and distinctions we have
mentioned. The first principle or primary being is not movable either in itself
or accidentally, but produces the primary eternal and single movement. But since
that which is moved must be moved by something, and the first mover must be in
itself unmovable, and eternal movement must be produced by something eternal and
a single movement by a single thing, and since we see that besides the simple
spatial movement of the universe, which we say the first and unmovable substance
produces, there are other spatial movements – those of the planets – which are
eternal (for a body which moves in a circle is eternal and unresting; we have
proved these points in the physical treatises), each of these movements also
must be caused by a substance both unmovable in itself and eternal. For the
nature of the stars is eternal just because it is a certain kind of substance,
and the mover is eternal and prior to the moved, and that which is prior to a
substance must be a substance. Evidently, then, there must be substances which
are of the same number as the movements of the stars, and in their nature
eternal, and in themselves unmovable, and without magnitude, for the reason
before mentioned. That the movers are substances, then, and that one of these is
first and another second according to the same order as the movements of the
stars, is evident. But in the number of the movements we reach a problem which
must be treated from the standpoint of that one of the mathematical sciences
which is most akin to philosophy – viz. of astronomy; for this science
speculates about substance which is perceptible but eternal, but the other
mathematical sciences, i.e. arithmetic and geometry, treat of no substance. That
the movements are more numerous than the bodies that are moved is evident to
those who have given even moderate attention to the matter; for each of the
planets has more than one movement. But as to the actual number of these
movements, we now – to give some notion of the subject – quote what some of the
mathematicians say, that our thought may have some definite number to grasp;
but, for the rest, we must partly investigate for ourselves, Partly learn from
other investigators, and if those who study this subject form an opinion
contrary to what we have now stated, we must esteem both parties indeed, but
follow the more accurate.
Eudoxus supposed that the motion of the sun or
of the moon involves, in either case, three spheres, of which the first is the
sphere of the fixed stars, and the second moves in the circle which runs along
the middle of the zodiac, and the third in the circle which is inclined across
the breadth of the zodiac; but the circle in which the moon moves is inclined at
a greater angle than that in which the sun moves. And the motion of the planets
involves, in each case, four spheres, and of these also the first and second are
the same as the first two mentioned above (for the sphere of the fixed stars is
that which moves all the other spheres, and that which is placed beneath this
and has its movement in the circle which bisects the zodiac is common to all),
but the poles of the third sphere of each planet are in the circle which bisects
the zodiac, and the motion of the fourth sphere is in the circle which is
inclined at an angle to the equator of the third sphere; and the poles of the
third sphere are different for each of the other planets, but those of Venus and
Mercury are the same.
Callippus made the position of the spheres the
same as Eudoxus did, but while he assigned the same number as Eudoxus did to
Jupiter and to Saturn, he thought two more spheres should be added to the sun
and two to the moon, if one is to explain the observed facts; and one more to
each of the other planets.
But it is necessary, if all the spheres
combined are to explain the observed facts, that for each of the planets there
should be other spheres (one fewer than those hitherto assigned) which
counteract those already mentioned and bring back to the same position the
outermost sphere of the star which in each case is situated below the star in
question; for only thus can all the forces at work produce the observed motion
of the planets. Since, then, the spheres involved in the movement of the planets
themselves are – eight for Saturn and Jupiter and twenty-five for the others,
and of these only those involved in the movement of the lowest-situated planet
need not be counteracted the spheres which counteract those of the outermost two
planets will be six in number, and the spheres which counteract those of the
next four planets will be sixteen; therefore the number of all the spheres –
both those which move the planets and those which counteract these – will be
fifty-five. And if one were not to add to the moon and to the sun the movements
we mentioned, the whole set of spheres will be forty-seven in
number.
Let this, then, be taken as the number of the
spheres, so that the unmovable substances and principles also may probably be
taken as just so many; the assertion of necessity must be left to more powerful
thinkers. But if there can be no spatial movement which does not conduce to the
moving of a star, and if further every being and every substance which is immune
from change and in virtue of itself has attained to the best must be considered
an end, there can be no other being apart from these we have named, but this
must be the number of the substances. For if there are others, they will cause
change as being a final cause of movement; but there cannot he other movements
besides those mentioned. And it is reasonable to infer this from a consideration
of the bodies that are moved; for if everything that moves is for the sake of
that which is moved, and every movement belongs to something that is moved, no
movement can be for the sake of itself or of another movement, but all the
movements must be for the sake of the stars. For if there is to be a movement
for the sake of a movement, this latter also will have to be for the sake of
something else; so that since there cannot be an infinite regress, the end of
every movement will be one of the divine bodies which move through the
heaven.
(Evidently there is but one heaven. For if
there are many heavens as there are many men, the moving principles, of which
each heaven will have one, will be one in form but in number many. But all
things that are many in number have matter; for one and the same definition,
e.g. that of man, applies to many things, while Socrates is one. But the primary
essence has not matter; for it is complete reality. So the unmovable first mover
is one both in definition and in number; so too, therefore, is that which is
moved always and continuously; therefore there is one heaven alone.) Our
forefathers in the most remote ages have handed down to their posterity a
tradition, in the form of a myth, that these bodies are gods, and that the
divine encloses the whole of nature. The rest of the tradition has been added
later in mythical form with a view to the persuasion of the multitude and to its
legal and utilitarian expediency; they say these gods are in the form of men or
like some of the other animals, and they say other things consequent on and
similar to these which we have mentioned. But if one were to separate the first
point from these additions and take it alone – that they thought the first
substances to be gods, one must regard this as an inspired utterance, and
reflect that, while probably each art and each science has often been developed
as far as possible and has again perished, these opinions, with others, have
been preserved until the present like relics of the ancient treasure. Only thus
far, then, is the opinion of our ancestors and of our earliest predecessors
clear to us.
9
The nature of the divine thought involves
certain problems; for while thought is held to be the most divine of things
observed by us, the question how it must be situated in order to have that
character involves difficulties. For if it thinks of nothing, what is there here
of dignity? It is just like one who sleeps. And if it thinks, but this depends
on something else, then (since that which is its substance is not the act of
thinking, but a potency) it cannot be the best substance; for it is through
thinking that its value belongs to it. Further, whether its substance is the
faculty of thought or the act of thinking, what does it think of? Either of
itself or of something else; and if of something else, either of the same thing
always or of something different. Does it matter, then, or not, whether it
thinks of the good or of any chance thing? Are there not some things about which
it is incredible that it should think? Evidently, then, it thinks of that which
is most divine and precious, and it does not change; for change would be change
for the worse, and this would be already a movement. First, then, if ‘thought’
is not the act of thinking but a potency, it would be reasonable to suppose that
the continuity of its thinking is wearisome to it. Secondly, there would
evidently be something else more precious than thought, viz. that which is
thought of. For both thinking and the act of thought will belong even to one who
thinks of the worst thing in the world, so that if this ought to be avoided (and
it ought, for there are even some things which it is better not to see than to
see), the act of thinking cannot be the best of things. Therefore it must be of
itself that the divine thought thinks (since it is the most excellent of
things), and its thinking is a thinking on thinking.
But evidently knowledge and perception and
opinion and understanding have always something else as their object, and
themselves only by the way. Further, if thinking and being thought of are
different, in respect of which does goodness belong to thought? For to he an act
of thinking and to he an object of thought are not the same thing. We answer
that in some cases the knowledge is the object. In the productive sciences it is
the substance or essence of the object, matter omitted, and in the theoretical
sciences the definition or the act of thinking is the object. Since, then,
thought and the object of thought are not different in the case of things that
have not matter, the divine thought and its object will be the same, i.e. the
thinking will be one with the object of its thought.
A further question is left – whether the object
of the divine thought is composite; for if it were, thought would change in
passing from part to part of the whole. We answer that everything which has not
matter is indivisible – as human thought, or rather the thought of composite
beings, is in a certain period of time (for it does not possess the good at this
moment or at that, but its best, being something different from it, is attained
only in a whole period of time), so throughout eternity is the thought which has
itself for its object.
10
We must consider also in which of two ways the
nature of the universe contains the good, and the highest good, whether as
something separate and by itself, or as the order of the parts. Probably in both
ways, as an army does; for its good is found both in its order and in its
leader, and more in the latter; for he does not depend on the order but it
depends on him. And all things are ordered together somehow, but not all alike,
– both fishes and fowls and plants; and the world is not such that one thing has
nothing to do with another, but they are connected. For all are ordered together
to one end, but it is as in a house, where the freemen are least at liberty to
act at random, but all things or most things are already ordained for them,
while the slaves and the animals do little for the common good, and for the most
part live at random; for this is the sort of principle that constitutes the
nature of each. I mean, for instance, that all must at least come to be
dissolved into their elements, and there are other functions similarly in which
all share for the good of the whole.
We must not fail to observe how many impossible
or paradoxical results confront those who hold different views from our own, and
what are the views of the subtler thinkers, and which views are attended by
fewest difficulties. All make all things out of contraries. But neither ‘all
things’ nor ‘out of contraries’ is right; nor do these thinkers tell us how all
the things in which the contraries are present can be made out of the
contraries; for contraries are not affected by one another. Now for us this
difficulty is solved naturally by the fact that there is a third element. These
thinkers however make one of the two contraries matter; this is done for
instance by those who make the unequal matter for the equal, or the many matter
for the one. But this also is refuted in the same way; for the one matter which
underlies any pair of contraries is contrary to nothing. Further, all things,
except the one, will, on the view we are criticizing, partake of evil; for the
bad itself is one of the two elements. But the other school does not treat the
good and the bad even as principles; yet in all things the good is in the
highest degree a principle. The school we first mentioned is right in saying
that it is a principle, but how the good is a principle they do not say –whether
as end or as mover or as form.
Empedocles also has a paradoxical view; for he
identifies the good with love, but this is a principle both as mover (for it
brings things together) and as matter (for it is part of the mixture). Now even
if it happens that the same thing is a principle both as matter and as mover,
still the being, at least, of the two is not the same. In which respect then is
love a principle? It is paradoxical also that strife should be imperishable; the
nature of his ‘evil’ is just strife.
Anaxagoras makes the good a motive principle;
for his ‘reason’ moves things. But it moves them for an end, which must be
something other than it, except according to our way of stating the case; for,
on our view, the medical art is in a sense health. It is paradoxical also not to
suppose a contrary to the good, i.e. to reason. But all who speak of the
contraries make no use of the contraries, unless we bring their views into
shape. And why some things are perishable and others imperishable, no one tells
us; for they make all existing things out of the same principles. Further, some
make existing things out of the nonexistent; and others to avoid the necessity
of this make all things one.
Further, why should there always be becoming,
and what is the cause of becoming? – This no one tells us. And those who suppose
two principles must suppose another, a superior principle, and so must those who
believe in the Forms; for why did things come to participate, or why do they
participate, in the Forms? And all other thinkers are confronted by the
necessary consequence that there is something contrary to Wisdom, i.e. to the
highest knowledge; but we are not. For there is nothing contrary to that which
is primary; for all contraries have matter, and things that have matter exist
only potentially; and the ignorance which is contrary to any knowledge leads to
an object contrary to the object of the knowledge; but what is primary has no
contrary.
Again, if besides sensible things no others
exist, there will be no first principle, no order, no becoming, no heavenly
bodies, but each principle will have a principle before it, as in the accounts
of the theologians and all the natural philosophers. But if the Forms or the
numbers are to exist, they will be causes of nothing; or if not that, at least
not of movement. Further, how is extension, i.e. a continuum, to be produced out
of unextended parts? For number will not, either as mover or as form, produce a
continuum. But again there cannot be any contrary that is also essentially a
productive or moving principle; for it would be possible for it not to be. Or at
least its action would be posterior to its potency. The world, then, would not
be eternal. But it is; one of these premisses, then, must be denied. And we have
said how this must be done. Further, in virtue of what the numbers, or the soul
and the body, or in general the form and the thing, are one – of this no one
tells us anything; nor can any one tell, unless he says, as we do, that the
mover makes them one. And those who say mathematical number is first and go on
to generate one kind of substance after another and give different principles
for each, make the substance of the universe a mere series of episodes (for one
substance has no influence on another by its existence or nonexistence), and
they give us many governing principles; but the world refuses to be governed
badly.
‘The rule of many is not good; one ruler let
there be.’
1
We have stated what is the substance of
sensible things, dealing in the treatise on physics with matter, and later with
the substance which has actual existence. Now since our inquiry is whether there
is or is not besides the sensible substances any which is immovable and eternal,
and, if there is, what it is, we must first consider what is said by others, so
that, if there is anything which they say wrongly, we may not be liable to the
same objections, while, if there is any opinion common to them and us, we shall
have no private grievance against ourselves on that account; for one must be
content to state some points better than one’s predecessors, and others no
worse.
Two opinions are held on this subject; it is
said that the objects of mathematics – i.e. numbers and lines and the like – are
substances, and again that the Ideas are substances. And (1) since some
recognize these as two different classes – the Ideas and the mathematical
numbers, and (2) some recognize both as having one nature, while (3) some others
say that the mathematical substances are the only substances, we must consider
first the objects of mathematics, not qualifying them by any other
characteristic – not asking, for instance, whether they are in fact Ideas or
not, or whether they are the principles and substances of existing things or
not, but only whether as objects of mathematics they exist or not, and if they
exist, how they exist. Then after this we must separately consider the Ideas
themselves in a general way, and only as far as the accepted mode of treatment
demands; for most of the points have been repeatedly made even by the
discussions outside our school, and, further, the greater part of our account
must finish by throwing light on that inquiry, viz. when we examine whether the
substances and the principles of existing things are numbers and Ideas; for
after the discussion of the Ideas this remans as a third
inquiry.
If the objects of mathematics exist, they must
exist either in sensible objects, as some say, or separate from sensible objects
(and this also is said by some); or if they exist in neither of these ways,
either they do not exist, or they exist only in some special sense. So that the
subject of our discussion will be not whether they exist but how they
exist.
2
That it is impossible for mathematical objects
to exist in sensible things, and at the same time that the doctrine in question
is an artificial one, has been said already in our discussion of difficulties we
have pointed out that it is impossible for two solids to be in the same place,
and also that according to the same argument the other powers and
characteristics also should exist in sensible things and none of them
separately. This we have said already. But, further, it is obvious that on this
theory it is impossible for any body whatever to be divided; for it would have
to be divided at a plane, and the plane at a line, and the line at a point, so
that if the point cannot be divided, neither can the line, and if the line
cannot, neither can the plane nor the solid. What difference, then, does it make
whether sensible things are such indivisible entities, or, without being so
themselves, have indivisible entities in them? The result will be the same; if
the sensible entities are divided the others will be divided too, or else not
even the sensible entities can be divided.
But, again, it is not possible that such
entities should exist separately. For if besides the sensible solids there are
to be other solids which are separate from them and prior to the sensible
solids, it is plain that besides the planes also there must be other and
separate planes and points and lines; for consistency requires this. But if
these exist, again besides the planes and lines and points of the mathematical
solid there must be others which are separate. (For incomposites are prior to
compounds; and if there are, prior to the sensible bodies, bodies which are not
sensible, by the same argument the planes which exist by themselves must be
prior to those which are in the motionless solids. Therefore these will be
planes and lines other than those that exist along with the mathematical solids
to which these thinkers assign separate existence; for the latter exist along
with the mathematical solids, while the others are prior to the mathematical
solids.) Again, therefore, there will be, belonging to these planes, lines, and
prior to them there will have to be, by the same argument, other lines and
points; and prior to these points in the prior lines there will have to be other
points, though there will be no others prior to these. Now (1) the accumulation
becomes absurd; for we find ourselves with one set of solids apart from the
sensible solids; three sets of planes apart from the sensible planes – those
which exist apart from the sensible planes, and those in the mathematical
solids, and those which exist apart from those in the mathematical solids; four
sets of lines, and five sets of points. With which of these, then, will the
mathematical sciences deal? Certainly not with the planes and lines and points
in the motionless solid; for science always deals with what is prior. And (the
same account will apply also to numbers; for there will be a different set of
units apart from each set of points, and also apart from each set of realities,
from the objects of sense and again from those of thought; so that there will be
various classes of mathematical numbers.
Again, how is it possible to solve the
questions which we have already enumerated in our discussion of difficulties?
For the objects of astronomy will exist apart from sensible things just as the
objects of geometry will; but how is it possible that a heaven and its parts –
or anything else which has movement – should exist apart? Similarly also the
objects of optics and of harmonics will exist apart; for there will be both
voice and sight besides the sensible or individual voices and sights. Therefore
it is plain that the other senses as well, and the other objects of sense, will
exist apart; for why should one set of them do so and another not? And if this
is so, there will also be animals existing apart, since there will be
senses.
Again, there are certain mathematical theorems
that are universal, extending beyond these substances. Here then we shall have
another intermediate substance separate both from the Ideas and from the
intermediates, – a substance which is neither number nor points nor spatial
magnitude nor time. And if this is impossible, plainly it is also impossible
that the former entities should exist separate from sensible
things.
And, in general, conclusion contrary alike to
the truth and to the usual views follow, if one is to suppose the objects of
mathematics to exist thus as separate entities. For because they exist thus they
must be prior to sensible spatial magnitudes, but in truth they must be
posterior; for the incomplete spatial magnitude is in the order of generation
prior, but in the order of substance posterior, as the lifeless is to the
living.
Again, by virtue of what, and when, will
mathematical magnitudes be one? For things in our perceptible world are one in
virtue of soul, or of a part of soul, or of something else that is reasonable
enough; when these are not present, the thing is a plurality, and splits up into
parts. But in the case of the subjects of mathematics, which are divisible and
are quantities, what is the cause of their being one and holding
together?
Again, the modes of generation of the objects
of mathematics show that we are right. For the dimension first generated is
length, then comes breadth, lastly depth, and the process is complete. If, then,
that which is posterior in the order of generation is prior in the order of
substantiality, the solid will be prior to the plane and the line. And in this
way also it is both more complete and more whole, because it can become animate.
How, on the other hand, could a line or a plane be animate? The supposition
passes the power of our senses.
Again, the solid is a sort of substance; for it
already has in a sense completeness. But how can lines be substances? Neither as
a form or shape, as the soul perhaps is, nor as matter, like the solid; for we
have no experience of anything that can be put together out of lines or planes
or points, while if these had been a sort of material substance, we should have
observed things which could be put together out of them.
Grant, then, that they are prior in definition.
Still not all things that are prior in definition are also prior in
substantiality. For those things are prior in substantiality which when
separated from other things surpass them in the power of independent existence,
but things are prior in definition to those whose definitions are compounded out
of their definitions; and these two properties are not coextensive. For if
attributes do not exist apart from the substances (e.g. a ‘mobile’ or a pale’),
pale is prior to the pale man in definition, but not in substantiality. For it
cannot exist separately, but is always along with the concrete thing; and by the
concrete thing I mean the pale man. Therefore it is plain that neither is the
result of abstraction prior nor that which is produced by adding determinants
posterior; for it is by adding a determinant to pale that we speak of the pale
man.
It has, then, been sufficiently pointed out
that the objects of mathematics are not substances in a higher degree than
bodies are, and that they are not prior to sensibles in being, but only in
definition, and that they cannot exist somewhere apart. But since it was not
possible for them to exist in sensibles either, it is plain that they either do
not exist at all or exist in a special sense and therefore do not ‘exist’
without qualification. For ‘exist’ has many senses.
3
For just as the universal propositions of
mathematics deal not with objects which exist separately, apart from extended
magnitudes and from numbers, but with magnitudes and numbers, not however qua
such as to have magnitude or to be divisible, clearly it is possible that there
should also be both propositions and demonstrations about sensible magnitudes,
not however qua sensible but qua possessed of certain definite qualities. For as
there are many propositions about things merely considered as in motion, apart
from what each such thing is and from their accidents, and as it is not
therefore necessary that there should be either a mobile separate from
sensibles, or a distinct mobile entity in the sensibles, so too in the case of
mobiles there will be propositions and sciences, which treat them however not
qua mobile but only qua bodies, or again only qua planes, or only qua lines, or
qua divisibles, or qua indivisibles having position, or only qua indivisibles.
Thus since it is true to say without qualification that not only things which
are separable but also things which are inseparable exist (for instance, that
mobiles exist), it is true also to say without qualification that the objects of
mathematics exist, and with the character ascribed to them by mathematicians.
And as it is true to say of the other sciences too, without qualification, that
they deal with such and such a subject – not with what is accidental to it (e.g.
not with the pale, if the healthy thing is pale, and the science has the healthy
as its subject), but with that which is the subject of each science – with the
healthy if it treats its object qua healthy, with man if qua man: – so too is it
with geometry; if its subjects happen to be sensible, though it does not treat
them qua sensible, the mathematical sciences will not for that reason be
sciences of sensibles – nor, on the other hand, of other things separate from
sensibles. Many properties attach to things in virtue of their own nature as
possessed of each such character; e.g. there are attributes peculiar to the
animal qua female or qua male (yet there is no ‘female’ nor ‘male’ separate from
animals); so that there are also attributes which belong to things merely as
lengths or as planes. And in proportion as we are dealing with things which are
prior in definition and simpler, our knowledge has more accuracy, i.e.
simplicity. Therefore a science which abstracts from spatial magnitude is more
precise than one which takes it into account; and a science is most precise if
it abstracts from movement, but if it takes account of movement, it is most
precise if it deals with the primary movement, for this is the simplest; and of
this again uniform movement is the simplest form.
The same account may be given of harmonics and
optics; for neither considers its objects qua sight or qua voice, but qua lines
and numbers; but the latter are attributes proper to the former. And mechanics
too proceeds in the same way. Therefore if we suppose attributes separated from
their fellow attributes and make any inquiry concerning them as such, we shall
not for this reason be in error, any more than when one draws a line on the
ground and calls it a foot long when it is not; for the error is not included in
the premisses.
Each question will be best investigated in this
way – by setting up by an act of separation what is not separate, as the
arithmetician and the geometer do. For a man qua man is one indivisible thing;
and the arithmetician supposed one indivisible thing, and then considered
whether any attribute belongs to a man qua indivisible. But the geometer treats
him neither qua man nor qua indivisible, but as a solid. For evidently the
properties which would have belonged to him even if perchance he had not been
indivisible, can belong to him even apart from these attributes. Thus, then,
geometers speak correctly; they talk about existing things, and their subjects
do exist; for being has two forms – it exists not only in complete reality but
also materially.
Now since the good and the beautiful are
different (for the former always implies conduct as its subject, while the
beautiful is found also in motionless things), those who assert that the
mathematical sciences say nothing of the beautiful or the good are in error. For
these sciences say and prove a great deal about them; if they do not expressly
mention them, but prove attributes which are their results or their definitions,
it is not true to say that they tell us nothing about them. The chief forms of
beauty are order and symmetry and definiteness, which the mathematical sciences
demonstrate in a special degree. And since these (e.g. order and definiteness)
are obviously causes of many things, evidently these sciences must treat this
sort of causative principle also (i.e. the beautiful) as in some sense a cause.
But we shall speak more plainly elsewhere about these
matters.
4
So much then for the objects of mathematics; we
have said that they exist and in what sense they exist, and in what sense they
are prior and in what sense not prior. Now, regarding the Ideas, we must first
examine the ideal theory itself, not connecting it in any way with the nature of
numbers, but treating it in the form in which it was originally understood by
those who first maintained the existence of the Ideas. The supporters of the
ideal theory were led to it because on the question about the truth of things
they accepted the Heraclitean sayings which describe all sensible things as ever
passing away, so that if knowledge or thought is to have an object, there must
be some other and permanent entities, apart from those which are sensible; for
there could be no knowledge of things which were in a state of flux. But when
Socrates was occupying himself with the excellences of character, and in
connexion with them became the first to raise the problem of universal
definition (for of the physicists Democritus only touched on the subject to a
small extent, and defined, after a fashion, the hot and the cold; while the
Pythagoreans had before this treated of a few things, whose definitions – e.g.
those of opportunity, justice, or marriage – they connected with numbers; but it
was natural that Socrates should be seeking the essence, for he was seeking to
syllogize, and ‘what a thing is’ is the starting-point of syllogisms; for there
was as yet none of the dialectical power which enables people even without
knowledge of the essence to speculate about contraries and inquire whether the
same science deals with contraries; for two things may be fairly ascribed to
Socrates – inductive arguments and universal definition, both of which are
concerned with the starting-point of science): – but Socrates did not make the
universals or the definitions exist apart: they, however, gave them separate
existence, and this was the kind of thing they called Ideas. Therefore it
followed for them, almost by the same argument, that there must be Ideas of all
things that are spoken of universally, and it was almost as if a man wished to
count certain things, and while they were few thought he would not be able to
count them, but made more of them and then counted them; for the Forms are, one
may say, more numerous than the particular sensible things, yet it was in
seeking the causes of these that they proceeded from them to the Forms. For to
each thing there answers an entity which has the same name and exists apart from
the substances, and so also in the case of all other groups there is a one over
many, whether these be of this world or eternal.
Again, of the ways in which it is proved that
the Forms exist, none is convincing; for from some no inference necessarily
follows, and from some arise Forms even of things of which they think there are
no Forms. For according to the arguments from the sciences there will be Forms
of all things of which there are sciences, and according to the argument of the
‘one over many’ there will be Forms even of negations, and according to the
argument that thought has an object when the individual object has perished,
there will be Forms of perishable things; for we have an image of these. Again,
of the most accurate arguments, some lead to Ideas of relations, of which they
say there is no independent class, and others introduce the ‘third
man’.
And in general the arguments for the Forms
destroy things for whose existence the believers in Forms are more zealous than
for the existence of the Ideas; for it follows that not the dyad but number is
first, and that prior to number is the relative, and that this is prior to the
absolute – besides all the other points on which certain people, by following
out the opinions held about the Forms, came into conflict with the principles of
the theory.
Again, according to the assumption on the
belief in the Ideas rests, there will be Forms not only of substances but also
of many other things; for the concept is single not only in the case of
substances, but also in that of non-substances, and there are sciences of other
things than substance; and a thousand other such difficulties confront them. But
according to the necessities of the case and the opinions about the Forms, if
they can be shared in there must be Ideas of substances only. For they are not
shared in incidentally, but each Form must be shared in as something not
predicated of a subject. (By ‘being shared in incidentally’ I mean that if a
thing shares in ‘double itself’, it shares also in ‘eternal’, but incidentally;
for ‘the double’ happens to be eternal.) Therefore the Forms will be substance.
But the same names indicate substance in this and in the ideal world (or what
will be the meaning of saying that there is something apart from the particulars
– the one over many?). And if the Ideas and the things that share in them have
the same form, there will be something common: for why should ‘2’ be one and the
same in the perishable 2’s, or in the 2’s which are many but eternal, and not
the same in the ‘2 itself’ as in the individual 2? But if they have not the same
form, they will have only the name in common, and it is as if one were to call
both Callias and a piece of wood a ‘man’, without observing any community
between them.
But if we are to suppose that in other respects
the common definitions apply to the Forms, e.g. that ‘plane figure’ and the
other parts of the definition apply to the circle itself, but ‘what really is’
has to be added, we must inquire whether this is not absolutely meaningless. For
to what is this to be added? To ‘centre’ or to ‘plane’ or to all the parts of
the definition? For all the elements in the essence are Ideas, e.g. ‘animal’ and
‘two-footed’. Further, there must be some Ideal answering to ‘plane’ above, some
nature which will be present in all the Forms as their
genus.
5
Above all one might discuss the question what
in the world the Forms contribute to sensible things, either to those that are
eternal or to those that come into being and cease to be; for they cause neither
movement nor any change in them. But again they help in no wise either towards
the knowledge of other things (for they are not even the substance of these,
else they would have been in them), or towards their being, if they are not in
the individuals which share in them; though if they were, they might be thought
to be causes, as white causes whiteness in a white object by entering into its
composition. But this argument, which was used first by Anaxagoras, and later by
Eudoxus in his discussion of difficulties and by certain others, is very easily
upset; for it is easy to collect many and insuperable objections to such a
view.
But, further, all other things cannot come from
the Forms in any of the usual senses of ‘from’. And to say that they are
patterns and the other things share in them is to use empty words and poetical
metaphors. For what is it that works, looking to the Ideas? And any thing can
both be and come into being without being copied from something else, so that,
whether Socrates exists or not, a man like Socrates might come to be. And
evidently this might be so even if Socrates were eternal. And there will be
several patterns of the same thing, and therefore several Forms; e.g. ‘animal’
and ‘two-footed’, and also ‘man-himself’, will be Forms of man. Again, the Forms
are patterns not only of sensible things, but of Forms themselves also; i.e. the
genus is the pattern of the various forms-of-a-genus; therefore the same thing
will be pattern and copy.
Again, it would seem impossible that substance
and that whose substance it is should exist apart; how, therefore, could the
Ideas, being the substances of things, exist apart?
In the Phaedo the case is stated in this way –
that the Forms are causes both of being and of becoming. Yet though the Forms
exist, still things do not come into being, unless there is something to
originate movement; and many other things come into being (e.g. a house or a
ring) of which they say there are no Forms. Clearly therefore even the things of
which they say there are Ideas can both be and come into being owing to such
causes as produce the things just mentioned, and not owing to the Forms. But
regarding the Ideas it is possible, both in this way and by more abstract and
accurate arguments, to collect many objections like those we have
considered.
6
Since we have discussed these points, it is
well to consider again the results regarding numbers which confront those who
say that numbers are separable substances and first causes of things. If number
is an entity and its substance is nothing other than just number, as some say,
it follows that either (1) there is a first in it and a second, each being
different in species, – and either (a) this is true of the units without
exception, and any unit is inassociable with any unit, or (b) they are all
without exception successive, and any of them are associable with any, as they
say is the case with mathematical number; for in mathematical number no one unit
is in any way different from another. Or (c) some units must be associable and
some not; e.g. suppose that 2 is first after 1, and then comes 3 and then the
rest of the number series, and the units in each number are associable, e.g.
those in the first 2 are associable with one another, and those in the first 3
with one another, and so with the other numbers; but the units in the ‘2-itself’
are inassociable with those in the ‘3-itself’; and similarly in the case of the
other successive numbers. And so while mathematical number is counted thus –
after 1, 2 (which consists of another 1 besides the former 1), and 3 which
consists of another 1 besides these two), and the other numbers similarly, ideal
number is counted thus – after 1, a distinct 2 which does not include the first
1, and a 3 which does not include the 2 and the rest of the number series
similarly. Or (2) one kind of number must be like the first that was named, one
like that which the mathematicians speak of, and that which we have named last
must be a third kind.
Again, these kinds of numbers must either be
separable from things, or not separable but in objects of perception (not
however in the way which we first considered, in the sense that objects of
perception consists of numbers which are present in them) – either one kind and
not another, or all of them.
These are of necessity the only ways in which
the numbers can exist. And of those who say that the 1 is the beginning and
substance and element of all things, and that number is formed from the 1 and
something else, almost every one has described number in one of these ways; only
no one has said all the units are inassociable. And this has happened reasonably
enough; for there can be no way besides those mentioned. Some say both kinds of
number exist, that which has a before and after being identical with the Ideas,
and mathematical number being different from the Ideas and from sensible things,
and both being separable from sensible things; and others say mathematical
number alone exists, as the first of realities, separate from sensible things.
And the Pythagoreans, also, believe in one kind of number – the mathematical;
only they say it is not separate but sensible substances are formed out of it.
For they construct the whole universe out of numbers – only not numbers
consisting of abstract units; they suppose the units to have spatial magnitude.
But how the first 1 was constructed so as to have magnitude, they seem unable to
say.
Another thinker says the first kind of number,
that of the Forms, alone exists, and some say mathematical number is identical
with this.
The case of lines, planes, and solids is
similar. For some think that those which are the objects of mathematics are
different from those which come after the Ideas; and of those who express
themselves otherwise some speak of the objects of mathematics and in a
mathematical way – viz. those who do not make the Ideas numbers nor say that
Ideas exist; and others speak of the objects of mathematics, but not
mathematically; for they say that neither is every spatial magnitude divisible
into magnitudes, nor do any two units taken at random make 2. All who say the 1
is an element and principle of things suppose numbers to consist of abstract
units, except the Pythagoreans; but they suppose the numbers to have magnitude,
as has been said before. It is clear from this statement, then, in how many ways
numbers may be described, and that all the ways have been mentioned; and all
these views are impossible, but some perhaps more than
others.
7
First, then, let us inquire if the units are
associable or inassociable, and if inassociable, in which of the two ways we
distinguished. For it is possible that any unity is inassociable with any, and
it is possible that those in the ‘itself’ are inassociable with those in the
‘itself’, and, generally, that those in each ideal number are inassociable with
those in other ideal numbers. Now (1) all units are associable and without
difference, we get mathematical number – only one kind of number, and the Ideas
cannot be the numbers. For what sort of number will man-himself or animal-itself
or any other Form be? There is one Idea of each thing e.g. one of man-himself
and another one of animal-itself; but the similar and undifferentiated numbers
are infinitely many, so that any particular 3 is no more man-himself than any
other 3. But if the Ideas are not numbers, neither can they exist at all. For
from what principles will the Ideas come? It is number that comes from the 1 and
the indefinite dyad, and the principles or elements are said to be principles
and elements of number, and the Ideas cannot be ranked as either prior or
posterior to the numbers.
But (2) if the units are inassociable, and
inassociable in the sense that any is inassociable with any other, number of
this sort cannot be mathematical number; for mathematical number consists of
undifferentiated units, and the truths proved of it suit this character. Nor can
it be ideal number. For 2 will not proceed immediately from 1 and the indefinite
dyad, and be followed by the successive numbers, as they say ‘2,3,4’ for the
units in the ideal are generated at the same time, whether, as the first holder
of the theory said, from unequals (coming into being when these were equalized)
or in some other way – since, if one unit is to be prior to the other, it will
be prior also to 2 the composed of these; for when there is one thing prior and
another posterior, the resultant of these will be prior to one and posterior to
the other. Again, since the
1-itself is first, and then there is a particular 1 which is first among the
others and next after the 1-itself, and again a third which is next after the
second and next but one after the first 1, – so the units must be prior to the
numbers after which they are named when we count them; e.g. there will be a
third unit in 2 before 3 exists, and a fourth and a fifth in 3 before the
numbers 4 and 5 exist. – Now none of these thinkers has said the units are
inassociable in this way, but according to their principles it is reasonable
that they should be so even in this way, though in truth it is impossible. For
it is reasonable both that the units should have priority and posteriority if
there is a first unit or first 1, and also that the 2’s should if there is a
first 2; for after the first it is reasonable and necessary that there should be
a second, and if a second, a third, and so with the others successively. (And to
say both things at the same time, that a unit is first and another unit is
second after the ideal 1, and that a 2 is first after it, is impossible.) But
they make a first unit or 1, but not also a second and a third, and a first 2,
but not also a second and a third. Clearly, also, it is not possible, if all the
units are inassociable, that there should be a 2-itself and a 3-itself; and so
with the other numbers. For whether the units are undifferentiated or different
each from each, number must be counted by addition, e.g. 2 by adding another 1
to the one, 3 by adding another 1 to the two, and similarly. This being so,
numbers cannot be generated as they generate them, from the 2 and the 1; for 2
becomes part of 3 and 3 of 4 and the same happens in the case of the succeeding
numbers, but they say 4 came from the first 2 and the indefinite which makes it
two 2’s other than the 2-itself; if not, the 2-itself will be a part of 4 and
one other 2 will be added. And similarly 2 will consist of the 1-itself and
another 1; but if this is so, the other element cannot be an indefinite 2; for
it generates one unit, not, as the indefinite 2 does, a definite
2.
Again, besides the 3-itself and the 2-itself
how can there be other 3’s and 2’s? And how do they consist of prior and
posterior units? All this is absurd and fictitious, and there cannot be a first
2 and then a 3-itself. Yet there must, if the 1 and the indefinite dyad are to
be the elements. But if the results are impossible, it is also impossible that
these are the generating principles.
If the units, then, are differentiated, each
from each, these results and others similar to these follow of necessity. But
(3) if those in different numbers are differentiated, but those in the same
number are alone undifferentiated from one another, even so the difficulties
that follow are no less. E.g. in the 10-itself their are ten units, and the 10
is composed both of them and of two 5’s. But since the 10-itself is not any
chance number nor composed of any chance 5’s – or, for that matter, units – the
units in this 10 must differ. For if they do not differ, neither will the 5’s of
which the 10 consists differ; but since these differ, the units also will
differ. But if they differ, will there be no other 5’s in the 10 but only these
two, or will there be others? If there are not, this is paradoxical; and if
there are, what sort of 10 will consist of them? For there is no other in the 10
but the 10 itself. But it is actually necessary on their view that the 4 should
not consist of any chance 2’s; for the indefinite as they say, received the
definite 2 and made two 2’s; for its nature was to double what it
received.
Again, as to the 2 being an entity apart from
its two units, and the 3 an entity apart from its three units, how is this
possible? Either by one’s sharing in the other, as ‘pale man’ is different from
‘pale’ and ‘man’ (for it shares in these), or when one is a differentia of the
other, as ‘man’ is different from ‘animal’ and
‘two-footed’.
Again, some things are one by contact, some by
intermixture, some by position; none of which can belong to the units of which
the 2 or the 3 consists; but as two men are not a unity apart from both, so must
it be with the units. And their being indivisible will make no difference to
them; for points too are indivisible, but yet a pair of them is nothing apart
from the two.
But this consequence also we must not forget,
that it follows that there are prior and posterior 2 and similarly with the
other numbers. For let the 2’s in the 4 be simultaneous; yet these are prior to
those in the 8 and as the 2 generated them, they generated the 4’s in the
8-itself. Therefore if the first 2 is an Idea, these 2’s also will be Ideas of
some kind. And the same account applies to the units; for the units in the first
2 generate the four in 4, so that all the units come to be Ideas and an Idea
will be composed of Ideas. Clearly therefore those things also of which these
happen to be the Ideas will be composite, e.g. one might say that animals are
composed of animals, if there are Ideas of them.
In general, to differentiate the units in any
way is an absurdity and a fiction; and by a fiction I mean a forced statement
made to suit a hypothesis. For neither in quantity nor in quality do we see unit
differing from unit, and number must be either equal or unequal – all number but
especially that which consists of abstract units – so that if one number is
neither greater nor less than another, it is equal to it; but things that are
equal and in no wise differentiated we take to be the same when we are speaking
of numbers. If not, not even the 2 in the 10-itself will be undifferentiated,
though they are equal; for what reason will the man who alleges that they are
not differentiated be able to give?
Again, if every unit + another unit makes two,
a unit from the 2-itself and one from the 3-itself will make a 2. Now (a) this
will consist of differentiated units; and will it be prior to the 3 or
posterior? It rather seems that it must be prior; for one of the units is
simultaneous with the 3 and the other is simultaneous with the 2. And we, for
our part, suppose that in general 1 and 1, whether the things are equal or
unequal, is 2, e.g. the good and the bad, or a man and a horse; but those who
hold these views say that not even two units are 2.
If the number of the 3-itself is not greater
than that of the 2, this is surprising; and if it is greater, clearly there is
also a number in it equal to the 2, so that this is not different from the
2-itself. But this is not possible, if there is a first and a second
number.
Nor will the Ideas be numbers. For in this
particular point they are right who claim that the units must be different, if
there are to be Ideas; as has been said before. For the Form is unique; but if
the units are not different, the 2’s and the 3’s also will not be different.
This is also the reason why they must say that when we count thus – ‘1,2’ – we
do not proceed by adding to the given number; for if we do, neither will the
numbers be generated from the indefinite dyad, nor can a number be an Idea; for
then one Idea will be in another, and all Forms will be parts of one Form. And
so with a view to their hypothesis their statements are right, but as a whole
they are wrong; for their view is very destructive, since they will admit that
this question itself affords some difficulty – whether, when we count and say –
1,2,3 – we count by addition or by separate portions. But we do both; and so it
is absurd to reason back from this problem to so great a difference of
essence.
8
First of all it is well to determine what is
the differentia of a number – and of a unit, if it has a differentia. Units must
differ either in quantity or in quality; and neither of these seems to be
possible. But number qua number differs in quantity. And if the units also did
differ in quantity, number would differ from number, though equal in number of
units. Again, are the first units greater or smaller, and do the later ones
increase or diminish? All these are irrational suppositions. But neither can
they differ in quality. For no attribute can attach to them; for even to numbers
quality is said to belong after quantity. Again, quality could not come to them
either from the 1 or the dyad; for the former has no quality, and the latter
gives quantity; for this entity is what makes things to be many. If the facts
are really otherwise, they should state this quite at the beginning and
determine if possible, regarding the differentia of the unit, why it must exist,
and, failing this, what differentia they mean.
Evidently then, if the Ideas are numbers, the
units cannot all be associable, nor can they be inassociable in either of the
two ways. But neither is the way in which some others speak about numbers
correct. These are those who do not think there are Ideas, either without
qualification or as identified with certain numbers, but think the objects of
mathematics exist and the numbers are the first of existing things, and the
1-itself is the starting-point of them. It is paradoxical that there should be a
1 which is first of 1’s, as they say, but not a 2 which is first of 2’s, nor a 3
of 3’s; for the same reasoning applies to all. If, then, the facts with regard
to number are so, and one supposes mathematical number alone to exist, the 1 is
not the starting-point (for this sort of 1 must differ from the other units; and
if this is so, there must also be a 2 which is first of 2’s, and similarly with
the other successive numbers). But if the 1 is the starting-point, the truth
about the numbers must rather be what Plato used to say, and there must be a
first 2 and 3 and numbers must not be associable with one another. But if on the
other hand one supposes this, many impossible results, as we have said, follow.
But either this or the other must be the case, so that if neither is, number
cannot exist separately.
It is evident, also, from this that the third
version is the worst, – the view ideal and mathematical number is the same. For
two mistakes must then meet in the one opinion. (1) Mathematical number cannot
be of this sort, but the holder of this view has to spin it out by making
suppositions peculiar to himself. And (2) he must also admit all the
consequences that confront those who speak of number in the sense of
‘Forms’.
The Pythagorean version in one way affords
fewer difficulties than those before named, but in another way has others
peculiar to itself. For not thinking of number as capable of existing separately
removes many of the impossible consequences; but that bodies should be composed
of numbers, and that this should be mathematical number, is impossible. For it
is not true to speak of indivisible spatial magnitudes; and however much there
might be magnitudes of this sort, units at least have not magnitude; and how can
a magnitude be composed of indivisibles? But arithmetical number, at least,
consists of units, while these thinkers identify number with real things; at any
rate they apply their propositions to bodies as if they consisted of those
numbers.
If, then, it is necessary, if number is a
self-subsistent real thing, that it should exist in one of these ways which have
been mentioned, and if it cannot exist in any of these, evidently number has no
such nature as those who make it separable set up for it.
Again, does each unit come from the great and
the small, equalized, or one from the small, another from the great? (a) If the
latter, neither does each thing contain all the elements, nor are the units
without difference; for in one there is the great and in another the small,
which is contrary in its nature to the great. Again, how is it with the units in
the 3-itself? One of them is an odd unit. But perhaps it is for this reason that
they give 1-itself the middle place in odd numbers. (b) But if each of the two
units consists of both the great and the small, equalized, how will the 2 which
is a single thing, consist of the great and the small? Or how will it differ
from the unit? Again, the unit is prior to the 2; for when it is destroyed the 2
is destroyed. It must, then, be the Idea of an Idea since it is prior to an
Idea, and it must have come into being before it. From what, then? Not from the
indefinite dyad, for its function was to double.
Again, number must be either infinite or
finite; for these thinkers think of number as capable of existing separately, so
that it is not possible that neither of those alternatives should be true.
Clearly it cannot be infinite; for infinite number is neither odd nor even, but
the generation of numbers is always the generation either of an odd or of an
even number; in one way, when 1 operates on an even number, an odd number is
produced; in another way, when 2 operates, the numbers got from 1 by doubling
are produced; in another way, when the odd numbers operate, the other even
numbers are produced. Again, if every Idea is an Idea of something, and the
numbers are Ideas, infinite number itself will be an Idea of something, either
of some sensible thing or of something else. Yet this is not possible in view of
their thesis any more than it is reasonable in itself, at least if they arrange
the Ideas as they do.
But if number is finite, how far does it go?
With regard to this not only the fact but the reason should be stated. But if
number goes only up to 10 as some say, firstly the Forms will soon run short;
e.g. if 3 is man-himself, what number will be the horse-itself? The series of
the numbers which are the several things-themselves goes up to 10. It must,
then, be one of the numbers within these limits; for it is these that are
substances and Ideas. Yet they will run short; for the various forms of animal
will outnumber them. At the same time it is clear that if in this way the 3 is
man-himself, the other 3’s are so also (for those in identical numbers are
similar), so that there will be an infinite number of men; if each 3 is an Idea,
each of the numbers will be man-himself, and if not, they will at least be men.
And if the smaller number is part of the greater (being number of such a sort
that the units in the same number are associable), then if the 4-itself is an
Idea of something, e.g. of ‘horse’ or of ‘white’, man will be a part of horse,
if man is It is paradoxical also that there should be an Idea of 10 but not of
11, nor of the succeeding numbers. Again, there both are and come to be certain
things of which there are no Forms; why, then, are there not Forms of them also?
We infer that the Forms are not causes. Again, it is paradoxical – if the number
series up to 10 is more of a real thing and a Form than 10 itself. There is no
generation of the former as one thing, and there is of the latter. But they try
to work on the assumption that the series of numbers up to 10 is a complete
series. At least they generate the derivatives – e.g. the void, proportion, the
odd, and the others of this kind – within the decade. For some things, e.g.
movement and rest, good and bad, they assign to the originative principles, and
the others to the numbers. This is why they identify the odd with 1; for if the
odd implied 3 how would 5 be odd? Again, spatial magnitudes and all such things
are explained without going beyond a definite number; e.g. the first, the
indivisible, line, then the 2 &c.; these entities also extend only up to
10.
Again, if number can exist separately, one
might ask which is prior –1, or 3 or 2? Inasmuch as the number is composite, 1
is prior, but inasmuch as the universal and the form is prior, the number is
prior; for each of the units is part of the number as its matter, and the number
acts as form. And in a sense the right angle is prior to the acute, because it
is determinate and in virtue of its definition; but in a sense the acute is
prior, because it is a part and the right angle is divided into acute angles. As
matter, then, the acute angle and the element and the unit are prior, but in
respect of the form and of the substance as expressed in the definition, the
right angle, and the whole consisting of the matter and the form, are prior; for
the concrete thing is nearer to the form and to what is expressed in the
definition, though in generation it is later. How then is 1 the starting-point?
Because it is not divisiable, they say; but both the universal, and the
particular or the element, are indivisible. But they are starting-points in
different ways, one in definition and the other in time. In which way, then, is
1 the starting-point? As has been said, the right angle is thought to be prior
to the acute, and the acute to the right, and each is one. Accordingly they make
1 the starting-point in both ways. But this is impossible. For the universal is
one as form or substance, while the element is one as a part or as matter. For
each of the two is in a sense one – in truth each of the two units exists
potentially (at least if the number is a unity and not like a heap, i.e. if
different numbers consist of differentiated units, as they say), but not in
complete reality; and the cause of the error they fell into is that they were
conducting their inquiry at the same time from the standpoint of mathematics and
from that of universal definitions, so that (1) from the former standpoint they
treated unity, their first principle, as a point; for the unit is a point
without position. They put things together out of the smallest parts, as some
others also have done. Therefore the unit becomes the matter of numbers and at
the same time prior to 2; and again posterior, 2 being treated as a whole, a
unity, and a form. But (2) because they were seeking the universal they treated
the unity which can be predicated of a number, as in this sense also a part of
the number. But these characteristics cannot belong at the same time to the same
thing.
If the 1-itself must be unitary (for it differs
in nothing from other 1’s except that it is the starting-point), and the 2 is
divisible but the unit is not, the unit must be liker the 1-itself than the 2
is. But if the unit is liker it, it must be liker to the unit than to the 2;
therefore each of the units in 2 must be prior to the 2. But they deny this; at
least they generate the 2 first. Again, if the 2-itself is a unity and the
3-itself is one also, both form a 2. From what, then, is this 2
produced?
9
Since there is not contact in numbers, but
succession, viz. between the units between which there is nothing, e.g. between
those in 2 or in 3 one might ask whether these succeed the 1-itself or not, and
whether, of the terms that succeed it, 2 or either of the units in 2 is
prior.
Similar difficulties occur with regard to the
classes of things posterior to number, – the line, the plane, and the solid. For
some construct these out of the species of the ‘great and small’; e.g. lines
from the ‘long and short’, planes from the ‘broad and narrow’, masses from the
‘deep and shallow’; which are species of the ‘great and small’. And the
originative principle of such things which answers to the 1 different thinkers
describe in different ways, And in these also the impossibilities, the fictions,
and the contradictions of all probability are seen to be innumerable. For (i)
geometrical classes are severed from one another, unless the principles of these
are implied in one another in such a way that the ‘broad and narrow’ is also
‘long and short’ (but if this is so, the plane will be line and the solid a
plane; again, how will angles and figures and such things be explained?). And
(ii) the same happens as in regard to number; for ‘long and short’, &c., are
attributes of magnitude, but magnitude does not consist of these, any more than
the line consists of ‘straight and curved’, or solids of ‘smooth and
rough’.
(All these views share a difficulty which
occurs with regard to species-of-a-genus, when one posits the universals, viz.
whether it is animal-itself or something other than animal-itself that is in the
particular animal. True, if the universal is not separable from sensible things,
this will present no difficulty; but if the 1 and the numbers are separable, as
those who express these views say, it is not easy to solve the difficulty, if
one may apply the words ‘not easy’ to the impossible. For when we apprehend the
unity in 2, or in general in a number, do we apprehend a thing-itself or
something else?).
Some, then, generate spatial magnitudes from
matter of this sort, others from the point – and the point is thought by them to
be not 1 but something like 1 – and from other matter like plurality, but not
identical with it; about which principles none the less the same difficulties
occur. For if the matter is one, line and plane – and soli will be the same; for
from the same elements will come one and the same thing. But if the matters are
more than one, and there is one for the line and a second for the plane and
another for the solid, they either are implied in one another or not, so that
the same results will follow even so; for either the plane will not contain a
line or it will he a line.
Again, how number can consist of the one and
plurality, they make no attempt to explain; but however they express themselves,
the same objections arise as confront those who construct number out of the one
and the indefinite dyad. For the one view generates number from the universally
predicated plurality, and not from a particular plurality; and the other
generates it from a particular plurality, but the first; for 2 is said to be a
‘first plurality’. Therefore there is practically no difference, but the same
difficulties will follow, – is it intermixture or position or blending or
generation? and so on. Above all one might press the question ‘if each unit is
one, what does it come from?’ Certainly each is not the one-itself. It must,
then, come from the one itself and plurality, or a part of plurality. To say
that the unit is a plurality is impossible, for it is indivisible; and to
generate it from a part of plurality involves many other objections; for (a)
each of the parts must be indivisible (or it will be a plurality and the unit
will be divisible) and the elements will not be the one and plurality; for the
single units do not come from plurality and the one. Again, (,the holder of this
view does nothing but presuppose another number; for his plurality of
indivisibles is a number. Again, we must inquire, in view of this theory also,
whether the number is infinite or finite. For there was at first, as it seems, a
plurality that was itself finite, from which and from the one comes the finite
number of units. And there is another plurality that is plurality-itself and
infinite plurality; which sort of plurality, then, is the element which
co-operates with the one? One might inquire similarly about the point, i.e. the
element out of which they make spatial magnitudes. For surely this is not the
one and only point; at any rate, then, let them say out of what each of the
points is formed. Certainly not of some distance + the point-itself. Nor again
can there be indivisible parts of a distance, as the elements out of which the
units are said to be made are indivisible parts of plurality; for number
consists of indivisibles, but spatial magnitudes do not.
All these objections, then, and others of the
sort make it evident that number and spatial magnitudes cannot exist apart from
things. Again, the discord about numbers between the various versions is a sign
that it is the incorrectness of the alleged facts themselves that brings
confusion into the theories. For those who make the objects of mathematics alone
exist apart from sensible things, seeing the difficulty about the Forms and
their fictitiousness, abandoned ideal number and posited mathematical. But those
who wished to make the Forms at the same time also numbers, but did not see, if
one assumed these principles, how mathematical number was to exist apart from
ideal, made ideal and mathematical number the same in words, since in fact
mathematical number has been destroyed; for they state hypotheses peculiar to
themselves and not those of mathematics. And he who first supposed that the
Forms exist and that the Forms are numbers and that the objects of mathematics
exist, naturally separated the two. Therefore it turns out that all of them are
right in some respect, but on the whole not right. And they themselves confirm
this, for their statements do not agree but conflict. The cause is that their
hypotheses and their principles are false. And it is hard to make a good case
out of bad materials, according to Epicharmus: ‘as soon as ‘tis said, ‘tis seen
to be wrong.’
But regarding numbers the questions we have
raised and the conclusions we have reached are sufficient (for while he who is
already convinced might be further convinced by a longer discussion, one not yet
convinced would not come any nearer to conviction); regarding the first
principles and the first causes and elements, the views expressed by those who
discuss only sensible substance have been partly stated in our works on nature,
and partly do not belong to the present inquiry; but the views of those who
assert that there are other substances besides the sensible must be considered
next after those we have been mentioning. Since, then, some say that the Ideas
and the numbers are such substances, and that the elements of these are elements
and principles of real things, we must inquire regarding these what they say and
in what sense they say it.
Those who posit numbers only, and these
mathematical, must be considered later; but as regards those who believe in the
Ideas one might survey at the same time their way of thinking and the difficulty
into which they fall. For they at the same time make the Ideas universal and
again treat them as separable and as individuals. That this is not possible has
been argued before. The reason why those who described their substances as
universal combined these two characteristics in one thing, is that they did not
make substances identical with sensible things. They thought that the
particulars in the sensible world were a state of flux and none of them
remained, but that the universal was apart from these and something different.
And Socrates gave the impulse to this theory, as we said in our earlier
discussion, by reason of his definitions, but he did not separate universals
from individuals; and in this he thought rightly, in not separating them. This
is plain from the results; for without the universal it is not possible to get
knowledge, but the separation is the cause of the objections that arise with
regard to the Ideas. His successors, however, treating it as necessary, if there
are to be any substances besides the sensible and transient substances, that
they must be separable, had no others, but gave separate existence to these
universally predicated substances, so that it followed that universals and
individuals were almost the same sort of thing. This in itself, then, would be
one difficulty in the view we have mentioned.
10
Let us now mention a point which presents a
certain difficulty both to those who believe in the Ideas and to those who do
not, and which was stated before, at the beginning, among the problems. If we do
not suppose substances to be separate, and in the way in which individual things
are said to be separate, we shall destroy substance in the sense in which we
understand ‘substance’; but if we conceive substances to be separable, how are
we to conceive their elements and their principles?
If they are individual and not universal, (a)
real things will be just of the same number as the elements, and (b) the
elements will not be knowable. For (a) let the syllables in speech be
substances, and their elements elements of substances; then there must be only
one ‘ba’ and one of each of the syllables, since they are not universal and the
same in form but each is one in number and a ‘this’ and not a kind possessed of
a common name (and again they suppose that the ‘just what a thing is’ is in each
case one). And if the syllables are unique, so too are the parts of which they
consist; there will not, then, be more a’s than one, nor more than one of any of
the other elements, on the same principle on which an identical syllable cannot
exist in the plural number. But if this is so, there will not be other things
existing besides the elements, but only the elements.
(b) Again, the elements will not be even
knowable; for they are not universal, and knowledge is of universals. This is
clear from demonstrations and from definitions; for we do not conclude that this
triangle has its angles equal to two right angles, unless every triangle has its
angles equal to two right angles, nor that this man is an animal, unless every
man is an animal.
But if the principles are universal, either the
substances composed of them are also universal, or non-substance will be prior
to substance; for the universal is not a substance, but the element or principle
is universal, and the element or principle is prior to the things of which it is
the principle or element.
All these difficulties follow naturally, when
they make the Ideas out of elements and at the same time claim that apart from
the substances which have the same form there are Ideas, a single separate
entity. But if, e.g. in the case of the elements of speech, the a’s and the b’s
may quite well be many and there need be no a-itself and b-itself besides the
many, there may be, so far as this goes, an infinite number of similar
syllables. The statement that an knowledge is universal, so that the principles
of things must also be universal and not separate substances, presents indeed,
of all the points we have mentioned, the greatest difficulty, but yet the
statement is in a sense true, although in a sense it is not. For knowledge, like
the verb ‘to know’, means two things, of which one is potential and one actual.
The potency, being, as matter, universal and indefinite, deals with the
universal and indefinite; but the actuality, being definite, deals with a
definite object, being a ‘this’, it deals with a ‘this’. But per accidens sight
sees universal colour, because this individual colour which it sees is colour;
and this individual a which the grammarian investigates is an a. For if the
principles must be universal, what is derived from them must also be universal,
as in demonstrations; and if this is so, there will be nothing capable of
separate existence – i.e. no substance. But evidently in a sense knowledge is
universal, and in a sense it is not.
1
Regarding this kind of substance, what we have said must be taken as sufficient. All philosophers make the first principles contraries: as in natural things, so also in the case of unchangeable substances. But since there cannot be anything prior to the first principle of all things, the principle cannot be the principle and yet be an attribute of something else. To suggest this is like saying that the white is a first principle, not qua anything else but qua white, but yet that it is predicable of a subject, i.e. that its being white presupposes its being something else; this is absurd, for then that subject will be prior. But all things which are generated from their contraries involve an underlying subject; a subject, then, must be present in the case of contraries, if anywhere. All contraries, then, are always predicable of a subject, and none can exist apart, but just as appearances suggest that there is nothing contrary to substance, argument confirms this. No contrary, then, is the first principle of all things in the full sense; the first principle is something different.
But these thinkers make one of the contraries
matter, some making the unequal which they take to be the essence of
plurality-matter for the One, and others making plurality matter for the One.
(The former generate numbers out of the dyad of the unequal, i.e. of the great
and small, and the other thinker we have referred to generates them out of
plurality, while according to both it is generated by the essence of the One.)
For even the philosopher who says the unequal and the One are the elements, and
the unequal is a dyad composed of the great and small, treats the unequal, or
the great and the small, as being one, and does not draw the distinction that
they are one in definition, but not in number. But they do not describe rightly
even the principles which they call elements, for some name the great and the
small with the One and treat these three as elements of numbers, two being
matter, one the form; while others name the many and few, because the great and
the small are more appropriate in their nature to magnitude than to number; and
others name rather the universal character common to these – ‘that which exceeds
and that which is exceeded’. None of these varieties of opinion makes any
difference to speak of, in view of some of the consequences; they affect only
the abstract objections, which these thinkers take care to avoid because the
demonstrations they themselves offer are abstract, – with this exception, that
if the exceeding and the exceeded are the principles, and not the great and the
small, consistency requires that number should come from the elements before
does; for number is more universal than as the exceeding and the exceeded are
more universal than the great and the small. But as it is, they say one of these
things but do not say the other. Others oppose the different and the other to
the One, and others oppose plurality to the One. But if, as they claim, things
consist of contraries, and to the One either there is nothing contrary, or if
there is to be anything it is plurality, and the unequal is contrary to the
equal, and the different to the same, and the other to the thing itself, those
who oppose the One to plurality have most claim to plausibility, but even their
view is inadequate, for the One would on their view be a few; for plurality is
opposed to fewness, and the many to the few.
‘The one’ evidently means a measure. And in
every case there is some underlying thing with a distinct nature of its own,
e.g. in the scale a quarter-tone, in spatial magnitude a finger or a foot or
something of the sort, in rhythms a beat or a syllable; and similarly in gravity
it is a definite weight; and in the same way in all cases, in qualities a
quality, in quantities a quantity (and the measure is indivisible, in the former
case in kind, and in the latter to the sense); which implies that the one is not
in itself the substance of anything. And this is reasonable; for ‘the one’ means
the measure of some plurality, and ‘number’ means a measured plurality and a
plurality of measures. (Thus it is natural that one is not a number; for the
measure is not measures, but both the measure and the one are starting-points.)
The measure must always be some identical thing predicable of all the things it
measures, e.g. if the things are horses, the measure is ‘horse’, and if they are
men, ‘man’. If they are a man, a horse, and a god, the measure is perhaps
‘living being’, and the number of them will be a number of living beings. If the
things are ‘man’ and ‘pale’ and ‘walking’, these will scarcely have a number,
because all belong to a subject which is one and the same in number, yet the
number of these will be a number of ‘kinds’ or of some such
term.
Those who treat the unequal as one thing, and
the dyad as an indefinite compound of great and small, say what is very far from
being probable or possible. For (a) these are modifications and accidents,
rather than substrata, of numbers and magnitudes – the many and few of number,
and the great and small of magnitude – like even and odd, smooth and rough,
straight and curved. Again, (b) apart from this mistake, the great and the
small, and so on, must be relative to something; but what is relative is least
of all things a kind of entity or substance, and is posterior to quality and
quantity; and the relative is an accident of quantity, as was said, not its
matter, since something with a distinct nature of its own must serve as matter
both to the relative in general and to its parts and kinds. For there is nothing
either great or small, many or few, or, in general, relative to something else,
which without having a nature of its own is many or few, great or small, or
relative to something else. A sign that the relative is least of all a substance
and a real thing is the fact that it alone has no proper generation or
destruction or movement, as in respect of quantity there is increase and
diminution, in respect of quality alteration, in respect of place locomotion, in
respect of substance simple generation and destruction. In respect of relation
there is no proper change; for, without changing, a thing will be now greater
and now less or equal, if that with which it is compared has changed in
quantity. And (c) the matter of each thing, and therefore of substance, must be
that which is potentially of the nature in question; but the relative is neither
potentially nor actually substance. It is strange, then, or rather impossible,
to make not-substance an element in, and prior to, substance; for all the
categories are posterior to substance. Again, (d) elements are not predicated of
the things of which they are elements, but many and few are predicated both
apart and together of number, and long and short of the line, and both broad and
narrow apply to the plane. If there is a plurality, then, of which the one term,
viz. few, is always predicated, e.g. 2 (which cannot be many, for if it were
many, 1 would be few), there must be also one which is absolutely many, e.g. 10
is many (if there is no number which is greater than 10), or 10,000. How then,
in view of this, can number consist of few and many? Either both ought to be
predicated of it, or neither; but in fact only the one or the other is
predicated.
2
We must inquire generally, whether eternal
things can consist of elements. If they do, they will have matter; for
everything that consists of elements is composite. Since, then, even if a thing
exists for ever, out of that of which it consists it would necessarily also, if
it had come into being, have come into being, and since everything comes to be
what it comes to be out of that which is it potentially (for it could not have
come to be out of that which had not this capacity, nor could it consist of such
elements), and since the potential can be either actual or not, – this being so,
however everlasting number or anything else that has matter is, it must be
capable of not existing, just as that which is any number of years old is as
capable of not existing as that which is a day old; if this is capable of not
existing, so is that which has lasted for a time so long that it has no limit.
They cannot, then, be eternal, since that which is capable of not existing is
not eternal, as we had occasion to show in another context. If that which we are
now saying is true universally – that no substance is eternal unless it is
actuality – and if the elements are matter that underlies substance, no eternal
substance can have elements present in it, of which it
consists.
There are some who describe the element which
acts with the One as an indefinite dyad, and object to ‘the unequal’, reasonably
enough, because of the ensuing difficulties; but they have got rid only of those
objections which inevitably arise from the treatment of the unequal, i.e. the
relative, as an element; those which arise apart from this opinion must confront
even these thinkers, whether it is ideal number, or mathematical, that they
construct out of those elements.
There are many causes which led them off into
these explanations, and especially the fact that they framed the difficulty in
an obsolete form. For they thought that all things that are would be one (viz.
Being itself), if one did not join issue with and refute the saying of
Parmenides:
‘For never will this he proved, that things
that are not are.’
They thought it necessary to prove that that
which is not is; for only thus – of that which is and something else – could the
things that are be composed, if they are many.
But, first, if ‘being’ has many senses (for it
means sometimes substance, sometimes that it is of a certain quality, sometimes
that it is of a certain quantity, and at other times the other categories), what
sort of ‘one’, then, are all the things that are, if non-being is to be supposed
not to be? Is it the substances that are one, or the affections and similarly
the other categories as well, or all together – so that the ‘this’ and the
‘such’ and the ‘so much’ and the other categories that indicate each some one
class of being will all be one? But it is strange, or rather impossible, that
the coming into play of a single thing should bring it about that part of that
which is is a ‘this’, part a ‘such’, part a ‘so much’, part a
‘here’.
Secondly, of what sort of non-being and being
do the things that are consist? For ‘nonbeing’ also has many senses, since
‘being’ has; and ‘not being a man’ means not being a certain substance, ‘not
being straight’ not being of a certain quality, ‘not being three cubits long’
not being of a certain quantity. What sort of being and non-being, then, by
their union pluralize the things that are? This thinker means by the non-being
the union of which with being pluralizes the things that are, the false and the
character of falsity. This is also why it used to be said that we must assume
something that is false, as geometers assume the line which is not a foot long
to be a foot long. But this cannot be so. For neither do geometers assume
anything false (for the enunciation is extraneous to the inference), nor is it
non-being in this sense that the things that are are generated from or resolved
into. But since ‘non-being’ taken in its various cases has as many senses as
there are categories, and besides this the false is said not to be, and so is
the potential, it is from this that generation proceeds, man from that which is
not man but potentially man, and white from that which is not white but
potentially white, and this whether it is some one thing that is generated or
many.
The question evidently is, how being, in the
sense of ‘the substances’, is many; for the things that are generated are
numbers and lines and bodies. Now it is strange to inquire how being in the
sense of the ‘what’ is many, and not how either qualities or quantities are
many. For surely the indefinite dyad or ‘the great and the small’ is not a
reason why there should be two kinds of white or many colours or flavours or
shapes; for then these also would be numbers and units. But if they had attacked
these other categories, they would have seen the cause of the plurality in
substances also; for the same thing or something analogous is the cause. This
aberration is the reason also why in seeking the opposite of being and the one,
from which with being and the one the things that are proceed, they posited the
relative term (i.e. the unequal), which is neither the contrary nor the
contradictory of these, and is one kind of being as ‘what’ and quality also
are.
They should have asked this question also, how
relative terms are many and not one. But as it is, they inquire how there are
many units besides the first 1, but do not go on to inquire how there are many
unequals besides the unequal. Yet they use them and speak of great and small,
many and few (from which proceed numbers), long and short (from which proceeds
the line), broad and narrow (from which proceeds the plane), deep and shallow
(from which proceed solids); and they speak of yet more kinds of relative term.
What is the reason, then, why there is a plurality of
these?
It is necessary, then, as we say, to presuppose
for each thing that which is it potentially; and the holder of these views
further declared what that is which is potentially a ‘this’ and a substance but
is not in itself being – viz. that it is the relative (as if he had said ‘the
qualitative’), which is neither potentially the one or being, nor the negation
of the one nor of being, but one among beings. And it was much more necessary,
as we said, if he was inquiring how beings are many, not to inquire about those
in the same category – how there are many substances or many qualities – but how
beings as a whole are many; for some are substances, some modifications, some
relations. In the categories other than substance there is yet another problem
involved in the existence of plurality. Since they are not separable from
substances, qualities and quantities are many just because their substratum
becomes and is many; yet there ought to be a matter for each category; only it
cannot be separable from substances. But in the case of ‘thises’, it is possible
to explain how the ‘this’ is many things, unless a thing is to be treated as
both a ‘this’ and a general character. The difficulty arising from the facts
about substances is rather this, how there are actually many substances and not
one.
But further, if the ‘this’ and the quantitative
are not the same, we are not told how and why the things that are are many, but
how quantities are many. For all ‘number’ means a quantity, and so does the
‘unit’, unless it means a measure or the quantitatively indivisible. If, then,
the quantitative and the ‘what’ are different, we are not told whence or how the
‘what’ is many; but if any one says they are the same, he has to face many
inconsistencies.
One might fix one’s attention also on the
question, regarding the numbers, what justifies the belief that they exist. To
the believer in Ideas they provide some sort of cause for existing things, since
each number is an Idea, and the Idea is to other things somehow or other the
cause of their being; for let this supposition be granted them. But as for him
who does not hold this view because he sees the inherent objections to the Ideas
(so that it is not for this reason that he posits numbers), but who posits
mathematical number, why must we believe his statement that such number exists,
and of what use is such number to other things? Neither does he who says it
exists maintain that it is the cause of anything (he rather says it is a thing
existing by itself), nor is it observed to be the cause of anything; for the
theorems of arithmeticians will all be found true even of sensible things, as
was said before.
3
As for those, then, who suppose the Ideas to
exist and to be numbers, by their assumption in virtue of the method of setting
out each term apart from its instances – of the unity of each general term they
try at least to explain somehow why number must exist. Since their reasons,
however, are neither conclusive nor in themselves possible, one must not, for
these reasons at least, assert the existence of number. Again, the Pythagoreans,
because they saw many attributes of numbers belonging te sensible bodies,
supposed real things to be numbers – not separable numbers, however, but numbers
of which real things consist. But why? Because the attributes of numbers are
present in a musical scale and in the heavens and in many other things. Those,
however, who say that mathematical number alone exists cannot according to their
hypotheses say anything of this sort, but it used to be urged that these
sensible things could not be the subject of the sciences. But we maintain that
they are, as we said before. And it is evident that the objects of mathematics
do not exist apart; for if they existed apart their attributes would not have
been present in bodies. Now the Pythagoreans in this point are open to no
objection; but in that they construct natural bodies out of numbers, things that
have lightness and weight out of things that have not weight or lightness, they
seem to speak of another heaven and other bodies, not of the sensible. But those
who make number separable assume that it both exists and is separable because
the axioms would not be true of sensible things, while the statements of
mathematics are true and ‘greet the soul’; and similarly with the spatial
magnitudes of mathematics. It is evident, then, both that the rival theory will
say the contrary of this, and that the difficulty we raised just now, why if
numbers are in no way present in sensible things their attributes are present in
sensible things, has to be solved by those who hold these
views.
There are some who, because the point is the
limit and extreme of the line, the line of the plane, and the plane of the
solid, think there must be real things of this sort. We must therefore examine
this argument too, and see whether it is not remarkably weak. For (i) extremes
are not substances, but rather all these things are limits. For even walking,
and movement in general, has a limit, so that on their theory this will be a
‘this’ and a substance. But that is absurd. Not but what (ii) even if they are
substances, they will all be the substances of the sensible things in this
world; for it is to these that the argument applied. Why then should they be
capable of existing apart?
Again, if we are not too easily satisfied, we
may, regarding all number and the objects of mathematics, press this difficulty,
that they contribute nothing to one another, the prior to the posterior; for if
number did not exist, none the less spatial magnitudes would exist for those who
maintain the existence of the objects of mathematics only, and if spatial
magnitudes did not exist, soul and sensible bodies would exist. But the observed
facts show that nature is not a series of episodes, like a bad tragedy. As for
the believers in the Ideas, this difficulty misses them; for they construct
spatial magnitudes out of matter and number, lines out of the number planes
doubtless out of solids out of or they use other numbers, which makes no
difference. But will these magnitudes be Ideas, or what is their manner of
existence, and what do they contribute to things? These contribute nothing, as
the objects of mathematics contribute nothing. But not even is any theorem true
of them, unless we want to change the objects of mathematics and invent
doctrines of our own. But it is not hard to assume any random hypotheses and
spin out a long string of conclusions. These thinkers, then, are wrong in this
way, in wanting to unite the objects of mathematics with the Ideas. And those
who first posited two kinds of number, that of the Forms and that which is
mathematical, neither have said nor can say how mathematical number is to exist
and of what it is to consist. For they place it between ideal and sensible
number. If (i) it consists of the great and small, it will be the same as the
other-ideal-number (he makes spatial magnitudes out of some other small and
great). And if (ii) he names some other element, he will be making his elements
rather many. And if the principle of each of the two kinds of number is a 1,
unity will be something common to these, and we must inquire how the one is
these many things, while at the same time number, according to him, cannot be
generated except from one and an indefinite dyad.
All this is absurd, and conflicts both with
itself and with the probabilities, and we seem to see in it Simonides ‘long
rigmarole’ for the long rigmarole comes into play, like those of slaves, when
men have nothing sound to say. And the very elements – the great and the small –
seem to cry out against the violence that is done to them; for they cannot in
any way generate numbers other than those got from 1 by
doubling.
It is strange also to attribute generation to
things that are eternal, or rather this is one of the things that are
impossible. There need be no doubt whether the Pythagoreans attribute generation
to them or not; for they say plainly that when the one had been constructed,
whether out of planes or of surface or of seed or of elements which they cannot
express, immediately the nearest part of the unlimited began to be constrained
and limited by the limit. But since they are constructing a world and wish to
speak the language of natural science, it is fair to make some examination of
their physical theorics, but to let them off from the present inquiry; for we
are investigating the principles at work in unchangeable things, so that it is
numbers of this kind whose genesis we must study.
4
These thinkers say there is no generation of
the odd number, which evidently implies that there is generation of the even;
and some present the even as produced first from unequals – the great and the
small – when these are equalized. The inequality, then, must belong to them
before they are equalized. If they had always been equalized, they would not
have been unequal before; for there is nothing before that which is always.
Therefore evidently they are not giving their account of the generation of
numbers merely to assist contemplation of their nature.
A difficulty, and a reproach to any one who
finds it no difficulty, are contained in the question how the elements and the
principles are related to the good and the beautiful; the difficulty is this,
whether any of the elements is such a thing as we mean by the good itself and
the best, or this is not so, but these are later in origin than the elements.
The theologians seem to agree with some thinkers of the present day, who answer
the question in the negative, and say that both the good and the beautiful
appear in the nature of things only when that nature has made some progress.
(This they do to avoid a real objection which confronts those who say, as some
do, that the one is a first principle. The objection arises not from their
ascribing goodness to the first principle as an attribute, but from their making
the one a principle – and a principle in the sense of an element – and
generating number from the one.) The old poets agree with this inasmuch as they
say that not those who are first in time, e.g. Night and Heaven or Chaos or
Ocean, reign and rule, but Zeus. These poets, however, are led to speak thus
only because they think of the rulers of the world as changing; for those of
them who combine the two characters in that they do not use mythical language
throughout, e.g. Pherecydes and some others, make the original generating agent
the Best, and so do the Magi, and some of the later sages also, e.g. both
Empedocles and Anaxagoras, of whom one made love an element, and the other made
reason a principle. Of those who maintain the existence of the unchangeable
substances some say the One itself is the good itself; but they thought its
substance lay mainly in its unity.
This, then, is the problem, – which of the two
ways of speaking is right. It would be strange if to that which is primary and
eternal and most self-sufficient this very quality – self-sufficiency and
self-maintenance – belongs primarily in some other way than as a good. But
indeed it can be for no other reason indestructible or self-sufficient than
because its nature is good. Therefore to say that the first principle is good is
probably correct; but that this principle should be the One or, if not that, at
least an element, and an element of numbers, is impossible. Powerful objections
arise, to avoid which some have given up the theory (viz. those who agree that
the One is a first principle and element, but only of mathematical number). For
on this view all the units become identical with species of good, and there is a
great profusion of goods. Again, if the Forms are numbers, all the Forms are
identical with species of good. But let a man assume Ideas of anything he
pleases. If these are Ideas only of goods, the Ideas will not be substances; but
if the Ideas are also Ideas of substances, all animals and plants and all
individuals that share in Ideas will be good.
These absurdities follow, and it also follows
that the contrary element, whether it is plurality or the unequal, i.e. the
great and small, is the bad-itself. (Hence one thinker avoided attaching the
good to the One, because it would necessarily follow, since generation is from
contraries, that badness is the fundamental nature of plurality; while others
say inequality is the nature of the bad.) It follows, then, that all things
partake of the bad except one – the One itself, and that numbers partake of it
in a more undiluted form than spatial magnitudes, and that the bad is the space
in which the good is realized, and that it partakes in and desires that which
tends to destroy it; for contrary tends to destroy contrary. And if, as we were
saying, the matter is that which is potentially each thing, e.g. that of actual
fire is that which is potentially fire, the bad will be just the potentially
good.
All these objections, then, follow, partly
because they make every principle an element, partly because they make
contraries principles, partly because they make the One a principle, partly
because they treat the numbers as the first substances, and as capable of
existing apart, and as Forms.
5
If, then, it is equally impossible not to put
the good among the first principles and to put it among them in this way,
evidently the principles are not being correctly described, nor are the first
substances. Nor does any one conceive the matter correctly if he compares the
principles of the universe to that of animals and plants, on the ground that the
more complete always comes from the indefinite and incomplete – which is what
leads this thinker to say that this is also true of the first principles of
reality, so that the One itself is not even an existing thing. This is
incorrect, for even in this world of animals and plants the principles from
which these come are complete; for it is a man that produces a man, and the seed
is not first.
It is out of place, also, to generate place
simultaneously with the mathematical solids (for place is peculiar to the
individual things, and hence they are separate in place; but mathematical
objects are nowhere), and to say that they must be somewhere, but not say what
kind of thing their place is.
Those who say that existing things come from
elements and that the first of existing things are the numbers, should have
first distinguished the senses in which one thing comes from another, and then
said in which sense number comes from its first
principles.
By intermixture? But (1) not everything is
capable of intermixture, and (2) that which is produced by it is different from
its elements, and on this view the one will not remain separate or a distinct
entity; but they want it to be so.
By juxtaposition, like a syllable? But then (1)
the elements must have position; and (2) he who thinks of number will be able to
think of the unity and the plurality apart; number then will be this – a unit
and plurality, or the one and the unequal.
Again, coming from certain things means in one
sense that these are still to be found in the product, and in another that they
are not; which sense does number come from these elements? Only things that are
generated can come from elements which are present in them. Does number come,
then, from its elements as from seed? But nothing can be excreted from that
which is indivisible. Does it come from its contrary, its contrary not
persisting? But all things that come in this way come also from something else
which does persist. Since, then, one thinker places the 1 as contrary to
plurality, and another places it as contrary to the unequal, treating the 1 as
equal, number must be being treated as coming from contraries. There is, then,
something else that persists, from which and from one contrary the compound is
or has come to be. Again, why in the world do the other things that come from
contraries, or that have contraries, perish (even when all of the contrary is
used to produce them), while number does not? Nothing is said about this. Yet
whether present or not present in the compound the contrary destroys it, e.g.
‘strife’ destroys the ‘mixture’ (yet it should not; for it is not to that that
is contrary).
Once more, it has not been determined at all in
which way numbers are the causes of substances and of being – whether (1) as
boundaries (as points are of spatial magnitudes). This is how Eurytus decided
what was the number of what (e.g. one of man and another of horse), viz. by
imitating the figures of living things with pebbles, as some people bring
numbers into the forms of triangle and square. Or (2) is it because harmony is a
ratio of numbers, and so is man and everything else? But how are the attributes
– white and sweet and hot – numbers? Evidently it is not the numbers that are
the essence or the causes of the form; for the ratio is the essence, while the
number the causes of the form; for the ratio is the essence, while the number is
the matter. E.g. the essence of flesh or bone is number only in this way, ‘three
parts of fire and two of earth’. And a number, whatever number it is, is always
a number of certain things, either of parts of fire or earth or of units; but
the essence is that there is so much of one thing to so much of another in the
mixture; and this is no longer a number but a ratio of mixture of numbers,
whether these are corporeal or of any other kind.
Number, then, whether it be number in general
or the number which consists of abstract units, is neither the cause as agent,
nor the matter, nor the ratio and form of things. Nor, of course, is it the
final cause.
6
One might also raise the question what the good
is that things get from numbers because their composition is expressible by a
number, either by one which is easily calculable or by an odd number. For in
fact honey-water is no more wholesome if it is mixed in the proportion of three
times three, but it would do more good if it were in no particular ratio but
well diluted than if it were numerically expressible but strong. Again, the
ratios of mixtures are expressed by the adding of numbers, not by mere numbers;
e.g. it is ‘three parts to two’, not ‘three times two’. For in any
multiplication the genus of the things multiplied must be the same; therefore
the product 1x2x3 must be measurable by 1, and 4x5x6 by 4 and therefore all
products into which the same factor enters must be measurable by that factor.
The number of fire, then, cannot be 2x5x3x6 and at the same time that of water
2x3.
If all things must share in number, it must
follow that many things are the same, and the same number must belong to one
thing and to another. Is number the cause, then, and does the thing exist
because of its number, or is this not certain? E.g. the motions of the sun have
a number, and again those of the moon, – yes, and the life and prime of each
animal. Why, then, should not some of these numbers be squares, some cubes, and
some equal, others double? There is no reason why they should not, and indeed
they must move within these limits, since all things were assumed to share in
number. And it was assumed that things that differed might fall under the same
number. Therefore if the same number had belonged to certain things, these would
have been the same as one another, since they would have had the same form of
number; e.g. sun and moon would have been the same. But why need these numbers
be causes? There are seven vowels, the scale consists of seven strings, the
Pleiades are seven, at seven animals lose their teeth (at least some do, though
some do not), and the champions who fought against Thebes were seven. Is it then
because the number is the kind of number it is, that the champions were seven or
the Pleiad consists of seven stars? Surely the champions were seven because
there were seven gates or for some other reason, and the Pleiad we count as
seven, as we count the Bear as twelve, while other peoples count more stars in
both. Nay they even say that X, Ps and Z are concords and that because there are
three concords, the double consonants also are three. They quite neglect the
fact that there might be a thousand such letters; for one symbol might be
assigned to GP. But if they say that each of these three is equal to two of the
other letters, and no other is so, and if the cause is that there are three
parts of the mouth and one letter is in each applied to sigma, it is for this
reason that there are only three, not because the concords are three; since as a
matter of fact the concords are more than three, but of double consonants there
cannot be more.
These people are like the old-fashioned Homeric
scholars, who see small resemblances but neglect great ones. Some say that there
are many such cases, e.g. that the middle strings are represented by nine and
eight, and that the epic verse has seventeen syllables, which is equal in number
to the two strings, and that the scansion is, in the right half of the line nine
syllables, and in the left eight. And they say that the distance in the letters
from alpha to omega is equal to that from the lowest note of the flute to the
highest, and that the number of this note is equal to that of the whole choir of
heaven. It may be suspected that no one could find difficulty either in stating
such analogies or in finding them in eternal things, since they can be found
even in perishable things.
But the lauded characteristics of numbers, and
the contraries of these, and generally the mathematical relations, as some
describe them, making them causes of nature, seem, when we inspect them in this
way, to vanish; for none of them is a cause in any of the senses that have been
distinguished in reference to the first principles. In a sense, however, they
make it plain that goodness belongs to numbers, and that the odd, the straight,
the square, the potencies of certain numbers, are in the column of the
beautiful. For the seasons and a particular kind of number go together; and the
other agreements that they collect from the theorems of mathematics all have
this meaning. Hence they are like coincidences. For they are accidents, but the
things that agree are all appropriate to one another, and one by analogy. For in
each category of being an analogous term is found – as the straight is in
length, so is the level in surface, perhaps the odd in number, and the white in
colour.
Again, it is not the ideal numbers that are the
causes of musical phenomena and the like (for equal ideal numbers differ from
one another in form; for even the units do); so that we need not assume Ideas
for this reason at least.
These, then, are the results of the theory, and
yet more might be brought together. The fact that our opponnts have much trouble
with the generation of numbers and can in no way make a system of them, seems to
indicate that the objects of mathematics are not separable from sensible things,
as some say, and that they are not the first
principles.