[
995a]
[24]
It is necessary, with a view to the
science which we are investigating, that we first describe the
questions which should first be discussed. These consist of all the
divergent views which are held about the first principles; and also of
any other view apart from these which happens to have been
overlooked.Now for
those who wish to get rid of perplexities it is a good plan to go into
them thoroughly; for the subsequent certainty is a release from the
previous perplexities, and release is impossible when we do not know
the knot. The perplexity of the mind shows that there is a "knot" in
the subject; for in its perplexity it is in much the same condition as
men who are fettered: in both cases it is impossible to make any
progress.Hence we
should first have studied all the difficulties, both for the reasons
given and also because those who start an inquiry without first
considering the difficulties are like people who do not know where
they are going; besides, one does not even know whether the thing
required has been found or not.
[
995b]
[1]
To such a man the
end is not clear; but it is clear to one who has
already faced the difficulties.Further, one who has heard all the conflicting
theories, like one who has heard both sides in a lawsuit, is
necessarily more competent to judge.
The first
difficulty is concerned with the subjects
1 which we discussed in our prefatory remarks. (1.) Does the
study of the causes belong to one science or to more than one?
2(2.)
Has that science only to contemplate the first principles of
substance, or is it also concerned with the principles which all use
for demonstration—e.g. whether it is possible at the same
time to assert and deny one and the same thing, and other similar
principles?
3And if it is concerned with substance, (3.) is there one science
which deals with all substances, or more than one; and if more than
one, are they all cognate, or should we call some of them "kinds of
Wisdom" and others something different?
4This too is a question which demands inquiry: (iv.) should we hold
that only sensible substances exist, or that there are other besides?
And should we hold that there is only one class of non-sensible
substances, or more than one (as do those who posit the Forms and the
mathematical objects as intermediate between the Forms and sensible
things)?
5These
questions, then, as I say, must be considered; and also (v.) whether
our study is concerned only with substances,
[20]
or also with the essential attributes
of substance;and further,
with regard to Same and Other, and Like and Unlike and Contrariety,
and Prior and Posterior, and all other such terms which dialecticians
try to investigate, basing their inquiry merely upon popular opinions;
we must consider whose province it is to study all of these.Further, we must consider all
the essential attributes of these same things, and not merely what
each one of them is, but also whether each one has one opposite
6; and (vi.) whether the first
principles and elements of things are the genera under which they fall
or the pre-existent parts into which each thing is divided; and if the
genera, whether they are those which are predicated ultimately of
individuals, or the primary genera—e.g., whether "animal" or
"man" is the first principle and the more independent of the
individual.
7Above all we must
consider and apply ourselves to the question (7.) whether there is any
other cause
per se besides matter, and if so whether it
is dissociable from matter, and whether it is numerically one or
several; and whether there is anything apart from the concrete thing
(by the concrete thing I mean matter together with whatever is
predicated of it) or nothing; or whether there is in some cases but
not in others; and what these cases are.
8
[
996a]
[1]
Further, (8.) we must ask whether the first principles are limited
in number or in kind
9—both those in the definitions and those
in the substrate—and (ix.) whether the principles of
perishable and of imperishable things are the same or different; and
whether all are imperishable, or those of perishable things are
perishable.
10Further, there is the hardest and most
perplexing question of all: (x.) whether Unity and Being (as the
Pythagoreans and Plato maintained) are not distinct, but are the
substance of things; or whether this is not so, and the substrate is
something distinct
11(as Empedocles holds of Love,
12 another thinker
13 of fire, and another
14 of water or air
15);and (xi.) whether the first
principles are universal or like individual things
16; and (12.) whether they exist potentially or
actually; and further whether their potentiality or actuality depends
upon anything other than motion
17; for these
questions may involve considerable difficulty.Moreover we must ask (13.) whether
numbers and lines and figures and points are substances in any sense,
or not; and if they are, whether they are separate from sensible
things or inherent in them.
18 With
regard to these problems not only is it difficult to attain to the
truth, but it is not even easy to state all the difficulties
adequately.
19(1.)
Firstly, then, with respect to the first point raised: whether it is
the province of one science or of more than one to study all the kinds
of causes.
[20]
How can
one science comprehend the first principles unless they
are contraries? Again, in many things they are not all
present.How can a
principle of motion be in immovable things? or the "nature of the
Good"? for everything which is good in itself and of its own nature is
an
end and thus a cause, because for its sake other
things come to be and exist; and the
end and
purpose is the end of some action, and all actions
involve motion; thus it would be impossible either for this principle
to exist in motionless things or for there to be any
absolute Good.Hence in mathematics too nothing is proved by means of this cause,
nor is there any demonstration of the kind "because it is better or
worse"; indeed no one takes any such consideration into
account.And so for
this reason some of the sophists, e.g. Aristippus,
20 spurned mathematics, on the
ground that in the other arts, even the mechanical ones such as
carpentry and cobbling, all explanation is of the kind "because it is
better or worse," while mathematics takes no account of good and
bad.
21
[
996b]
[1]
On the other hand if there are several
sciences of the causes, and a different one for each different
principle, which of them shall we consider to be the one which we are
seeking, or whom of the masters of these sciences shall we consider to
be most learned in the subject which we are investigating?For it is possible for all the
kinds of cause to apply to the same object; e.g. in the case of a
house the source of motion is the art and the architect; the final
cause is the function; the matter is earth and stones, and the form is
the definition. Now to judge from our discussion some time ago
22 as to which of the sciences should
be called Wisdom, there is some case for applying the name to each of
them.Inasmuch as
Wisdom is the most sovereign and authoritative kind of knowledge,
which the other sciences, like slaves, may not contradict, the
knowledge of the
end and of the
Good
resembles Wisdom (since everything else is for the sake of the
end ); but inasmuch as it has been defined as
knowledge of the first principles and of the most knowable, the
knowledge of the essence will resemble Wisdom.For while there are many ways of
understanding the same thing, we say that the man who recognizes a
thing by its being something knows more than he who recognizes it by
its not being something; and even in the former case one knows more
than another, and most of all he who knows
what it is,
and not he who knows its size or quality or natural capacity for
acting or being acted upon.Further, in all other cases too, even in such as admit of
demonstration,
[20]
we
consider that we know a particular thing when we know
what it is (e.g. what is the squaring of a rectangle?
answer, the finding of a mean proportional to its sides; and similarly
in other instances); but in the case of generations and actions and
all kinds of change, when we know the source of motion.This is distinct from and
opposite to the
end . Hence it might be supposed that the
study of each of these causes pertained to a different science.
23(2.) Again, with respect to the demonstrative
principles as well, it may be disputed whether they too are the
objects of one science
24 or of
several.
25By demonstrative I mean the axioms from
which all demonstration proceeds, e.g. "everything must be either
affirmed or denied," and "it is impossible at once to be and not to
be," and all other such premisses. Is there one science both of these
principles and of substance, or two distinct sciences? and if there is
not one, which of the two should we consider to be the one which we
are now seeking?
It is not probable that both subjects
belong to one science; for why should the claim to understand these
principles be peculiar to geometry rather than to any other science?
Then if it pertains equally to any science, and yet cannot pertain to
all,
[
997a]
[1]
comprehension of these principles is no more
peculiar to the science which investigates substances than to any
other science.Besides, in
what sense can there in be a science of these principles? We know
already just what each of them is; at any rate other sciences employ
them as being known to us.
26 If,
however there is a demonstrative science of them, there will have to
be some underlying genus, and some of the principles will be derived
from axioms, and others will be unproved(for there cannot be demonstration of
everything), since demonstration must proceed from something, and have
some subject matter, and prove something. Thus it follows that there
is some one genus of demonstrable things; for all the demonstrative
sciences employ axioms.
On the other
hand, if the science of substance is distinct from the science of
these principles, which is of its own nature the more authoritative
and ultimate?The axioms
are most universal, and are the first principles of everything. And
whose province will it be, if not the philosopher's, to study truth
and error with respect to them?
27(3.) And
in general, is there one science of all substances, or more than
one?
28 if there is not one,
with what sort of substance must we assume that this science is
concerned?On the
other hand, it is not probable that there is one science of all
substances; for then there would be one demonstrative of all
attributes—assuming that every demonstrative
science
[20]
proceeds from
accepted beliefs and studies the essential attributes concerned with
some definite subject matter.Thus to study the essential attributes
connected with the same genus is the province of the same science
proceeding from the same beliefs. For the subject matter belongs to
one science, and so do the axioms, whether to the same science or to a
different one; hence so do the attributes, whether they are studied by
these sciences themselves or by one derived from them.
29(v.) Further, is this study
concerned only with substances, or with their attributes as well?
30 I mean, e.g., if the solid is a
kind of substance, and so too lines and planes, is it the province of
the same science to investigate both these and their attributes, in
every class of objects about which mathematics demonstrates anything,
or of a different science?If of the same, then the science of substance too would be in some
sense demonstrative; but it does not seem that there is any
demonstration of the "what is it?" And if of a different science, what
will be the science which studies the attributes of substance? This is
a very difficult question to answer.
31(iv.) Further, are we to say that only sensible substances exist, or
that others do as well? and is there really only one kind of
substance, or more than one
[
997b]
[1]
(as they hold who
speak of the Forms and the Intermediates, which they maintain to be
the objects of the mathematical sciences)?In what sense we Platonists hold the Forms to
be both causes and independent substances has been stated
32 in our original discussion on this subject.
But while they involve difficulty in many respects, not the least
absurdity is the doctrine that there are certain entities apart from
those in the sensible universe, and that these are the same as
sensible things except in that the former are eternal and the latter
perishable.
33For Platonists say nothing more or less than that there is an
absolute Man, and Horse, and Health; in which they closely resemble
those who state that there are Gods, but of human form; for as the
latter invented nothing more or less than eternal men, so the former
simply make the Forms eternal sensibles.
Again, if anyone posits Intermediates distinct from Forms and
sensible things, he will have many difficulties;because obviously not only will there
be lines apart from both Ideal and sensible lines, but it will be the
same with each of the other classes.
34
Thus since astronomy is one of the mathematical sciences, there will
have to be a heaven besides the sensible heaven, and a sun and moon,
and all the other heavenly bodies.But how are we to believe this? Nor is it
reasonable that the heaven should be immovable; but that it should
move
[20]
is utterly
impossible.
35 It is the same
with the objects of optics and the mathematical theory of harmony;
these too, for the same reasons, cannot exist apart from sensible
objects. Because if there are intermediate objects of sense and
sensations, clearly there will also be animals intermediate between
the Ideal animals and the perishable animals.
36One might also
raise the question with respect to what kind of objects we are to look
for these sciences. For if we are to take it that the only difference
between mensuration and geometry is that the one is concerned with
things which we can perceive and the other with things which we
cannot, clearly there will be a science parallel to medicine (and to
each of the other sciences), intermediate between Ideal medicine and
the medicine which we know.Yet how is this possible? for then there would be a class of healthy
things apart from those which are sensible and from the Ideally
healthy. Nor, at the same time, is it true that mensuration is
concerned with sensible and perishable magnitudes; for then it would
perish as they do. Nor, again, can astronomy be concerned with
sensible magnitudes or with this heaven of ours;
[
998a]
[1]
for as sensible
lines are not like those of which the geometrician speaks (since there
is nothing sensible which is straight or curved in that sense; the
circle
37
touches the ruler not at a point, but <along a line> as
Protagoras used to say in refuting the geometricians), so the paths
and orbits of our heaven are not like those which astronomy discusses,
nor have the symbols of the astronomer the same nature as the
stars.
Some, however, say that these so-called
Intermediates between Forms and sensibles do exist: not indeed
separately from the sensibles, but in them. It would take too long to
consider in detail all the impossible consequences of this theory, but
it will be sufficient to observe the following.On this view it is not logical that
only this should be so; in clearly it would be possible for the Forms
also to be in sensible things; for the same argument applies to both.
Further, it follows necessarily that two solids must occupy the same
space; and that the Forms cannot be immovable, being present in
sensible things, which move.And in general, what is the object of assuming
that Intermediates exist, but only in sensible things? The same
absurdities as before will result: there will be a heaven besides the
sensible one, only not apart from it, but in the same place; which is
still more impossible.
38
[20]
Thus it is very
difficult to say, not only what view we should adopt in the foregoing
questions in order to arrive at the truth, but also in the case of the
first principles (vi.) whether we should assume that the genera, or
the simplest constituents of each particular thing, are more truly the
elements and first principles of existing things. E.g., it is
generally agreed that the elements and first principles of speech are
those things of which, in their simplest form, all speech is composed;
and not the common term "speech"; and in the case of geometrical
propositions we call those the "elements"
39 whose proofs are embodied in the proofs of all or
most of the rest.Again, in
the case of bodies, both those who hold that there are several
elements and those who hold that there is one call the things of which
bodies are composed and constituted first principles. E.g., Empedocles
states that fire and water and the other things associated with them
are the elements which are present in things and of which things are
composed; he does not speak of them as genera of things.Moreover in the case of other
things too, if a man wishes to examine their nature
[
998b]
[1]
he observes, e.g., of what parts a bed consists and
how they are put together; and then he comprehends its nature. Thus to
judge from these arguments the first principles will not be the genera
of things.
But from the point of view
that it is through definitions that we get to know each particular
thing, and that the genera are the first principles of definitions,
the genera must also be the first principles of the things
defined.And if to
gain scientific knowledge of things is to gain it of the species after
which things are named, the genera are first principles of the
species. And apparently some even of those
40 who call Unity
or Being or the Great and Small elements of things treat them as
genera.
Nor again is it possible
to speak of the first principles in both senses.The formula of substance is one; but
the definition by genera will be different from that which tells us of
what
parts a thing is composed.
Moreover, assuming that the genera are first
principles in the truest sense, are we to consider the
primary genera to be first principles, or the final terms
predicated of individuals? This question too involves some
dispute.For if
universals are always more truly first principles, clearly the answer
will be "the highest genera," since these are predicated of
everything. Then there will be as many first principles of
things
[20]
as there are
primary genera, and so both Unity and Being will be first principles
and substances, since they are in the highest degree predicated of all
things.But it is
impossible for either Unity or Being to be one genus of existing
things. For there must
be differentiae of each genus, and
each differentia must be
one41; but it is impossible either for the
species of the genus to be predicated of the specific differentiae, or
for the genus to be predicated without its species.
42 Hence if
Unity or Being is a genus, there will be no differentia Being or
Unity.But if they
are not genera, neither will they be first principles, assuming that
it is the genera that are first principles. And further, the
intermediate terms, taken together with the differentiae, will be
genera, down to the individuals; but in point of fact, although some
are thought to be such, others are not. Moreover the differentiae are
more truly principles than are the genera; and if they also are
principles, we get an almost infinite number of principles, especially
if one makes the ultimate genus a principle.
[
999a]
[1]
Moreover, if Unity is really more of the
nature of a principle, and the indivisible is a unity, and every thing
indivisible is such either in quantity or in kind, and the indivisible
in kind is prior to the divisible, and the genera are divisible into
species, then it is rather the lowest predicate that will be a unity
(for "man" is not the genus
43 of individual men).Further, in the case of things which
admit of priority and posteriority, that which is predicated of the
things cannot exist apart from them. E.g., if 2 is the first number,
there will be no Number apart from the species of number; and
similarly there will be no Figure apart from the species of figures.
But if the genera do not exist apart from the species in these cases,
they will scarcely do so in others; because it is assumed that genera
are most likely to exist in these cases.In individuals, however, there is no priority
and posteriority. Further, where there is a question of better or
worse, the better is always prior; so there will be no genus in these
cases either.
From these considerations
it seems that it is the terms predicated of individuals, rather than
the genera, that are the first principles. But again on the other hand
it is not easy to say in what sense we are to understand these to be
principles;for the
first principle and cause must be apart from the things of which it is
a principle, and must be able to exist when separated from them. But
why should we assume that such a thing exists
[20]
alongside of the individual, except in
that it is predicated universally and of all the terms? And indeed if
this is a sufficient reason, it is the more universal concepts that
should rather be considered to be principles; and so the primary
genera will be the principles.
44In this
connection there is a difficulty which is the hardest and yet the most
necessary of all to investigate, and with which our inquiry is now
concerned. (7.) If nothing exists apart from individual things, and
these are infinite in number, how is it possible to obtain knowledge
of the numerically infinite? For we acquire our knowledge of all
things only in so far as they contain something universal, some one
and identical characteristic.But if this is essential, and there must be
something apart from individual things, it must be the genera; either
the lowest or the highest; but we have just concluded that this is
impossible.
45Further,
assuming that when something is predicated of matter there is in the
fullest sense something apart from the concrete whole, if there is
something, must it exist apart from
all concrete wholes,
or apart from some but not others, or apart from none?
[
999b]
[1]
If
nothing exists apart from individual things, nothing will be
intelligible; everything will be sensible, and there will be no
knowledge of anything—unless it be maintained that
sense-perception is knowledge. Nor again will anything be eternal or
immovable, since sensible things are all perishable and in
motion.Again, if
nothing is eternal, even generation is impossible; for there must be
something which becomes something, i.e. out of which something is
generated, and of this series the ultimate term must be ungenerated;
that is if there is any end to the series and generation cannot take
place out of nothing.Further, if there is generation and motion, there must be limit too.
For (a) no motion is infinite, but every one has an end; (b) that
which cannot be completely generated cannot begin to be generated, and
that which has been generated must
be as soon as it has
been generated.Further, if
matter exists apart in virtue of being ungenerated, it is still more
probable that the substance, i.e. that which the matter is at any
given time becoming, should exist. And if neither one nor the other
exists, nothing will exist at all. But if this is impossible, there
must be something, the shape or form, apart from the concrete
whole.
But again, if we assume this, there is a
difficulty: in what cases shall we, and in what shall we not, assume
it? Clearly it cannot be done in all cases; for we should not assume
that a particular house exists apart from particular houses.
[20]
Moreover, are we to regard the
essence of all things, e.g. of men, as one? This is absurd; for all
things whose essence is one are one.Then is it many and diverse? This too is
illogical. And besides, how does the matter become each individual one
of these things, and how is the concrete whole both matter and
form?
46(8.) Further,
the following difficulty might be raised about the first principles.
If they are one in kind, none of them will be one in number, not even
the Idea of Unity or of Being. And how can there be knowledge unless
there is some universal term?
47On the other hand if they are numerically one,
and each of the principles is one, and not, as in the case of sensible
things, different in different instances (e.g. since a given syllable
is always the same in kind, its first principles are always the same
in kind, but only in kind, since they are essentially different in
number)—if the first principles are one, not in this sense,
but numerically, there will be nothing else apart from the elements;
for "numerically one" and "individual" are identical in meaning. This
is what we mean by "individual": the numerically one; but by
"universal" we mean what is predicable of individuals.
[
1000a]
[1]
Hence
just as, if the elements of language
48 were limited in
number, the whole of literature would be no more than those
elements—that is, if there were not two nor more than two of
the same <so it would be in the case of existing things and
their principles>.
49(ix.) There is a
difficulty, as serious as any, which has been left out of account both
by present thinkers and by their predecessors: whether the first
principles of perishable and imperishable things are the same or
different. For if they are the same, how is it that some things are
perishable and others imperishable, and for what cause?The school of Hesiod, and all
the cosmologists, considered only what was convincing to themselves,
and gave no consideration to us. For they make the first principles
Gods or generated from Gods, and say that whatever did not taste of
the nectar and ambrosia became mortal—clearly using these
terms in a sense significant to themselves;but as regards the actual applications of
these causes their statements are beyond our comprehension. For if it
is for pleasure that the Gods partake of them, the nectar and ambrosia
are in no sense causes of their existence; but if it is to support
life, how can Gods who require nourishment be eternal?
However, it is not worth while to consider seriously the subtleties
of mythologists; we must ascertain
[20]
by cross-examining those who offer demonstration of
their statements why exactly things which are derived from the same
principles are some of an eternal nature and some perishable. And
since these thinkers state no reason for this view, and it is
unreasonable that things should be so, obviously the causes and
principles of things cannot be the same.Even the thinker who might be supposed to
speak most consistently, Empedocles, is in the same case; for he
posits Strife as a kind of principle which is the cause of
destruction, but none the less Strife would seem to produce everything
except the One; for everything except God
50 proceeds from it.At any rate he says
From which grew all that was and is and shall
be
In time to come: the trees, and
men and women,
The beasts and birds and
water-nurtured fish,
And the long-living
Gods.
51And it is obvious even apart
from this;
[
1000b]
[1]
for if there had not been Strife in
things, all things would have been one, he says; for when they came
together "then Strife came to stand outermost."
52 Hence it follows on his theory that God, the
most blessed being, is less wise than the others, since He does not
know all the elements; for He has no Strife in Him, and knowledge is
of like by like:
By earth (he says) we earth perceive,
by water water,
By air bright air, by
fire consuming fire,
Love too by love,
and strife by grievous strife.
53But—and this is the point from which we
started—thus much is clear: that it follows on his theory
that Strife is no more the cause of destruction than it is of Being.
Nor, similarly, is Love the cause of Being; for in combining things
into one it destroys everything else.
54Moreover, of the actual process of change he gives no explanation,
except that it is so by nature:
But when
Strife waxing great among the members
55Sprang up to honor as the time came round
Appointed them in turn by a mighty
oath,
56as though change
were a necessity; but he exhibits no cause for the
necessity.However,
thus much of his theory is consistent: he does not represent some
things to be perishable and others imperishable, but makes
everything
[20]
perishable
except the elements. But the difficulty now being stated is why some
things are perishable and others not, assuming that they are derived
from the same principles.
The foregoing
remarks may suffice to show that the principles cannot be the
same.If however
they are different, one difficulty is whether they too are to be
regarded as imperishable or as perishable. For if they are perishable,
it is clearly necessary that they too must be derived from something
else, since everything passes upon dissolution into that from which it
is derived. Hence it follows that there are other principles prior to
the first principles;but
this is impossible, whether the series stops or proceeds to infinity.
And further, how can perishable things exist if their principles are
abolished? On the other hand if the principles are imperishable, why
should some imperishable principles produce perishable things, and
others imperishable things? This is not reasonable; either it is
impossible or it requires much explanation.Further, no one has so much as attempted to
maintain different principles; they maintain the same principles for
everything.
[
1001a]
[1]
But they swallow down the difficulty
which we raised first
57 as though
they took it to be trifling.
58But the hardest question of all to investigate and also the most
important with a view to the discovery of the truth, is whether after
all Being and Unity are substances of existing things, and each of
them is nothing else than Being and Unity respectively, or whether we
should inquire what exactly Being and Unity are, there being some
other nature underlying them.Some take the former, others the latter view
of the nature of Being and Unity. Plato and the Pythagoreans hold that
neither Being nor Unity is anything else than itself, and that this is
their nature, their essence being simply Being and Unity.But the physicists, e.g.
Empedocles, explain what Unity is by reducing it to something, as it
were, more intelligible—or it would seem that by Love
Empedocles means Unity; at any rate Love is the cause of Unity in all
things. Others identify fire and others air with this Unity and Being
of which things consist and from which they have been
generated.Those who
posit more numerous elements also hold the same view; for they too
must identify Unity and Being with all the principles which they
recognize.
[20]
And it
follows that unless one assumes Unity and Being to be substance in
some sense, no other universal term can be substance; for Unity and
Being are the most universal of all terms,and if there is no absolute Unity or absolute
Being, no other concept can well exist apart from the so-called
particulars. Further, if Unity is not substance, clearly number cannot
be a separate characteristic of things; for number is units, and the
unit is simply a particular kind of one.
On the other
hand, if there is absolute Unity and Being, their substance must be
Unity and Being; for no other term is predicated universally of Unity
and Being, but only these terms themselves. Again, if there is to be
absolute Being and absolute Unity, it is very hard to see how there
can be anything else besides these; I mean, how things can be more
than one.For that which
is other than what is, is not; and so by Parmenides' argument
59 it must follow that all things are one, i.e.
Being.
[
1001b]
[1]
In either case there is a difficulty;
for whether Unity is not a substance or whether there is absolute
Unity, number cannot be a substance.It has already been stated why this is so if
Unity is not a substance; and if it is, there is the same difficulty
as about Being. For whence, if not from the absolute One or Unity, can
there be another one? It must be not-one; but all things are either
one, or many of which each is one. Further, if absolute Unity is
indivisible, by Zeno's axiom
it will be nothing.For
that which neither when added makes a thing greater nor when
subtracted makes it smaller is not an existent thing, he says
60; clearly assuming
that what exists is spatial magnitude. And if it is a spatial
magnitude it is corporeal, since the corporeal exists in all
dimensions, whereas the other magnitudes, the plane or line, when
added to a thing in one way will increase it, but when added in
another will not; and the point or unit will not increase a thing in
any way whatever.But
since Zeno's view is unsound, and it is possible for a thing to be
indivisible in such a way that it can be defended even against his
argument (for such a thing
61 when added will
increase a thing in number though not in size)—still how can
a
magnitude be composed of one or more such indivisible
things? It is like saying that the line is composed of
points.Moreover,
even if one supposes the case to be
[20]
such that number is generated, as some say, from
the One itself and from something else which is not one, we must none
the less inquire why and how it is that the thing generated will be at
one time number and at another magnitude, if the not-one was
inequality and the same principle in both cases.
62 For it is
not clear how magnitude can be generated either from One and this
principle, or from a number and this principle.
63(13.) Out of this arises the
question whether numbers, bodies, planes and points are substances or
not. If not, the question of what Being is, what the substances of
things are, baffles us; for modifications and motions and relations
and dispositions and ratios do not seem to indicate the substance of
anything; they are all predicated of a substrate, and none of them is
a definite thing.As for
those things which might be especially supposed to indicate
substance—water, earth, fire and air, of which composite
bodies are composed—
[
1002a]
[1]
their heat and cold
and the like are modifications, not substances; and it is only the
body which undergoes these modifications that persists as something
real and a kind of substance.Again, the body is less truly substance than
the plane, and the plane than the line, and the line than the unit or
point; for it is by these that the body is defined, and it seems that
they are possible without the body, but that the body cannot exist
without them.This is why
the vulgar and the earlier thinkers supposed that substance and Being
are Body, and everything else the modifications of Body; and hence
also that the first principles of bodies are the first principles of
existing things; whereas later thinkers with a greater reputation for
wisdom supposed that substance and Being are numbers.
As we
have said, then, if these things are not substance, there is no
substance or Being at all; for the attributes of these things surely
have no right to be called existent things. On the other hand, if it
be agreed that lines and points are more truly substance than bodies
are, yet unless we can see to what
kind of bodies they
belong (for they cannot be in sensible bodies) there will still be no
substance.Further,
it is apparent that all these lines are divisions of Body, either in
breadth
[20]
or in depth or
in length. Moreover every kind of shape is equally present in a solid,
so that if "Hermes is not in the stone,"
64
neither is the half-cube in the cube as a determinate shape.Hence neither is the plane; for
if any kind of plane were in it, so would that plane be which defines
the half-cube. The same argument applies to the line and to the point
or unit. Hence however true it may be that body is substance, if
planes, lines and points are more truly substance than Body is, and
these are not substance in any sense, the question of what Being is
and what is the substance of things baffles us.Because, in addition to the above
arguments, absurd results follow from a consideration of generation
and destruction; for it seems that if substance, not having existed
before, now exists, or having existed before, subsequently does not
exist it suffers these changes in the process of generation and
destruction. But points, lines and planes, although they exist at one
time and at another do not, cannot be in process of being either
generated or destroyed;for
whenever bodies are joined or divided,
[
1002b]
[1]
at one
time, when they are joined one surface is instantaneously produced,
and at another, when they are divided, two. Thus when the bodies are
combined the surface does not exist but has perished; and when they
are divided, surfaces exist which did not exist before. (The
indivisible point is of course never divided into two.) And if they
are generated and destroyed, from what are they
generated?It is
very much the same with "the present moment" in time. This too cannot
be generated and destroyed; but nevertheless it seems always to be
different, not being a substance. And obviously it is the same with
points, lines and planes, for the argument is the same; they are all
similarly either limits or divisions.
65In general one might wonder why
we should seek for other entities apart from sensible things and the
Intermediates:
66 e.g., for the
Forms which we Platonists assume.If it is for the reason that the objects of
mathematics, while differing from the things in our world in another
respect, resemble them in being a plurality of objects similar in
form, so that their principles cannot be numerically determined (just
as the principles of all language in this world of ours are
determinate not in number but in kind—unless one takes such
and such a particular syllable
[20]
or sound, for the principles of these are
determinate in number too—and similarly with the Intermediates, for in
their case too there is an infinity of objects similar in form), then
if there is not another set of objects apart from sensible and
mathematical objects, such as the Forms are said to be, there will be
no substance which is one both in kind and in number, nor will the
principles of things be determinate in number, but in kind
only.Thus if this is
necessarily so, it is necessary for this reason to posit the Forms
also. For even if their exponents do not articulate their theory
properly, still this is what they are trying to express, and it must
be that they maintain the Forms on the ground that each of them is a
substance, and none of them exists by accident.On the other hand, if we are to assume
that the Forms exist, and that the first principles are one in number
but not in kind, we have already stated
67 the impossible consequences which must follow.
68(12.) Closely
connected with these questions is the problem whether the elements
exist potentially or in some other sense.If in some other sense, there will be
something else prior to the first principles.
[
1003a]
[1]
For
the potentiality is prior to the actual cause, and the potential need
not necessarily always become actual. On the other hand, if the
elements exist potentially, it is possible for nothing to exist; for
even that which does not yet exist is capable of existing. That which
does not exist may come to be, but nothing which cannot exist comes to
be.
69(xi.) Besides the foregoing problems about the first principles we
must also raise the question whether they are universal or such as we
describe the particulars to be. For if they are universal, there will
be no substances; for no common term denotes an individual thing, but
a type; and substance is an individual thing.But if the common predicate be hypostatized as
an individual thing, Socrates
will be several beings: himself, and Man, and Animal—that
is, if each predicate denotes one particular thing.These then are the consequences if the
principles are universal. If on the other hand they are not universal
but like particulars, they will not be knowable; for the knowledge of
everything is universal. Hence there will have to be other universally
predicated principles prior to the first principles, if there is to be
any knowledge of them.
70