But we must inquire in general whether eternal things can be composed of elements. If so, they will have matter; for everything which consists of elements is composite.
Assuming, then, that that which consists of anything, whether it has always existed or it came into being, must come into being 〈if at all〉 out of that of which it consists; and that everything comes to be that which it comes to be out of that which is it potentially (for it could not have come to be out of that which was not potentially such, nor could it have consisted of it); and that the potential can either be actualized or not; then however everlasting number or anything else which has matter may be, it would be possible for it not to exist, just as that which is any number of years old is as capable of not existing as that which is one day old. And if this is so, that which has existed for so long a time that there is no limit to it may also not exist.
Therefore things which contain matter cannot be eternal, that is, if that which is capable of not existing is not eternal, as we have had occasion to say elsewhere. Footnote 1Aristot. Met. 9.8.15-17, Aristot. De Caelo 1.12. Now if what we have just been saying—that no substance is eternal unless it is actuality—is true universally, and the elements are the matter of substance, an eternal substance can have no elements of which, as inherent in it, it consists.
There are some who, while making the element which acts conjointly with unity the indeterminate dyad, object to the unequal,
quite reasonably, on the score of the difficulties which it involves. But they are rid only of those difficulties Footnote 2Cf. Aristot. Met. 14.1.14-17. which necessarily attend the theory of those who make the unequal, i.e. the relative, an element; all the difficulties which are independent of this view must apply to their theories also, whether it is Ideal or mathematical number that they construct out of these elements.
There are many causes for their resorting to these explanations, the chief being that they visualized the problem in an archaic form. They supposed that all existing things would be one, absolute Being, unless they encountered and refuted Parmenides’ dictum:
It will ne’er be proved that things which are not, are, Footnote 3Parmenides Fr. 7 (Diels).
i.e., that they must show that that which is not, is; for only so—of that which is, and of something else—could existing things be composed, if they are more than one. Footnote 4Cf. Plat. Soph. 237a, 241d, 256e.
However, (i) in the first place, if being
has several meanings (for sometimes it means substance, sometimes quality, sometimes quantity, and so on with the other categories), what sort of unity will all the things that are constitute, if not-being is not to be? Will it be the substances that are one, or the affections (and similarly with the other categories), or all the categories together? in which case the this
and the such
and the so great,
and all the other categories which denote some sense of Being, will be one.
But it is absurd, or rather impossible, that the introduction of one thing should account for the fact that what is
sometimes means so-and-so,
sometimes such-and-such,
sometimes of such-and-such a size,
sometimes in such-and-such a place.
(2) Of what sort of not-being and Being do real things consist? Not-being, too, has several senses, inasmuch as Being has; and not-man
means not so-and-so,
whereas not straight
means not such-and-such,
and not five feet long
means not of such-and-such a size.
What sort of Being and not-being, then, make existing things a plurality?
This thinker means by the not-being which together with Being makes existing things a plurality, falsity and everything of this nature Footnote 5Plat. Soph. 237a, 240; but Aristotle’s statement assumes too much. ; and for this reason also it was said Footnote 6Presumably by some Platonist. that we must assume something which is false, just as geometricians assume that a line is a foot long when it is not.
But this cannot be so; for (a) the geometricians do not assume anything that is false (since the proposition is not part of the logical inference Footnote 7i.e., the validity of a geometrical proof does not depend upon the accuracy of the figure. ), and (b) existing things are not generated from or resolved into not-being in this sense. But not only has not-being
in its various cases as many meanings as there are categories, but moreover the false and the potential are called not-being
; and it is from the latter that generation takes place—man comes to be from that which is not man but is potentially man, and white from that which is not white but is potentially white; no matter whether one thing is generated or many.
Clearly the point at issue is how being
in the sense of the substances is many; for the things that are generated are numbers and lines and bodies. It is absurd to inquire how Being as substance is many, and not how qualities or quantities are many.
Surely the indeterminate dyad or the Great and Small is no reason why there should be two whites or many colors or flavors or shapes; for then these too would be numbers and units. But if the Platonists had pursued this inquiry, they would have perceived the cause of plurality in substances as well; for the cause Footnote 8Matter, according to Aristotle; and there is matter, or something analogous to it, in every category. Cf. Aristot. Met. 12.5. is the same, or analogous.
This deviation of theirs was the reason why in seeking the opposite of Being and unity, from which in combination with Being and unity existing things are derived, they posited the relative (i.e. the unequal), which is neither the contrary nor the negation of Being and unity, but is a single characteristic of existing things, just like substance or quality. They should have investigated this question also; how it is that relations are many, and not one.
As it is, they inquire how it is that there are many units besides the primary unity, but not how there are many unequal things besides the Unequal. Yet they employ in their arguments and speak of Great and Small, Many and Few (of which numbers are composed), Long and Short (of which the line is composed), Broad and Narrow (of which the plane is composed), Deep and Shallow (of which solids are composed); and they mention still further kinds of relation. Footnote 9Cf. Aristot. Met. 14.1.6, 18, Aristot. Met. 1.9.23. Now what is the cause of plurality in these relations?
We must, then, as I say, presuppose in the case of each thing that which is it potentially. The author Footnote 10Plato. of this theory further explained what it is that is potentially a particular thing or substance, but is not per se existent—that it is the relative (he might as well have said quality
); which is neither potentially unity or Being, nor a negation of unity or Being, but just a particular kind of Being.
And it was still more necessary, as we have said, Footnote 11sect. 11. that, if he was inquiring how it is that things are many, he should not confine his inquiry to things in the same category, and ask how it is that substances or qualities are many, but that he should ask how it is that things in general are many; for some things are substances, some affections, and some relations.
Now in the case of the other categories there is an additional difficulty in discovering how they are many. For it may be said that since they are not separable, it is because the substrate becomes or is many that qualities and quantities are many; yet there must be some matter for each class of entities, only it cannot be separable from substances.
In the case of particular substances, however, it is explicable how the particular thing can be many, if we do not regard a thing both as a particular substance and as a certain characteristic. Footnote 12This, according to Aristotle, is how the Platonists regard the Ideas. See Introduction. The real difficulty which arises from these considerations is how substances are actually many and not one.
Again, even if a particular thing and a quantity are not the same, it is not explained how and why existing things are many, but only how quantities are many;
for all number denotes quantity, and the unit, if it does not mean a measure, means that which is quantitatively indivisible. If, then, quantity and substance are different, it is not explained whence or how substance is many; but if they are the same, he who holds this has to face many logical contradictions.
One might fasten also upon the question with respect to numbers, whence we should derive the belief that they exist.
For one Footnote 13Plato and his orthodox followers. who posits Ideas, numbers supply a kind of cause for existing things; that is if each of the numbers is a kind of Idea, and the Idea is, in some way or other, the cause of existence for other things; for let us grant them this assumption.
But as for him Footnote 14Speusippus. who does not hold this belief, because he can see the difficulties inherent in the Ideal theory (and so has not this reason for positing numbers), and yet posits mathematical number, what grounds have we for believing his statement that there is a number of this kind, and what good is this number to other things? He who maintains its existence does not claim that it is the cause of anything, but regards it as an independent entity; nor can we observe it to be the cause of anything; for the theorems of the arithmeticians will all apply equally well to sensible things, as we have said. Footnote 15Aristot. Met. 13.3.1.