Matter and Number

A name sometimes means the composite substance, or the actuality or form.

For example, a ‘house’ can mean:

• the composite thing, ‘a covering consisting of bricks and stones laid thus and thus’, or
• the actual form ‘a covering’, and whether a line is ’twoness in length’ or ’twoness’

‘Animal’ can mean either:

• a soul in a body, or
• a soul.

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 is of no importance for the inquiry into sensible substance. For the essence certainly attaches to the form and the actuality.

‘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. 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.

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.

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.

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.

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.

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.

This is the generation and destruction of substances in what sense it is possible and in what sense impossible–and of the reduction of things to number.