47 On the Properties of Quantity
47: On the Properties of Quantity Next we should examine the properties of quantity. Aristotle claims that quantity has three properties. The first of these consists in the fact that nothing is contrary to quantity; thus, 'line' is not the contrary of 'surface', nor is 'two cubits' the contrary of 'three cubits'.
But from this property it seems to follow that quantity is neither substance nor quality. For suppose that quantity were quality. Since something is contrary to quality, something would also be contrary to quantity.
It should be said here as earlier that the term 'contrary' has a number of senses. Nevertheless, in denying that anything is contrary to quantity the Philosopher is using the expression 'contrary' for terms designating things that are contrary to other things. The things signified are in turn called contraries since they can be acquired by stages and cannot simultaneously but only successively exist in the same thing. Taking the term 'contrary' in this sense, it is clear that none of the items contained per se in the genus of quantity are contraries of any other predicables; for nothing contained per se in the genus is such that every one of its significata or consignificata is the contrary of and, therefore, naturally opposed to the significata or consignificata of some other term. This is clear from induction. It is something that would be granted even by those who think the following is true: 'Something is the contrary of some quantity' (where 'to be a contrary' means 'to resist simultaneous although not successive inherence in one and the same thing'). Nonetheless, this is true: 'Nothing contained in the genus of quantity per se has a contrary' (where we take 'to have a contrary' in the sense outlined). Thus, although whiteness and blackness are contraries, the terms 'two cubits' and 'three cubits' are not. Neither are the terms 'two' and 'three' nor the terms
'line', 'surface', etc. The whiteness that is three cubits is the contrary of the blackness that is two cubits, so that one quantity really is the contrary of another quantity. Nonetheless, the terms 'two cubits' and 'three cubits' are not contraries, because even though whiteness is the contrary of blackness,
'two cubits' signifies whiteness in the same way it signifies blackness.
It should be held then that for Aristotle 'One quantity is the contrary of another is true, provided that the terms supposit personally for the relevant external objects. Nevertheless, this is true: 'No terms contained per se under the genus of quantity are contraries in the sense that they always signify contrary things'. It is this proposition that Aristotle means when he says that nothing is contrary to quantity.
15 11, 6 19, 6° 26-27.
On the Properties of Quantity The second property is that quantity does not admit of more and less; that is, nothing which is contained under the genus of quantity is predicated of something sometimes with the adverb 'more' and sometimes with the adverb 'less'. Thus, it is not said that a thing is sometimes more two cubits and sometimes less two cubits in the way in which we say that a book is sometimes more white and sometimes less. Neither do we say that these things are more three than those, as we do say that this is more white than that.
The third property is that quantities can be said to be equal or unequal to each other. Thus, one solid is said to be equal or unequal to another solid. Similarly, in other cases.
From this property it is clear that it is not the Philosopher's intention to deny that quality is quantity nor that substance is quantity. According to the Philosopher this feature is most proper to quantity. Indeed, it is convertible with quantity. Thus, of whatever this property holds true 'quantity' is also predicated. But the following, although possibly not true per se, is nonetheless true: 'One piece of wood is equal to another; and one whiteness is equal to another; and one blackness is equal to another blackness or to a whiteness'. Therefore, 'Substance is quantity' is true, and similarly, 'Quality is quantity', although they are not true per se.
Nor can one deny that everything that is equal or unequal is a quantity by claiming that being equal or unequal is not the property distinctive of quantity, but rather being that according to which something is said to be equal or unequal. The Philosopher does not say that it is according to quantity that something is said to be equal or unequal. He says, rather, that what is
Proper to quantity is actually being equal or unequal. Thus, he says, "But what is most proper to quantity is that it is said to be equal or unequal. For a singular instance of what is said to be a quantity is said to be equal or uncqual.
Thus, one solid is said to be equal or unequal to another; a number to be equal or unequal to another. Time too is said to be equal or unequal. Similarly, in the case of other things that are said to be quantities—they are said to be equal or unequal."? From this passage it is clear that he holds that quantities themselves are equal or unequal and not that something else is said to be equal or unequal according to quantities; therefore it should be claimed that since both whiteness and substance are equal or unequal to something else (even if only per accidens), both substance and quality are quantities, although only per accidens. Nor does it matter that later the Philosopher says that nothing in the other categories is said to be equal or unequal;> for he does not mean to deny that 'equal' and 'unequal' can be predicated of things from the other categories. He only means that nothing