e. Against the Reasons for the Opinion

105. Against the reasons for the opinion [nn.72-73] I argue thus:

First against the first opinion [n.72], because quantity is not the reason for divisibility in individuals:

For whatever is the formal idea for any divisibility is formally in that which is divisible by this division; but quantity is not formally in a species as it is divisible into subjective parts; therefore it is not the formal idea for the divisibility of such a whole into such parts.

106. There is a confirmation for this argument, that a universal whole, which is divided into individuals and subjective parts, is predicated of any of those subjective parts (so that any subjective part is that universal [sc. as ‘animal’ is predicated of ‘horse’ and ‘man’ and of ‘this horse’ and ‘this man’]) - but quantitative parts, into which the division of a continuous whole is made, never receive the predication of the whole that is divided into them. And even if the division of a homogeneous whole into quantitative parts and the division of a species (or of a universal whole) go together, yet they are not divisions of the same divided whole, because a quantitative whole is divided by quantitative division and is not predicated of any of the parts dividing it, just as neither is a heterogeneous quantum predicated of the parts that divide it; for, universally, no quantitative part is the whole of which it is the part; but there goes, along with this, also the fact that there are many individuals possessing the same common being, and this common being is divided into individuals by another division; and the common being was not the quantum that was divided by quantitative division. There is then a different whole that is divided by this division and by that; and it is divided per accidens into the same parts, but formally into parts of different ideas, in respect of this [universal] whole and of that [quantitative] whole - because with respect to the latter the parts are integral parts, and with respect to the former they are subjective parts.Tr. Say, for example, that a line of 12 inches is divided into parts of 2 inches; each 2 inch part of the line is a line, or has the same universal whole (‘line’) predicated of it, but no part of the line is the whole quantity of the 12 inch line. ⁵⁷

107. And as for what is taken from the Philosopher [n.72], one must say that the Philosopher does not say that a quantity is divided into parts of the same idea, but that “a quantity is divisible into the things present in it, an individual of which, or each of which, is of a nature to be a thing and this thing.” He says ‘into the things present in it’ as the things that compose the whole they are in, and so not into subjective parts, which are not in it in this way; ‘each of which’ (if the division is into two) or ‘an individual of which’ (if the division is into several) ‘is of a nature to be a thing’, namely per se existing in the way that the whole is (because to the extent a thing is a quantitative part dividing the whole, to that extent it can per se exist just like the whole does that is divided), and this against the division of a composite into matter and form; ‘and this thing’ - against the division of a genus into its species. And if a number were composed of diverse numbers, it would not be against the idea of number for it to be divided into numbers of different idea [sc. if 6 were composed of 2 and 4, which are of different idea]; and in the same way it would not be against the arm for it to be divided into parts of different idea if it were composed of two cubits or three cubits - and these are different in species; so too it would not be against a quantity for the division of its subject to be into parts of different idea.

108. I concede the fact universally, then, that although a whole does not require to be divided into parts of the same idea, yet it does not require the parts to be of a distinct idea, because, insofar as the parts are parts of a quantity, they are not of a different idea; for although head, heart, and hand are quantitative parts and of different ideas, yet they are not parts of a different idea insofar precisely as they are parts of a quantity.

109. In the way, then, that it is true that a quantity may be divided into parts of the same idea (although this cannot be got from the Philosopher [n.107]), this is altogether not to the purpose, because the division is not into parts which include the idea of the divided thing, but into parts which were present in the divided thing - and they do have one idea, not the idea of the divided thing, but of something common to it and to themselves [sc. the idea of 12 inches is not included in the idea of its 2 inch divisions, but only the idea of length is common to them all]; but a species is divided into parts of the same idea, namely because they include the idea of the divided thing [sc. as ‘this man’ and ‘that man’ both include ‘man’] and not something else that is of a different idea, common to the divided thing and the things that divide it.

110. Further, I argue against the second argument [n.73]: the generator qua generator (with everything else removed) is distinguished from the generated qua generated (with everything else removed from the generated), because it is unintelligible for the same thing to generate itself (even in divine reality a person does not generate himself); but the generator qua generator does not include quantity as it includes its proper generative principle; nor does the generated qua generated include quantity as the per se or formal term of generation; therefore when both quantities are removed, namely the quantities of generator and generated, the latter substance is distinguished numerically from the former.