Exposition of the Opinion

71. Here the answer to the question is said to be yes, namely that material substance is singular and individual through quantity.Thomas Aquinas, Giles of Rome, Godfrey of Fontaines. Aquinas SG IV ch.65: “Now wherever there is understood a diversity of parts of the same species, there individuation is necessarily understood; for things that are of one species are not multiplied save by individuality. And because dimensive quantity possesses of its idea that whereby a multiplication of individuals in the same species can take place, the first root for this sort of multiplication seems to come from dimension; because even in the genus of substance multiplication happens by division of matter, and this can only be understood according as matter is considered under dimensions; for, once quantity is removed, every substance is indivisible, as is plain from the Philosopher Physics 1.2.185a32-b5.” ⁵⁰

72. And for this the following sort of reason is put forward,Godfrey of Fontaines Quodlibet 7 q.5: “For it belongs to quantity to be thus divided [into parts of the same idea, as a line into many parts of the same idea], and to be the reason of dividing for every substance in which it is; hence just as this per se belongs to quantity, so it belongs to matter insofar as matter is extended - and consequently to everything that thus in matter has existence through quantity it belongs also to have substantial parts of the same idea, insofar as through quantity the substance of matter is truly extended and truly divisible and is made to be divided. For it is clear that in two individuals there are two quantities essentially and formally differing from each other in the genus of quantity, though such that, for these two quantities thus to differ from each other, there is not presupposed anything else by which they thus have to be divided or extended save only a subject ‘in which’; but, for two substantial forms thus to differ formally from each other, there is something else presupposed whereby the matter (in which such extended and divisible forms exist) has extended and divisible being;” “composites of substance and accidents...are not one per se but per accidens.” ⁵¹ that what belongs first and per se to something belongs to any other thing whatever by reason of that something; but substance and quantity do not make a per se one but only a per accidens one; therefore, singularity will belong to that among these to which first and per se belongs divisibility into parts of the same idea; of this sort is quantity, because it has of itself the capacity to be divided infinitely (Metaphysics 5.13.1020a7-8); therefore what belongs to quantity first and per se does not belong to anything else save by reason of quantity. Such is the division of a species into its individuals, because these dividers [sc. individuals] are not formally of a different idea the way the species are that divide a genus. - But from this further [Godfrey]:Ibid.: “The aforesaid are plain from the description of quantity in Metaphysics 5, where it is said that ‘a quantum is what is divisible into the things that are in it, each one of which is of a nature to be each a single one-something and a this-something’. From which it is plain that neither quantity nor substance are per se divided but the composite which is a quantum; but yet this divisibility belongs to the composite by reason of quantity, since what is formal in a quantum as it is a quantum (which is here being defined) is quantity. And the divisibility is into parts of the same idea, because the parts that are in some one quantum (as it is a quantum) are of the same idea, because they are of the same species and form; which parts, indeed, when they are actually divided, are diverse individuals in the same species - for, as Aristotle says, each one of such things ‘is of a nature to be each a single one-something and a this-something’; but primary substance, which is an individual in the genus of substance, is one something and a this-something.” ⁵² to be divisible into parts of the same idea belongs to something by reason of quantity (from Metaphysics 5 above), and quantity is the principle of division in any nature and the principle of distinction between divided things; therefore it is by quantity that individuals are individually divided from each other. And from this the conclusion is drawn that division into individuals, individuals to which there belongs such a distinction, belongs to a thing through quantity; therefore an individual is an individual through quantity.

73. Further,Aquinas, SG 2 ch.49 arg.3: “The principle of the diversity of individuals of the same species is the division of matter according to quantity; for the form of this fire does not differ from the form of that fire save by the fact that it is in the diverse parts into which the matter is divided - and divided not otherwise than by division of quantity, without which a substance is indivisible; but what is received in a body is received in it according to division of quantity; therefore only form as individuated is received in a body.” Ibid., chs.80-81 ad 2: “For it is clear that the essence of the form of this fire is different from the essence of the form of that fire, and yet there is not in species a different fire or a different form.” ⁵³ this fire does not differ from that fire save because form differs from form, and form does not differ from form save because it is received in different parts of matter, nor does one part of matter differ from another save because it is under a different part of quantity; therefore the whole distinction of this fire from that fire is reduced to quantity as to the first distinguishing thing.

74. There is confirmation of this argumentGodfrey, Quodlibet 7 q.5: “Hence it is said in Metaphysics 7, “There is a diverse species (that is, form) in the generator and generated because of matter’ (the Commentator, ‘the cause of a multitude of things able to be generated by one generator is the multiplication of the matters on which the agent acts’). But since matter in itself is one and indivisible, it seems that the causality of such division and distinction or individuation should not be attributed to the matter in itself, but must be attributed to it as it is understood under quantity, from which it has extension and divisibility into parts of the same idea etc.” Ibid., 11 q.3: “Again, because matter is not susceptible of several forms in succession save through change, but because matter is not changeable save as it is presupposed to be extended and divisible in quantity (otherwise something indivisible could be changed and moved), and because too the generator generates something else because of a different matter and from a different matter, and because matter does not have this without quantity - therefore, just as matter must precede before the substantial form is introduced through generation, so also must quantity too be presupposed. And this quantity [according to Averroes Substance of the Orb ch.1] is called indeterminate...namely because of itself it does not determine for itself a form to be corrupted or even to generated, because, when the form to be corrupted is corrupted, the quantity itself does not seem to be corrupted, and, when the form to be generated is generated, the quantity does not seem to be generated; but just as the matter remains in substance under both terms, so too the same quantity seems in some way to remain. And for the same reason one should suppose an indeterminate quantity in matter, because just as a thing is not changed save because it is under a contrary, so it is not changed save because it is a quantum.” ⁵⁴ in that a generator does not generate another save because of distinctness of matter; but the matter of the thing generated is necessarily presupposed as a quantum and a quantum under distinct quantity; that it is presupposed as a quantum is plain, because a natural agent cannot act on a non-quantum; that it is presupposed as a quantum with a different quantity from the generator is also plain, because it cannot be a quantum with the quantity of the generator. But this quantity of the thing generated naturally precedes the being of the thing generated,     therefore it precedes also the distinction of the generator and the generated; but it would not naturally precede this distinction if it were not naturally and per se required as the distinguisher of the thing generated; therefore etc     .