c. The Third Way: from the Idea of Ordering within a Category

89. From the third way I argue thus: in any ordering in a category are all the things pertaining to that ordering, after removal of anything else whatever that is not essentially part of the ordering (the proof of this is that two orderings are primarily diverse, and so nothing of one ordering is the sort it is through the ordering of the other); but to the ordering as it is complete both upwards and downwards (according to the Philosopher Posterior Analytics 1. 20.82a21-24 [n.63]), just as there belongs to it the first predicate of which nothing is predicated, so there belongs to it the lowest subject for which nothing is subject; therefore the singular or the individual exists in any ordering by nothing in any other ordering.

90. Further second: in any ordering, after removal of everything whatever of another ordering, there exists the idea of species - for no opinion imagines that a species is in some genus by reason of an accident, speaking of absolute things; but it is of the idea of a species that it is predicable of several things differing in number; therefore in any ordering there can be found something intrinsically, individual and singular, of which the species is predicated - or at any rate there can be found something ‘not predicable of many’ (otherwise, if nothing of this sort can be subject, then nothing in this ordering will be a most specific species, in whose idea is contained that it can be predicate).

91. Further third: the lowest that can be a subject and is a subject receives per se the predication of any predicable whatever, just as the first predicable is predicated per se of any predicate in the ordering whatever; but a per accidens being, insofar as it is per accidens, receives the predication per se of nothing; therefore the lowest thing that can be subject cannot be a per accidens being (a per accidens being is an aggregate of things of diverse genera, according to the Philosopher Metaphysics 5.6.1015b16-36, ch. ‘On One’).

92. Further fourth: when something is precisely of a nature to belong to something according to some idea, then, whatever it belongs to essentially according to that idea, it belongs to simply and essentially according to that idea; but to be a universal in the ordering of the genus of substance belongs to something precisely insofar as it is part of that ordering, after removal of everything that is part of another ordering; therefore, what ‘commonness’ essentially belongs to insofar as it is part of the ordering, belongs to it simply and essentially. But however much it is contracted by something of another genus, nothing about it pertaining to its own ordering is taken away; for however much Socrates is determined by white or black (to which he was in potency), Socrates is not more determinately in the genus of substance than he was before, because he was before a ‘this’. Therefore, however much a nature in the genus of substance is posited to be contracted down to individuals by something of another genus, the nature will remain formally common (contracted just as when not contracted) - and therefore to posit that something common becomes an individual by what is of another genus is to posit that it is common and individual or singular at the same time.

93. So as to flee, perhaps, from the arguments of these two ways [nn.82, 89-92], the position about quantity is held in another manner [Giles of Rome, Godfrey of Fontaines]: namely in this manner, that just as the extension of the matter is different in nature from the nature of the quantity of the matter and adds nothing over and above the essence of matter, so the designation of the matter, which the matter has causally through quantity, is different from the designation of the quantity, being naturally prior to the designation that matter has through quantity; and this designation is different from the designation that belongs to quantity, but it is not different from substance - so that, just as matter does not have parts though the nature of quantity (because a part of matter is matter), so designated substance is only substance (for ‘designation’ only states a mode of disposition of substance).

94. To the contrary. This position seems to include contradictories in two ways.

First, because it is impossible for anything dependent naturally on a posterior to be the same naturally as a prior, because it would be both prior and not prior; but substance, for them, is prior naturally to quantity; therefore anything pre-requiring, in whatever way, the nature of quantity cannot be the same as substance. So it is not the case that this designation is a designation of substance and yet is caused by quantity.

95. Proof of the major: where there is a true and real identity (even if it is not formal), there it is impossible for the one to be and the other not to be, because then the really same thing would both be and not be; but it is possible for the naturally prior to be without the naturally posterior; therefore, and as a result, much more so without that which remains from, or is caused by, the natural posterior.

96. Further, that which is necessarily a condition of the cause in its causing cannot be possessed by the thing caused, because then the cause - insofar as it is sufficient for causing - would be caused by the caused, and the caused would be the cause of itself and would, to this extent, be able to give to the cause its own causation; but singularity - or singular designation - is a necessary condition in a substance for causing a quantity, because (as argued [n.87]) a caused singular requires a singular cause; therefore it is impossible for the designation of a designated substance or of a singular to be from a singular quantity (or to be from the caused) and not from the substance insofar as the substance is singular.

97. Further, what is it for quantity to leave remaining, or to cause, such a mode of being in a substance? If it is nothing but what was present before in the quantity, then in no way is the designation through quantity, because the designation simply of substance would naturally precede quantity. - But if it is something else, I ask how it is caused by quantity and in what genus of cause? The only genus it seems possible to assign is that of efficient cause; but quantity is not an active form;     therefore etc     .

98. Further, why does quantity leave such a mode remaining in the substance, the same really as the substance, more than quality does, like whiteness? There seems to be no reason, because just as whiteness itself is a form in the surface and is so without the mediation of any other form that is left remaining, so it seems that quantity is a form in the substance whereby the substance is a quantum and never leaves any other form remaining.

d. The Fourth Way: on the Part of Quantity

99. From the fourth way I argue as follows: the quantity by which a substance is a ‘this’, so designated, is either a terminated quantity or a non-terminated quantity. It is not a terminated quantity because this follows the being of the form in the matter and, consequently, the singularity of the substance - because if substance is the cause of quantity as terminated, ‘this substance’ is the cause of the quantity as it is ‘this terminated quantity’. If non-terminated quantity is the cause of this substance being a ‘this’ - on the contrary, this quantity, namely non-terminated quantity, remains the same in a body when generated and when corrupted; therefore it is not the cause of any designation of terminated quantity.

100. If you say that the consequence does not hold, because quantity is not posited as the cause of singularity save on the presupposition of specific unity, but a body when generated and corrupted is not of the same species - on the contrary: I posit that from water first fire is generated, and second from fire water is generated. There is the same quantity in the first water corrupted and in the second water generated - and not just nonterminated quantity but also terminated quantity, because it can have from the form the same term; or at any rate the same non-terminated quantity suffices, and that, for you, is the cause of singularity, on the presupposition of specific unity. Therefore the first water and the second water are numerically the same ‘this water’ - which seems impossible, because the numerically same individual is not made to return by natural action, from Physics 5.4.228a4-6 and On Generation 2.11.338b16-18.

101. Further, if quantity is what first individuates substance, then it itself - in itself - must be first ‘this quantity’ and numerically distinct of itself from ‘that quantity’, just as this substance is numerically distinct from that substance; but in that case your proposition is not true, namely that ‘every formal difference is specific difference’; for this quantity and that are forms, therefore they differ specifically.

102. And if you except from this fundamental proposition the quantity of a building going to ruin, how will formal difference be proved to be specific difference [nn.71-73 footnotes]?Tr. A building going to ruin does not differ from the unruined building in number (it is numerically the same building), but in quantity (its outline differs, for instance). So difference of quantity here cannot cause numerical difference, and so not specific difference either; but the quantity of something, however taken (its outline as in ruins or as unruined), is a form of the thing, namely an accidental form; therefore difference in form does not always cause difference in species. Aquinas and Godfrey [as quoted here and earlier by the Vatican editors] speak of two numerically differing lines as being two by difference of position, which is a difference of form. ⁵⁵ For any quantity adduced from the form will equally fit the proposition, since a quantity is a form just as also are the other categories.

103. And if you say, ‘on the contrary, quantity has of itself a determinate position, and it is by this distinct of itself from that quantity’ - on the contrary: of which position are you speaking? Either of predicamental position (which is one of the categories), and this category is naturally posterior to quantity.The ten categories follow in order of prior and posterior: substance, quantity, quality, relation, action, passion, position, having, where, when. Peter of Spain Logical Summaries tr.2 n.6. ⁵⁶ Or of position as it is a difference of quantity, insofar as a quantity is said to be made up of parts having position - and then the same question arises as before [n.101], namely why this position of this quantity differs from that position of that quantity; and this question is ‘how this quantity differs numerically from that’, and so it seems that you are assigning the idea to itself; for the fact that the permanent and continuous parts - within the very whole - are in themselves distinct from the permanent and continuous parts in the whole (and these two features, namely continuity and permanence, are included in position as position is a difference of quantity) - this fact is not more known than the fact that this quantity differs in itself from that quantity.

104. Further, all the arguments used against the opinion in the first question, to prove that flesh is not of itself a ‘this’ [nn.7-28], can be used the same to prove that quantity is not of itself a ‘this’; and it is manifest that the idea of line is of itself common to this line and to that, nor is there a greater contradiction in thinking of line under the idea of a universal than in thinking flesh so. And line even has some real unity less than numerical unity, just as flesh also has, on the ground of the same proofs as were set down in the second argument against the opinion of the first question [nn.8-28]. It is plain too that line and surface are of the same idea in this water and in that; why then is this water ‘this water’ and a singular? And I am not speaking of a vague and indeterminate singularity but of a designated and determinate one.