Question Four. Whether Material Substance is Individual or Singular through Quantity

66. I ask fourth whether material substance is individual or singular through quantity.a

a.a [Interpolation] About the fourth, namely whether material substance is individual through quantity, argument is made:

67. That it is:

Boethius On the Trinity ch.1, “Variety of accidents makes a difference in number, for three men do not differ in their genus or species but in their accidents; for if we separate in our mind, for example, all the accidents, still the place for them all is diverse, and we can in no way imagine one place for two; for two bodies will not occupy one place, which is an accident, and therefore they [sc. the three men] are numerically many to the extent the accidents [sc. the places of the three men] are many.” And the first among all accidents is quantity, which is even what ‘in place’ seems specifically to express (when we say that ‘we cannot imagine the same place’), and place belongs to bodies insofar as they have quantity.

68. Further, Damascene Elementary Introduction to Dogmas ch.4 (not counting the preface): “Everything in which a hypostasis differs from an hypostasis of the same species is said to be a difference from without and a characteristic property and a hypostatic quality; now this is an accident, in just the way that one man differs from another man because one is tall and the other short.”

69. Further, Avicenna Metaphysics 5.2 f.87va says, “A nature which lacks matter - to the being of this there come, from without, accidents and dispositions, by which accidents it is individuated.”

70. On the contrary:

Primary substance, as is argued for the second question [n.46], is per se generated and per se operates, and this insofar as it is distinguished from secondary substance, to which these features do not per se belong. But they do not belong to accidental being; as concerns ‘generated’ the point is plain from Metaphysics 6.2.1026b22-24; as concerns ‘operate’ the point is also plain, because one thing acting per se is one per se being, and this in one order of cause.

I. To the Question

A. The Opinion of Others

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     .

2. Rejection of the Opinion

75. Against this conclusion [n.71] I argue in four ways: first from the identity of numerical idea or of individuation or singularity; second from the order of substance to accidents; third from the idea of ordering in a category - and these three ways will prove in common that no accident can per se be the reason whereby material substance is individuated; the fourth way will be specifically against quantity as concerns the conclusion of the opinion [n.71] and argument will, fifthly, be made specifically against the reasons for the opinion [n.72-73].

a. The First Way: from the Identity of Individuation or Singularity

76. As concerns the first way I expound first what I understand by individuation or numerical unity or singularity. I do not indeed understand an indeterminate unity (by which anything whatever in a species is said to be one in number), but designated unity (as a ‘this’), such that, just as it was said before [n.48] that it is incompossible for an individual to be divided into subjective parts and that what is being asked for is the reason for this incompossibility, so I say that it is incompossible for an individual not to be a ‘this’ designated by this singularity, and that what is being asked for is not the cause of singularity in general but of ‘this’ singularity in particular, designated singularity, namely as it is determinately a ‘this’.

77. Understanding singularity in this manner I give, in the first way, two arguments:

First as follows: an actually existing substance, not changed by any substantial change, cannot become a non-this from a this, because this singularity - according to what was just said [n.76] - cannot be different in the same substance while the substance remains the same and is not substantially changed; but an actually existing substance, when no substantial change has been made in it or altered, can, without contradiction, be under a different quantity and under any different absolute accident whatever; therefore by no such accident is it formally ‘this substance’ with this designated singularity.

78. The minor premise is plain, because there is no contradiction in a substance quantified by this quantity being conserved by God and informed with another quantity; nor will this actually existing substance be, for this reason, changed by any substantial change, because there will be no change save from quantity to quantity. Likewise, if the substance is changed by any accident, it will not be changed with any substantial change; whether this is possible or impossible, it will not for this reason be formally not-this.

79. And if you say that this is a miracle and so is not conclusive against natural reason - on the contrary: there is no miracle in respect of contradictories, for which there is no potency. But it is a contradiction for the same abiding substance to be two substances without substantial change, and this both successively and at once - but this result however follows if a substance were formally ‘this substance’ by some accident; for then, when accident succeeds to accident, the same unchanged substance would be two substances in succession.

80. There is confirmation also for this through a likeness about specific unity, because it is impossible for one abiding substance - not substantially changed - to be at once or successively this species and not this species; therefore by likeness in the case of the issue at hand.

81. Second as follows: of two productions complete in substantial being there cannot be the same first term (the proof is that then each of the two would receive perfect substantial being from the fact the other of the two is complete, and so the same thing would be produced in completeness twice, - and also, if the two productions were not simultaneous, the same per se and actually existing substance would be produced when it already actually exists; so at least in the case of two successive productions the term cannot be the same). But ‘this bread’ was the first term of a generation of bread, and the transubstantiated bread exists with the same abiding quantity; so let another bread be created and affected with the abiding quantity - the consequence is that the term of the creation will be ‘this bread’, the same as the bread that was the term of the generation, because the former bread will be ‘this’ with the numerically same singularity as the latter bread was ‘this’; the consequence also is that ‘this bread’ is the same when transubstantiated and when non-transubstantiated - indeed the consequence is that no bread is transubstantiated (because universal bread is not, and ‘this bread’, the singular, is not, because, ex hypothesi [n.71], this bread remains when the quantity, by which it was formally ‘this’, is unchanged); therefore nothing altogether is transubstantiated into the body of Christ, which is a heretical thing to say.

b. The Second Way: from the Order of Substance to Accidents

82. From the second way I argue as follows: substance is naturally prior to every accident, according to the Philosopher Metaphysics 7.1.1028a10-b2. And his intention concerns the substance that is one of the dividers of being [sc. into categories], so that to expound ‘substance’ there of God or the first substance is not relevant to his intention. For he proves that substance is first in the way he proves that substance is of the number of the dividers of being - that it is prior to every accident, namely such that, in order to determine everything that divides being, it suffices to determine substance as what is first, because the knowledge of accidents is had from the fact they are attributed to substance; but this is only to the purpose about substance in its whole ordering; for nothing posterior to this ordering can be the formal reason whereby something is in that ordering. Therefore, from the idea of the priority of substance universally, as it is something common, sufficient determination is made about the ordering that is the ordering of primary substance, to which this natural priority to any accident belongs; so being a ‘this’ naturally prior to its determination by any accident belongs to primary substance in its idea.

83. And the consequence can be confirmed, because when something is prior to something else, the maximally first of that something is prior to the something else; but the maximally first in substance in general is primary substance; therefore primary substance is simply prior to every accident, and so it is first a ‘this’ before it is determined in any way by anything else.

84. Here it is said [by Godfrey of Fontaines] that although primary substance is prior to quantity in existing yet not in dividing - just as also secondary substance is prior in entity but not in divisibility.

85. On the contrary:

This response destroys itself, because if primary substance is naturally prior to quantity in existing, and if primary substance cannot be understood in its existence unless it be understood as it is a ‘this’, then it is not prior in existing unless it is prior as a ‘this’; therefore it is not a ‘this’ by quantity.

86. Further, form is prior simply to the composite, according to the Philosopher’s proof Metaphysics 7.2.1029a507. Therefore if quantity is the form of primary substance insofar as it is primary substance, then quantity will be simply prior in being to primary substance - because if quantity is not the form in being, then it is not the form in dividing either, or in the unity that belongs to primary substance insofar as primary substance is such a being (for any entity is followed by its proper unity, which unity does not have any other proper cause of itself than the cause of entity).

87. Further, substance, in the way that it is the subject for every accident, is naturally prior to every accident. For, insofar as it is the subject, it is proved to be prior in definition to every accident, for it is by way of addition thus posited in the order of any definition; but as it is the subject it is ‘this substance’, because, according to the Philosopher Physics 2.3.195b25-26 and Metaphysics 1.1.981a16-19, singulars are causes of singulars (in any genus of cause), so a singular subject is cause of a singular accident. And there is an especial confirmation of this as to an accident in an accident, because that is present first in a singular, according to the Philosopher Metaphysics 5.9.1017b35-1018a3 , ch. ‘On the Same’.

88. Further, everything that is prior in nature to something else is prior to it in duration, in the way that - as far as concerns it of itself - there is in it no repugnance of contradiction in its being able to be prior in duration to its posterior; for priority of nature universally includes in the prior thing the ability, without contradiction, to exist in the absence of its posterior, from Metaphysics 5.11.1019a2-4 ch. ‘On the Prior’. Therefore any substance (as far as concerns itself) can, without contradiction, exist prior in duration to any accident, and thus prior to quantity.

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.

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.

B. Scotus’ own Conclusion

111. Therefore, I concede the conclusions of all these arguments [nn.76-110], namely that it is impossible for substance to be individual through any accident, that is, impossible for substance to be divided into subjective parts [sc. into individuals] through something accidental to it and thereby have being ‘non-this’ repugnant to it.

II. To the Arguments for the Opinion of Others

112. As to the first argument for the opinion [n.72], it is plain from the fifth article [nn.105-109] how badly the minor is taken [sc. ‘to be divisible into parts of the same idea belongs to something by reason of quantity’], and that it cannot be got from the Philosopher [n.107]; and in the way in which the minor can be held to be true, it is not relevant to the division of a whole into quantitative parts [n.109].

113. When further too the premise is taken that ‘by the same thing is something divisible and distinguished into the parts that divide it’ [n.72: ‘quantity is the principle of division in any nature and the principle of distinction between divided things’] - this is false, for a common nature is divisible of itself into individuals, and the divisions of it are not distinguished by reason of the nature but by their own distinguishing differences; for thus does it appear in a genus, that a genus is divisible of itself into several genera and several species, and yet the genus is not the reason for the distinction of species but the differences are that constitute the species.

114. As to the second argument [n.73], it is plain how from it can be concluded that the same thing would generate itself [n.110]. But as to the form of the argument, I say that both premises are false: for although ‘a different form is in a different matter’ [n.73, ‘form does not differ from form save because it is received in different parts of matter’], yet it is not a different form because of difference of matter, but just as a form’s entity is prior so also is its difference; likewise the other premise - namely that ‘there is a different part of matter because there is a different part of quantity’ [n.73, ‘nor does one part of matter differ from another save because it is under a different part of quantity’] -is false, because, whether the distinction of parts of matter in themselves is quantitative or not, the distinction of parts of matter is prior to the distinction of quantity (for the subject of such an accident is a ‘this something’).

115. As for the proof, when it is said that ‘the generator does not generate save from a matter quantified by a different quantity’ [n.74, ‘a generator does not generate another save because of distinctness of matter etc.’] - whether this is so or not (about which elsewhere [n.208]), at any rate, in the case of parts of matter that are distinct in form of quantity, I say that unity is a metaphysical property [n.128], so that unity of matter naturally precedes any idea of quantity; for an idea of quantity does naturally precede such a natural generator, because the generator requires, externally, a matter of its own from which it generates, and it requires the quantity as a concomitant distinction of matter from matter. And yet what needs to be proved is that the quantity was the proper idea of such unity, that is, of singularity in the substance, and what is proved is that it is the idea sine qua non in respect of the ultimate thing [sc. the thing generated]; hence there is no place for the consequence.Tr. The contention seems to be that in the argument [in n.74]: ‘the generator does not generate save from a matter quantified by a different quantity; therefore quantity is the idea of distinction in the generator’ the conclusion does not follow. What follows rather is that a difference of quantity in the matter on which the generator works is required for the generator to be able to work on it. So all that follows is that such difference of quantity in the matter worked on is the sine qua non of the generator’s generating. It does not follow that the difference of the quantities in the matter of the thing worked on and in the matter of the generator working on it is what formally makes the generator’s own quantity to be ‘this quantity’. For it could still well be, as for as this argument goes, that ‘this quantity’ is a ‘this’ because it is the quantity of ‘this substance’. So the argument in n.74 does not prove, as it needs to, that the ‘this’ of ‘this substance’ is the result of the quantity’s being a ‘this’ and not, as Scotus contends, the cause of it. ⁵⁸

116. If the objection be raised that at least from the confirmation [n.74] one will get the result that quantity naturally precedes the individuation of substance (which is contrary to the conclusion of the second way rejecting the opinion [nn.82-83]) - for if the generator first requires a quantified matter before it may generate, then the quantity of the matter is naturally presupposed to the individuation of the thing generated - I reply and say that the quantity of the thing corrupted and all the accidents of the thing corrupted are presupposed, in the order of duration, to the individuation of the thing generated, because the thing corrupted with all its parts pre-exists; but herefrom nothing follows as to the minor, that there be a natural priority of quantity to the individuation of the thing generated [n.74, ‘the quantity of the thing generated naturally precedes the being of the thing generated’], or follows as to the individuation of the substance in which the quantity is - for the accidents of the thing corrupted, which precede in time the thing generated, follow the substance in which they are (and follow it even as it is singular), and in the same way do the accidents of the thing generated follow the substance of the thing generated.

117. But the argument [n.74] is taken still further back [by Godfrey], that ‘quantity - as it is in the thing corrupted - not only precedes the thing generated, but naturally precedes in the thing generated the form of the thing generated’. The proof is that, otherwise, in the instant in which the generator introduces the form, it would introduce it not into a quantum, and this seems contrary to the proposition that ‘a particular agent does not reach the substance of the matter but reaches the matter precisely insofar as it is a quantum’ [n.74, ‘a natural agent cannot act on a non-quantum’]; it seems likewise contrary to Averroes in his treatise On the Substance of the Globe ch.1, where he seems to hold that the quantity remains the same in the thing generated and in the thing corrupted, otherwise the generator would generate body from non-body.

118. Against this I argue as follows:

And first indeed it seems that this argument [n.117] should not be adduced for this opinion [n.71], because he [Godfrey] who seems to be the founder of this position seems to hold what is here adduced against it [n.117]. For he holds [Quodlibet 11 q.3, 7 q.5, 6 q.5, 2 q.7] that, since quantity is not the first act of matter, no form of corporeity remains the same in the thing generated and in the thing corrupted (he says, when speaking of corporeity in the genus of substance, that no quantity remains the same in number in the former and in the latter); and also, since he posits that quantity perfects the composite substance (and not the matter) immediately as subject, he should posit that the different quantity of the thing generated is naturally posterior to the thing generated, just as he should also posit that the quantity of the thing corrupted is naturally posterior to the thing corrupted - and thus the deduction about the priority of the quantity to the substance or the form of the thing generated (whatever may be true of Averroes) does not belong to the opinion of the one who posits that opinion [n.71]. This as to the man [Godfrey]. But as to the conclusion in itself, I say with him (as far as these matters are concerned) that if no form of corporeity remains the same formally in the fire and in the water, then altogether no accident - which requires a composite substance as subject - can remain the same in number, but each will be either in the thing corrupted as subject or in the thing generated as subject; and so quantity, and any other accident, will be naturally posterior to substance - and thus the quantity of the thing corrupted, and any other accident of it, was naturally posterior to the substance corrupted.

119. And then about that proposition [n.117, ‘a particular agent does not reach the substance of the matter but reaches the matter precisely insofar as it is a quantum’] I do not much care, because it seems impossible; for to be an agent that reaches the thing acted on in its idea as acted on seems to be nothing other than to introduce into it the act by which it is perfected; but the particular agent introduces a substantial form whereby the matter as matter is perfected - and not matter as a quantum, such that quantity is the ‘mediating idea’ between the agent and the thing acted on; therefore a natural agent reaches the matter in its bare essence as the acted on thing that is immediately changed by the agent.

120. As to Averroes [n.117], I say that a body could be generated from what was once a non-body, but perhaps a natural agent could not generate a body from a non-body as from a thing corrupted; but from what was a body up to the instant of generation, and this by the quantity inhering in it, a natural agent can in that instant generate something else that is a quantum with a different quantity; because, just as it can generate a substance that was not present before, so it can produce all the accidents consequent to that substance.

121. And if you say that, although it does not produce a body from a non-body as from a thing corrupted, yet it will from matter as from a non-quantum produce another body that is a quantum - I say that a composite must come to be or be produced from a non-composite as from a part, or there will be a process to infinity; and so, from matter according to its substance absolutely as from a part, a body can be produced that is a composite substance, and the substance as quantum is a concomitant, because quantity is a property of the composite substance (this response denies that an indeterminate dimension numerically the same remains in the thing generated and in the thing corrupted, about which elsewhere if occasion arise [Ord. 4 d.11 p.1 princ.1 q.2 nn.6-7, princ.2 q.1 nn.18-21 and 50]; but it has been touched on now because of the arguments [nn.118-121]).

III. To the Principal Arguments

122. To the first principal argument, from Boethius [n.67], I concede that variety of accidents makes a numerical difference in a substance in the way that the form is said to make a difference, because all distinct forms thus make some difference in the things they are in; but accidents cannot make a specific difference in the substance they are in (from Metaphysics 10.9.1058a29-b25); so they do make a difference in substances and that a numerical one; but they do not make the first difference (but there is another, prior, numerical difference), nor do they alone make the numerical difference. And the authority [from Boethius] says neither of these two things, and unless one of them is got from it the conclusion intended is not got from it.

123. But what about Boethius’ intention?

I say that Boethius intends to prove that there is no numerical difference in the divine persons. And although at the beginning of his little book On the Trinity such propositions could be got scattered about, yet he seems to argue as follows: ‘a variety of accidents makes a difference in number; but in the divine persons there is no such variety of accidents, because a simple form cannot be a subject; therefore there is in them no numerical difference’.

124. The argument, it seems, unless Boethius meant that only accidents could make a numerical distinction, is not valid; for if a numerical distinction could exist through something else, then the negation of numerical distinction would not follow from the negation of accident. I say that a distinction of accidents is concomitant to every numerical distinction, and so there can be no numerical distinction where there can be no variety of accidents; and on this basis the argument of Boethius can hold up, because since there cannot be any accident in divine reality (nor any variety of accidents), there cannot be there a numerical distinction or difference - not as from the denial precisely of the cause there follows the denial of that of which it is the cause, but as from the denial of a necessary concomitant there follows the negation of that which it is necessarily concomitant to.

125. But how, relative to this intention, is it true that a variety of accidents makes a numerical difference?

I say that it makes some difference but not the first difference, and some difference that necessarily follows every difference; and thus does the statement ‘they make a numerical difference’ have to be understood. Nor does this gloss seem to be forced from the words, but the words themselves make it to be understood so, since they [sc. Godfrey and his followers who quote Boethius, n.67] must necessarily expound what he himself subjoins there about place. For place is not the first thing that distinguishes individuals from each other, either when speaking of place as it is the property of the containing thing or when speaking of place as it is the property of the thing contained (namely the ‘where’ that remains in the thing contained). So if they must expound ‘place’ as ‘quantity’ (according to their opinion [n.71]), what is wrong with expounding ‘make a difference’ as ‘make not the first difference but some difference and it is concomitant to the first’?

126. To the second argument, from Damascene [n.68], the response is plain from himself at the end of the chapter, where he expounds how he there understands ‘accident’. He speaks thus: “Whatever is a hypostasis in some of the things that are of one species, but in others of them is not, is an accident and added from without.” I concede therefore that whatever is outside the idea per se of a specific nature itself, and is not a per se consequent of that nature, is accidental to such nature; and in this way whatever is posited to be the individuating principle is an accident; but it is not properly an accident the way others understand this [n.128].

127. And indeed that Damascene himself does not understand accident properly is plain from what he says in On the Orthodox Faith ch.8: “For we mean that Peter and Paul are of the same idea.” Later, “Hypostases have in themselves several things that separate them; they are divided in mind and in strength and in form (that is, in figure) and in habit and in complexion and in dignity and in invention and in all characteristic properties;” and he notably adds to ‘in all characteristic properties’, “to the extent that these do not exist in themselves in relation to each other but exist separately; hence they are called two men and three men and many men. And so on in every case.” - Note well: he says that, rather than by characteristic properties, all created hypostases whatever differ by ‘not existing in relation to each other but separately’; and this is said by way of an opposition in the same place, “the holy hypostases of the Trinity are in relation to each other”, the reason for which is unity of nature, personal distinction being presupposed (Ord. 1 d.2 nn.376-87). Division of nature, then, in created supposits is the first and greatest reason for distinction.

128. To the third argument, from Avicenna [n.69], I say that he is most principally considering quiddity insofar as it includes nothing that does not pertain to its per se idea, and in this way horseness is ‘just horseness, and is neither one nor many’. To whatever extent its unity is not something else added but is a necessary consequent of the entity (just as every being, according to any entity whatever, has also its own unity consequent to it), that unity is nevertheless not within the formal idea of the quiddity (as the quiddity is quiddity), but is a sort of property consequent to quiddity [nn.31, 34] - and everything of this sort is called by Avicenna an ‘accident’. And in this way too the Philosopher (who named the ‘fallacy of the accident’) sometimes takes accident for everything that is outside the formal idea of another (for everything such, in comparison to the other, is extraneous to that other); and in this way does a fallacy of the accident come about, and in this way too is genus accidental to difference; and whatever is the individuating principle is an accident of the specific nature, but not in the way they [Godfrey and others] understand accident. And so there is here an equivocation over the term ‘accident’.