Cursus Theologicus, Tomus I: In Primam Partem

33 From what was said in the preceding difficulty, it is sufficiently established that matter is the first and radical principle of the individuation of the whole composite, and consequently also of the substantial form. But once this has been explained, the question immediately presents itself: whether matter, taken in itself and precisely speaking, or matter marked by quantity, possesses the character of the aforementioned first and radical principle? Once this too has been explained, the entire question will remain clear. For although, in producing the determinate individuation of a composite, the union of matter and form also concurs directly, it is nevertheless certain that, in this union, individuation cannot ultimately be resolved, whether that of the whole itself or of matter or form: for the singular and individual union, insofar as it rests on the side of matter, certainly presupposes matter to be individual. Likewise, the individual union of form cannot fail to suppose form—and consequently matter also—to be singular and individual: for the union is this rather than that precisely because it is the form of this; and it is the form of this because this is the form of this matter, as was shown above. We therefore raise no further difficulty concerning the union. Since, however, the title of the difficulty involves some ambiguity, we must explain it before stating the opponents’ view.

§ I. Explanation of the title.

34 From the explanation of the title, it must be noted that three things can be understood by “matter marked by quantity.” First, a certain accidental composite arising from matter and from quantity itself, here taken in actuality and in act. Second, matter itself—not quantity taken formally, as the formal principle, and directly, but a certain mode superadded to that same matter, by reason of which it is determined or marked by a certain quantity, that is, by this quantity and not that one. Thus it entails a certain concrete, or quasi-concrete, arising from the aforesaid mode, seal, and glazing together with matter itself, by reason of which matter is said to be marked by the aforesaid quantity. Thus, although this mode and the determination or marking caused by it, and consequently matter, may be introduced directly as marked, quantity is nevertheless said to be marked by means of it, because quantity itself is introduced obliquely and cannot, without being so introduced, render matter marked with respect to a certain determinate substantial form and a certain determinate quantity. The whole question is therefore best explained by the fact that matter marked by quantity is the first principle of individuation, for in this complex both matter and the mode and marking are introduced directly, while quantity is introduced obliquely.

Third, matter itself insofar as it means pure and bare materiality, apart from the aforesaid mode superadded to it and naturally distinct from it, yet with something conjoined to it: namely, insofar as it means matter itself as having this quantity, and not that one, by the mode of the first root; or, as many hold, insofar as, by the mode of the first and radical principle, it means its connection or relation to this quantity rather than that one. For by reason of this it is designated and determined for this form and this composite rather than that one.

35 The title of the difficulty is therefore not understood to concern matter marked by quantity in the precise sense of any one of the markings just enumerated. Rather, abstracting from all of them, it means matter marked or determined by quantity, whether this determination occurs in the first or the second of the modes just described. In the following difficulties, however, we shall explain by which of those modes matter must be marked in order to be the first and radical principle of individuation, so that we may separate what is more certain and generally accepted from what is not so certain and accepted. For that matter marked by quantity is the principle of individuation is a point more certain and universally accepted among Thomists, even though it is not equally certain and accepted by which of the aforesaid modes it is marked or determined by quantity so as to be the first radical principle of individuation.

It follows that one can understand why St. Thomas and his disciples use the complex expression matter marked by quantity when investigating whether matter, insofar as it bears quantity in one of the ways described, possesses the character of the first and radical principle of individuation. Clearly, as we shall say below and have already touched upon, it is peculiar to matter, insofar as it imports quantity in one of the ways described, to be rendered apt, determinate, and marked for having this form rather than that one, for being a part of this composite rather than that one, and thus for being the root both of this form and of this composite as this and individual.

36 This can be explained further: for to ask whether matter marked by quantity is the first root of individuation is the same as to ask whether matter, insofar as it is this and is singular by its due mode, is altogether through quantity the principle of the aforesaid individuation. For being altogether singular and being matter marked are the same: since only singular matter can of itself and apart from anything else be designated as singular, and therefore the Dialecticians use the term “marked individual” to signify something wholly determinate to be singular or individual. Hence, if matter, insofar as it bears quantity in one of the ways described, can be the principle of individuation, it must be so: for by importing that quantity it becomes this and wholly singular, and consequently matter marked; and therefore, when investigating whether matter, insofar as it bears or involves quantity in one of the explained modes, is the first root and principle of individuation, St. Thomas and his disciples use this manner of investigation excellently: namely, whether matter marked by quantity—which is the same as matter made this, determinate, and singular by its due mode and designated through a determinate quantity—is the first principle of the aforesaid individuation.

§ II. The first opinion is introduced.

37 The first opinion asserts that matter, taken in itself and precisely speaking, but not matter sealed by quantity, is the first and radical principle of the individuation of the whole substantial composite. Thus Albertus, as cited by Flandria, 7 Metaphysic., quaest. 22, art. 1; Suarez and others agree in part, as is clear from what was said in the preceding difficulty.

First, it is proved. For St. Thomas absolutely affirms that matter is the first principle of the individuation of the substantial composite, without any mention of quantity or intervening marking: in 1 part., quaest. 3, art. 2 ad tertium, and in several other places cited under individuum in the Tabula aurea, num. 21, and especially in his little treatise On the Principle of Individuation, in these words: Therefore, whatever is the first subject of all things in the process of generation, and is incomplete insofar as nothing of that genus is predicated of it, namely matter, must necessarily be the first principle of being incommunicable, which is the first individual.

First, it is confirmed. For in the same treatise he not only said absolutely that matter is the first principle of individuation, but added that this pertains to matter alone insofar as it preserves the character of a first principle; and thus he says: For matter alone is in the principle of individuation insofar as it preserves the character of the first

Second, it is confirmed from the same holy Doctor, part. 1, quaest. 29, art. 1, where he establishes a distinction between the individuation of accidents and that of substance, according to which substance is individuated through itself rather than through accidents; and thus he says: Although the universal and the particular are found in all genera, the individual is nevertheless found in the genus of substance in a special way: for substance is individuated through itself, but accidents are individuated through their subject, which is substance; for this something is said insofar as it exists in this subject. Accordingly, the individuals of substance also appropriately have a special name in comparison with the others. As he also taught in q. 9, De potentia, art. 1 ad 8, saying: Accidents, however, are not individuated except through their subjects; but substance alone is individuated through itself and through its proper principles, and therefore the particular has an appropriate name of its own in the genus of substance alone. Therefore, if matter is once the first principle of the individuation of the whole material substance, as we said in the preceding difficulty, it cannot have the character of such a principle as accidents have, but only insofar as it is taken in itself and precisely speaking.

38 Secondly, it is proved from reason. Since matter, taken in itself and precisely speaking, is the first part and first root of the substantial composite, it will likewise be the first part, first root, and principle of its individuation. The antecedent seems evident, because, as our Complutensians teach in lib. Physicorum, disput. 15, num. 19 and thereafter, from a comparison between matter and form, which alone are the parts of the substantial composite, matter precedes form insofar as it is what has the potency to be produced into the other. Consequently, it is proved. For since each thing is one and individual in itself, as being is, it follows that whatever, taken precisely, is the first part and first root of the substantial composite must also be the first part and first root of individual unity, and consequently of its individuation.

Third, because specification is derived from form, so also individuation is derived from matter, as is clear from what was said in the preceding difficulty. Thus the individuation of the substantial composite is to be derived from the first root in matter taken in itself, not from matter insofar as it bears quantity in some way, or as matter marked by quantity. The consequence is evident. Because specification, precisely insofar as it is derived from form as from the first root, is derived from form alone according to what it bears of itself viewed precisely and by its proper merits, so also, precisely because individuation is derived from matter as from the first root, it must be derived from matter itself and according to what it bears of itself precisely viewed in its proper merits, not insofar as it bears quantity in some way.

39 Fourth, because generic unity is derived from matter alone as from the first root, according to what our Complutensians teach excellently in Logic, disput. 5, num. 75. Thus also individuation, or individual unity—the reason why one individual differs from another by number alone—is derived in the same way. The consequence is evident from the parity of reason. For generic unity is derived from matter alone as from the first root because such unity is material insofar as it is predicated exactly of a thing that stands in the place of matter and of potency with respect to specific differences. Thus, since individual unity is also material, it follows that it too is derived from matter alone. Especially because individual unity is more material than generic unity: for the genus is counted among the formal degrees with respect to species, even though it stands in the place of matter with respect to specific difference; individuation and individual unity, however, have being only through a mode of condition or material determination with respect to species.

It is confirmed. For matter is of itself incommunicable to anything in the same way in which the superior reason is present in inferiors: because it is of itself irreceptible into any other. Thus, of itself and according to its proper merits viewed precisely, it will be the first root of individuation. The consequence is evident. For what is most powerful in the individual as such is the reason of the altogether incommunicability just described. Thus, for the present purpose of a first root, what belongs to matter according to its proper merits and is incommunicable in the manner indicated suffices.

40 Fifth.

40 Fifth, because before matter actually receives this quantity rather than that one, or is determined by some mode naturally distinct from quantity to this one rather than that one, or has this one radically within itself, or bears a relation to it, it must be understood to be singular and individual. Thus matter itself, taken in itself and precisely speaking, will be individual and the first root of the individuation of the whole composite. The antecedent seems evident from itself. For this quantity rather than that one—or, equivalently, singular and individual quantity—cannot be received except in singular matter. Neither can common matter, but only singular matter, be determined or bear a relation to this quantity rather than that one, or contain it by the mode of a root; for common matter is of itself indifferent to any quantity.

The consequence in its first part follows from the antecedent. For precisely because matter is presupposed to be individual before it in some way imports singular quantity, it cannot in any way be rendered singular by it, just as neither can it be rendered singular by this substantial form rather than that one, or by any other singular accident: for substantial form and all singular accidents are likewise received in singular matter and consequently presuppose it as singularized. Matter must therefore be individual of itself.

In its second part, the same consequence is likewise clear. For matter is the first part of the substantial composite; and thus, precisely because it is of itself, rather than marked by quantity, individual, it cannot fail to be the first root of the composite’s individuation, just as by its own character it is the first root of its materiality.

41 Lastly, because matter cannot be the first root of the composite’s individuation insofar as it is actually affected by quantity and includes it, nor insofar as by some superadded mode naturally distinct from quantity it is determined to this quantity rather than that one, nor finally insofar as it in some way contains this numerical quantity, it can in no way be the principle of individuation insofar as it is sealed by quantity. The consequence needs no proof once the matters explained in the exposition of the title are posited: for, as is clear from itself and from what was said there, matter can be marked by quantity only in these three ways, and only thus marked can it be the first root of individuation.

The antecedent in its first part, however, seems certain. For no accident can be required for the individuation of a substantial composite as something actually and actively present, or intrinsically included either in the individual itself or in the principle of its individuation. Thus, even if God separated quantity and the other accidents from Peter, he would still remain with his individuation. Just as the accidents of bread can be separated from the bread itself in the sacrament of the Eucharist, those accidents nevertheless remain individual and singular. With greater reason, the same must be said of substance itself when separated from those accidents: for it depends on them less than they depend on it.

In its second part, too, the point is clear. For beyond matter, form, and union, no other entity or substantial mode is found in a substantial composite, as will be clearer from what is to be said in dub. 4. The same antecedent also holds for the third part. Because the numerical substantial form is introduced in matter before numerical quantity, as is clear from what our Complutensians teach in lib. De generatione, disput. 2, num. 68 and 76; for quantity is not received in matter alone, but in the whole composite. Thus matter will contain this substantial form by the mode of a root before this quantity; and consequently, since matter cannot fail to be singular in that same antecedent in which it contains this numerical form, it cannot be individuated by having this numerical quantity rather than that one.

42 It is confirmed. For if matter, insofar as marked by quantity, were the principle of individuation, it would follow that both matter and form, as actually and in execution conferring the first degree, namely substantial being, would be something not singular but merely common. This, however, is absurd; therefore, etc. The minor follows from itself, because whatever is actually and actively given on the part of a thing must be something singularized. The sequence, however, is proved. For, as St. Thomas teaches from Aristotle in 1 part., quaest. 76, art. 6, form is immediately united to matter with respect to the first degree it confers on matter, such that quantity is not required even by the mode of disposition or in the genus of material cause. This is because matter is of itself determined to receive the first degree that can come to it from substantial form, namely substantial being. Thus, if matter is not individual except insofar as sealed by quantity, it will not be able to be singular in that antecedent in which it actually receives form according to the degree just stated. Consequently, neither will form conferring being upon it in that same antecedent be singular.

§ III. The true and ancient opinion of Aristotle and St. Thomas.

43 It must nevertheless be said that matter sealed by quantity in one of the three modes enumerated in the explanation of the title from num. 34 through num. 37 is the first and radical principle of the individuation of the whole substantial composite, and consequently the principle of its substantial form. Thus Aristotle, 5 Metaphysic., text. 12, in these words: Moreover, some things are one according to number, others according to species, others according to genus, and others according to analogy: according to number, indeed, those whose matter is one, etc. St. Thomas explains these words as follows in ibid., lect. 8: He posits another division of the one: some things are one numerically, some in species, some in genus, and some by analogy. They are one according to number whose matter is one. For matter, insofar as it stands under marked dimensions, is the principle of the form’s individuation, and therefore the singular belongs to it from matter, insofar as it is one numerically as divided from others.

The Angelic Doctor likewise explains the same testimony of the Philosopher in his commentary on Boethius, De Trinitate, q. 4, art. 2 ad primum, in these words: When the Philosopher says that things are one numerically whose matter is one, this must be understood of matter marked by quantity, which underlies dimensions; otherwise he would have to say that all generables and corruptible things are one numerically, since their matter is one.

The Angelic Doctor teaches the same in De ente et essentia, cap. 2, letter H, where he speaks as follows: Therefore it should be noted that matter is not the principle of individuation when taken in just any way, but only matter marked by quantity. By matter marked by quantity I mean matter considered under determinate dimensions. This matter, however, is not included in the definition of man as man, but would be included in the definition of Socrates, if Socrates had a definition; whereas in the definition of man, unmarked matter is included. For this bone and this flesh are not included in the definition of man, but bone and flesh absolutely, which are the unmarked matter of man. In the cited treatise on Boethius, q. 4, art. 2, in the answer to the second, he says: Since dimensions are accidents in themselves, they cannot be the principle of the individual unity of substance; rather, matter insofar as it underlies such dimensions is understood to be the principle of such unity and multiplicity. In the answer to the fourth he asserts: Those things that differ numerically in the genus of substance do not differ only accidentally, but also in form and matter. But if it is asked why this form differs from that one, no other reason will be found except that it exists in this marked matter; nor is any other reason found why this matter is divided from that one except quantity. Thus matter subjected to dimension is understood to be the principle of this diversity.

44 The Angelic Doctor also taught this in 4 sentent., dist. 12, q. 1, art. 1, q. 3 ad tertium, and 3 part., q. 77, art. 2, where he requires two things for the individuation of a material thing: namely, the subject, or matter, and quantity. Finally, he defends this very point in 1 part., q. 3, art. 2 ad tertium; q. 30, art. 3; q. 50, art. 4; q. 54, art. 3 ad secundum; q. 56, art. 1 ad secundum; qq. 75 and 85, art. 1 ad secundum, and 1 contra gent., cap. 21, and 2 contra gent., cap. 92, and q. De malo, art. 1 ad octavum, and very often elsewhere. Thus both Aristotle and St. Thomas are followed by Capreolus in 2, dist. 3, q. 1, art. 2, concl. 2, and art. 3, in the answer to Scotus’s arguments, second in order, against the same conclusion; Cajetan, De ente et essentia, cap. 2, q. 5; Soncinas, 7 Metaphysic., qq. 33 and 34; Ferrara, 1 contra gent., cap. 21; Flandria, 7 Metaphys., q. 22, art. 3; Javellus, 5 Metaphysic., q. 15; Abulensis, 2 tom., on cap. 23; Exodi, q. 60, near the middle; Báñez, 1 part., q. 3, art. 2 ad secundum, and 1 De generat., cap. 5, q. 3, art. 8, asserting that our proposition as it stands must be accepted by all who profess themselves disciples of St. Thomas. The same is defended by Nazarenus, 1 part., q. 3, art. 2, unique controversy; González, q. 11, art. 1 ad 2, disput. 23, § 2, concl. 9; Ripa, q. 3, art. 2; Petrus a Jesu Maria, otherwise Serna Hispalensis, in his Logic, disput. 3, sect. 5, q. 5, q. 3, art. 1, asserting that this is the indisputable opinion of Aristotle and St. Thomas, and finally by very many others.

45 It makes no difference if, with Suarez, one answers that Aristotle never seems to have investigated and declared professedly and metaphysically the principle of individuation, but taught only in the physical manner, and as from a sign, that one material individual is distinguished numerically from another by quantity and other sensible accidents, that is, by matter marked by quantity. Thus the aforesaid matter has the character of the principle only insofar as it is known and perceived, not insofar as it is. In this same sense, it must be understood that St. Thomas says that matter itself marked by quantity is the first principle of individuation of material substance so many times.

It therefore makes no difference. First, because it would be strange that Aristotle in the same text should have treated at once both analogical, generic, and specific unity, on the one hand, and numerical unity, on the other, and that he should have assigned to the former their proper principle and root insofar as they are, while assigning to numerical unity alone a principle only insofar as it is known, not insofar as it is. Second, because Aristotle treated unity in the Metaphysics and in a metaphysical way, according as it stands in the place of a passion with respect to being, which is the proper object of metaphysics. Then, because the character of unity in this sense becomes very well known from recognizing the different modes of unity—namely, analogy, genus, and species—he also treated them in the same Metaphysics and in a metaphysical way, assigning to each its proper principle insofar as it is. Thus, when in the same place he also speaks of numerical unity and assigns its principle, he likewise treated it and its principle both insofar as it is and in a metaphysical way. For knowledge of this unity insofar as its being and its root no less contributes to an exact understanding of unity than knowledge of the other modes of unity. Especially because, as we saw from Aristotle in the preceding difficulty, the proper principle of the aforesaid unity insofar as it is cannot be form, but matter determined to this individual, or substantial composite, which, as will be clear from what is said immediately below, is nothing else than matter marked by quantity in one of the aforesaid modes.

46 It follows also that Suarez’s exposition cannot be adapted to the testimonies of St. Thomas. First, because Aristotle and the Angelic Doctor speak in the same way. Second, because the arguments we brought from Aristotle and St. Thomas in the preceding difficulty either prove nothing or merely suggest that matter marked by quantity is the principle of individuation insofar as it is, not only insofar as it is known, as will be clear to those considering them. Then, because the holy Master, both in the cited place from 3 part., q. 77, art. 2, and in treatise 70, q. 4, art. 2, and often elsewhere, concludes from this that matter, not taken in just any way but marked by quantity, is the first principle of the individuation of the whole substantial composite. For quantity in itself, as though from the first root, has a kind of individuation of its own. Thus matter insofar as it underlies quantity (in the manner explained at num. 116 and thereafter) must rightly be the first principle of individuation, according to the common maxim: nothing is such unless it is such of itself or subsists in it in some way something that is such of itself. This argument (as is clear from itself and will be clearer from what will be said at num. 49, 91, and 92, and in the following disputation from num. 21 through 27, and also at num. 38) proves that matter insofar as it underlies quantity, or is marked by quantity, has the character of the first principle of individuation, not only insofar as it is known, but also insofar as it is.

Finally, because Suarez’s exposition openly contradicts several testimonies of St. Thomas cited at num. 9 and 10, as is clear to the reader. Above all, however, it contradicts the testimony of the same holy Doctor in tract. 70, q. 4, art. 2, where he says: Matter considered in itself is neither the principle of diversity according to species nor according to number. But just as it is the principle of diversity according to genus insofar as it underlies a common form, so it is the principle of diversity according to number insofar as it underlies determinate dimensions. Thus, since these dimensions belong to the genus of accidents, numerical diversity is sometimes reduced to diversity of matter and sometimes to diversity of accidents, precisely by reason of the aforesaid dimensions. Other accidents, however, are not the principle of individuation; rather, they are the principle by which the distinction of individuals is known. In this way, too, individuation is attributed to the other accidents.

47 But if matter marked by quantity, and consequently quantity, were not in some sense—the sense explained below at num. 116 and thereafter—the principle of the individuation of material substance insofar as it is, there would be no such diversity as St. Thomas established in the place recently cited between quantity and the other accidents. For the other accidents also are signs by which the individuation of a substantial composite is known a posteriori, and the composite can be demonstrated through them. Accordingly, the two testimonies from St. Thomas, tract. 32, De natura materiae et dimensionibus interminatis, cap. 3, and tract. 29, De principio individuationis, which Suarez cites in disp. 5 of his Metaphysics, sect. 3, on his own behalf, do not press against this position; rather, as will be clear from what we shall cite below at num. 75, they strongly favor us, as will appear even more clearly from what will be said at num. 139.

§ IV. The opinion of Aristotle and St. Thomas is supported by a fundamental reason.

48 Because Francis Suarez says in the cited place, disput. 5, sect. 3, num. 4, concerning our assertion—which we have shown to be the very mind of Aristotle and St. Thomas by testimonies drawn from them—that he scarcely finds any foundation for it that can be reduced to Aristotle’s authority, after we have established the aforesaid assertion by testimonies of Aristotle and St. Thomas, and at the same time explained in what way the expositions adduced by Suarez to prevent an appearance of opposing the Philosopher and the Angelic Doctor are not correctly adapted to them, we have chosen to expound and explain from their roots a twofold fundamental reason in this and the following section, so that it may be clear whether the opinion of Aristotle and St. Thomas is established on solid foundations or not.

The first, therefore, and fundamental reason for the assertion is drawn from St. Thomas in the cited place on Boethius, De Trinitate, art. 2, and can be stated as follows. Because form cannot be the first root of the individuation of the whole substantial composite, and this must necessarily pertain to matter; but matter taken in itself and precisely speaking cannot possess the character of the aforesaid principle and root, matter itself, therefore, insofar as marked by quantity, will be the first principle and root of such individuation. The major follows from what we said at num. 11 and thereafter. The minor, however, is also clear. For matter taken in itself and precisely speaking is common to all forms and to all sublunar composites, and therefore cannot be proper to one individual rather than another. Thus it cannot be the first root of the individuation of this composite rather than that one.

The consequence plainly follows from both premises. First, because it is probable that by “quantity,” through which matter is marked, quantity is not understood mathematically but physically, that is, together with the qualities and sensible accidents by which it is affected. It is clear, however, that if the individuation of a substantial composite cannot be taken from the substantial form itself as from the first root, nor from matter itself taken precisely, then nothing else remains from which it can be taken except from matter as marked by accidents that dispose it to this substantial form rather than that one; or, equivalently, matter marked by sensible quantity understood physically.

49 Furthermore, and most importantly, because, as we shall explain in the following disputation at num. 24 and thereafter, quantity has this peculiarity among the other accidents: that in some way it has being as the root of its proper individuation. Thus matter, which taken in itself and precisely speaking is not the first root of individuation unless something is superadded to it, can possess the character of the aforesaid root if it is determined and marked through quantity. For just as, because fire is hot of itself and by nature, nothing can be hot unless it either is fire, contains fire, or in some way participates in it, so as to have a connection or order toward it, so quantity in itself in some way has material individuation and in some way is its first root. Therefore, nothing in material things has the character of an individual, or of its first root, unless it either is quantity, contains it, or bears a connection or relation to it—which amounts to the same thing—with matter marked by quantity in some way, as is clear from what was said at num. 34.

Finally, because the first root of the individuation of a substantial composite must be matter and not matter taken bare, it must be this same matter insofar as it imports some material accident on its part and concurs in a certain way with the reception of form, so that what is thereby preserved is that the first root of individuation is not substantial form but matter as such. For nothing except the aforesaid accident can be material on the part of matter and concur in a certain way with the aforesaid reception, as will be explained below at num. 116. And since quantity is the first material accident that holds on the part of matter (as was explained meanwhile by our Complutensians in the books De generatione, disput. 2, num. 97 and thereafter, and as we shall say from num. 119 through num. 124), it is necessary that matter, insofar as it in some way imports the aforesaid quantity and is marked by it, be the first root and principle of the individuation of the whole material composite.

50 It is confirmed and explained by a reason hinted at by the same Angelic Doctor. That which is the first root of the individuation of a substantial composite, when posited, first posits individuation; but when matter is marked through quantity, or—which is equivalent for the present purpose—marked by this quantity and not that one, the individuation of the whole composite is first posited. Thus matter, insofar as marked by the aforesaid quantity, will be the first root of such individuation. The major and its consequence are sufficiently clear. The minor, however, also follows from what was just said. For precisely when matter marked by this quantity is posited, matter is first posited as determined to this form and this composite rather than that one. But matter first determined to this form and composite rather than that one is that by which the individuation of the substantial form and the aforesaid composite is first posited. Consequently, matter insofar as marked by the aforesaid quantity will be that by which such individuation is first posited.

It makes no difference if one objects to this reason that if it proves anything, it proves quantity indeed to be the first and most powerful root of individuation, rather than matter, which is marked by quantity. This, however, seems absurd, because the first and most powerful root of substantial individuation cannot fail to be something substantial. Therefore, etc. The sequence is proved. For although matter marked by quantity may be the principle of individuation, when quantity and matter marked by it are compared, matter (as it is called in this reason) does not have being as the first root of individuation insofar as it is taken in itself, but insofar as it is marked by quantity. Thus it will have this by reason of quantity, and consequently quantity will be the most powerful root of the aforesaid individuation.

51 We answer that, if it is true that matter marked by quantity means matter insofar as it radically contains this quantity rather than that one, then the major concerning quantity so understood must be conceded, which, in the manner explained below at num. 133, is the same as matter itself insofar as it contains it. For when matter is considered in itself and insofar as it radically contains this quantity rather than that one, matter as containing it concurs more principally with individuation than matter itself taken in itself, as we shall say from num. 116 and thereafter. For matter insofar as it contains the aforesaid quantity is positively one numerically; taken in itself, however, it is at most one numerically in a negative sense.

Nevertheless, if matter marked by quantity means matter as actually affected by quantity and as informed by it through the mode of an inhering form, then it must be denied. For if it were true (as is considered in the following difficulty) that matter marked in this sense were the root of individuation, quantity actually present would either concur only obliquely, while matter would concur directly and thus more principally; or, if quantity concurred directly, it would not influence of itself what is prior and more essential in individuation, but what is posterior and bears the character of a property. Quantity actually inhering would thus have less principal influence, as will be clear from what will be said in the following difficulty.

§ V. The same opinion is established by another fully sufficient reason.

52 The second and most powerful reason for the same assertion is drawn from St. Thomas in the cited places, especially from the treatise On the nature of matter, and can be reduced to this form. Because material primary substances have from matter marked by quantity, as from the first root, the fact that they are material primary substances insofar as they are such, matter, insofar as marked by quantity, will be the first root of their individuation. The consequence seems evident, because the character of a material primary substance insofar as such consists in this, that it is individual and singular substance, as is clear from Aristotle’s Categories, in the chapter on substance. Thus, whatever was the first root of their primacy will also have the character of the first root of their individuation. The antecedent, however, is proved and explained. For material primary substances are constituted as primary because they are neither in a subject nor predicated of a subject. This occurs in them from the first root, namely, matter marked by quantity, according to the Philosopher’s words in 2 Metaphys., text. 30: The first in each genus is the cause and root of those that are after it in that genus. For matter marked by quantity is that to which it first belongs neither to be in a subject nor to be predicated of any subject, because it is itself the first subject and the first potency altogether irreceptible into anything else.

53 It is confirmed and explained by the reason touched upon above from St. Thomas, now, however, applied in this way. Because the generic character of material substance consists in a certain metaphysical character, holding by the mode of metaphysical potency with respect to the character of the difference, the generic character in them is therefore derived as from the first root from primary matter, which is primary and pure physical potency. Thus, because the individual and metaphysical character of the same material substance, or its character insofar as it is a primary substance in its own order, consists in this, that metaphysically speaking it is neither in a subject and hence is not predicated of a subject, it follows that it should be derived as from the first principle and physical root, from primary matter marked by quantity. For it is itself that to which it first belongs physically to be the first subject and first potency. By its being precisely such, it is repugnant of itself and essentially that it should be in any way in a subject, and hence that it should be predicated of any subject.

Second, it is confirmed, and this very point is explained more fully. Because that is the individual which is incommunicable to similar inferiors; but matter marked by quantity is the first foundation of this incommunicability. Thus it will also be the first foundation of individuation. The consequence together with the major is sufficiently clear. The minor, however, is proved. For form, because it is act, is communicable of itself; matter, because it is first potency, is of itself incommunicable. Thus, when form is received in matter marked by quantity, it is restricted through this reception so that it cannot in any way be communicated to anything else.

54 This confirmation is taken from St. Thomas in his commentary on Boethius, De Trinitate, q. 4, art. 2, in these words: No form, insofar as it is such, is this of itself. I say “insofar as it is such” on account of the rational soul, which in some way is this something of itself, but not insofar as it is form. Intellect, however, is naturally able to attribute to several things any form that can be received in something, whether in matter or in a subject, which is contrary to its character as this something. Thus form becomes this by being received in matter, and matter becomes this and marked insofar as it underlies dimensions.

This reason, together with its confirmations, is so efficacious that from it alone, when rightly expounded, the answers adduced against it by the opponents vanish. In the first place, from its exposition easily falls the answer that Suarez offers against this second principal reason in the cited disputation, sect. 3, num. 7, saying that it lacks efficacy because the reason of the subject of inherence is very different from the reason of the subject of predication or of inferiority. Although some proportion can indeed be conceived between these two subjects, since the superior is compared with the inferior subject to it, as form giving being, they are nevertheless simply not of the same character, nor is one founded upon the other. Thus, in simple and separated substances, such as the Angels, there is subjection or subordination of inferiors to superiors without a subject of inherence or information. Hence it is badly inferred from the fact that a primary substance, as such, is not in another as in a subject of inferiority or predication, or in the way in which the universal exists in its inferiors, that its individuation is derived as from the first root from matter, or the first physical subject marked by quantity.

55 This answer therefore easily falls if what has been said is rightly expounded. For just as the metaphysical potentiality of a genus, despite the different character of its metaphysical or potential reason and that of its physical genus or primary matter, is nevertheless taken as from the first root from the physical potentiality of matter, as our Complutensians explain excellently in Logic, disput. 5, num. 75, so, although the character of the first subject and first physical potency differs from that of the subject of inferiority or predication, because of the character posited for a material primary substance, consisting in this, that it has a substantial character so incommunicable that it is not in another as in a subject of inferiority or predication, it must nevertheless be derived as from the first root from matter marked by quantity. Its character is to be the first physical subject, and consequently that it is in no way physically in another as in a subject.

Therefore, in tract. De natura materiae, cap. 3, St. Thomas, expounding the character of a material primary substance and emphasizing that it is neither in a subject nor predicated of a subject, or equivalently that such a substance is the subject-side part of a substantial species, admits that this arises from primary matter, which is the first subject in the physical order, in these words: For when the subject in a certain species, or the subject-side part of a species, is the primary substance called the individual, that which holds the character of the first subject is the cause of individuation and of the division of the species into suppositia. The first subject, however, is that which cannot be received into another.

56 Nor does what Suarez adduces in favor of his position concerning the individuation of simple substances, namely God or the Angels, support him. The Angelic Doctor answers this point excellently in the cited treatise. After establishing the distinction between individuals of composite or received substance, which is received according to its form in something else, as in a subject, and individuals of simple or separated substance, and after the words just cited, in which he asserted that the first subject is that which cannot be received into another, he continues: Thus separated forms, precisely because they cannot be received into another, have the character of the first subject, and therefore they are individuated by themselves. Since there is in them nothing except form, there is form in them according to the character of form. Thus, when the same suppositum and the form by which they are individuated insofar as they have the character of the first subject are in them, with regard to the multiplication of suppositia, form is multiplied in them according to the character of form, of itself and not through another thing, because they are not received into another. For every such multiplication multiplies the species. Thus, in these there are as many species as there are individuals. In other forms, however, where there is a multiplicity of form through reception into another that has the character of the first subject and not according to the character of form, the same species remains in diverse suppositia. The recipient, however, is matter, not taken in just any way, as was stated, but insofar as it has the character of the first subject.

57 Divus Thomas also explained this elegantly in 1 part., q. 3, art. 2 ad tertium, in these words: It must be said that forms which are receivable in matter are individuated through matter, which cannot be in another because it is the first subsisting subject. Form, however, insofar as it is of itself, can be received by several things unless something else prevents it, but that form which cannot be received in matter, but subsists of itself, is individuated by the fact that it cannot be received into another. Such a form is God. Therefore, it does not follow that it has matter.

Likewise, the answer that Suarez gives to the second confirmation of this reason easily falls from what has been said. He says that it is badly inferred that matter is the root of the incommunicability required for individuation and consisting in this, that the individual is incommunicable to another in the way in which the superior is communicable to its inferior, simply because the aforesaid matter is the first subject and consequently is not in another as in a physical subject. He gives the following reason. Substantial and accidental forms are individual and singular, yet they are communicable to another as to a physical subject. Primary matter, however, is common and universal with respect to all matter, even though it is incommunicable to another as a physical subject. Thus, the aforesaid incommunicability or communicability makes no difference to, and poses no obstacle to, universality or singularity, or to their root.

58 Thus the answer easily falls from what has been said. For in answer to the first argument, it is clear, as we hinted from the Angelic Doctor, that although incomplete forms are singular and individual, they do not have this of themselves, but because they are received or are receivable in matter. The forms themselves, insofar as received or receivable in this numbered matter, cannot be received in another as in a subject. Consequently, they are incommunicable to another as a subject. Thus precisely by this they really and physically possess that physical incommunicability required to found formally the incommunicability sought for metaphysical singularity, namely, that they cannot be communicated to another in the way in which the superior is communicated to its inferior; yet they could found no other incommunicability. For just as any form that is singular and incomplete, and therefore receivable in a subject, looks to this subject rather than that one because it is commensurate with this one and not with that one, so, precisely because the aforesaid form does not look to any determinate subject, such as that in which it is received or is receivable, it will not be a singular form as such. In itself, however, it will be common and universal and able to found the character of the universal, as stated. On these matters, let those who wish consult what is said at num. 7 in the following disputation.

59 Second, regarding the second argument concerning primary matter, it is sufficiently clear that although matter according to its essence is in some way common (as was meanwhile explained in 1 Physicorum, disput. 3, num. 34, and disput. 6, num. 11, by our Complutensians), and likewise pertains (as already noted) to the common character of the substantial composite, this same matter is not positively individual. Consequently, according to its essence thus taken precisely, it is not of itself sufficient as the first principle of individuation, which alone concerns us at present, but only according to another special character, namely, according to its being marked by quantity. For it does not have the character of the aforesaid principle, into which all other principles are reduced, except insofar as it is this determinate first subject and not that one; or except insofar as it has a positively singular character, such that of itself and physically it is not in another as in a physical subject. It is clear, however, from what has been said, that matter does not have the aforesaid character except insofar as it is in some way marked by quantity. Thus, as often as it is the principle of diverse successive individuations, it concurs with a diverse relation toward them, namely, by being marked in different ways through different quantities.

Thus form is distinguished from matter in this, that form, both according to its essence and according to its relation to the line of form, as such and as proceeding from that same line, has being common and universal in itself. For insofar as it is of itself, it is communicable to another as a subject, and it becomes incommunicable and singular only as from the first root, through its participation in the line of the subject, because the subject receives it, as has been explained. In matter, however, its essence is one thing and can be common to several matters; its character, or its characters, through which it is the root of a peculiar individuation or of several successive individuations is another thing. These characters consist in some way in the precontainment of diverse quantities (as will be said from num. 116 onward), which, though they are certified a posteriori by quantities, are not taken as precontained but according to their formal being and as actually inhering in those individuals. Nevertheless, if considered in themselves, they pertain to the line of matter, as we shall explain more fully in this disputation at num. 118 and 133 and thereafter. And none of them can be common and universal.

60 This answer is taken from St. Thomas, tract. 29, De principio individuationis. When the holy Doctor had raised the objection that matter is common by its nature, just as form is, since the same matter can exist under several forms, and thus this community could prevent matter from being the principle of individuation, he answers in these words: But it must be noted that form cannot be united to matter unless it be particular, and unless a determinate quantity follow it, in which respect matter is not further communicable to any other form. For this quantity cannot be found with another form with the same determination. Thus matter is not communicable according to the same determination, just as form is, as was stated. For the character of matter under one form differs from its character under another, because its character is determined through quantity, which is required in a different proportion and dimension for different forms. The essence of matter, however, is not diversified under different forms, just as its character—that is, the character according to which it is the root of individuation, namely, matter itself as marked by quantity—diversifies. For the character of matter is not one and common, as its essence is. The character of form, indeed, is one in diverse matters, although it differs of itself. Thus community only according to the essence, which is that of matter itself, and not according to character, does not prevent matter from being the first principle of individuation.

§ VI. The arguments of the first opinion are answered.

61 To the first argument and its confirmation drawn from St. Thomas, what we shall say at num. 91 through num. 98 will give the answer. Add that, if it is true that matter marked by quantity does not mean matter insofar as affected by quantity, but only insofar as it radically contains this quantity rather than that one (which is considered in dub. 5), then saying that matter is marked by quantity signifies nothing really distinct from matter itself, but the same matter insofar as it radically contains it. For an effect, insofar as it has being in its cause, is not really distinguished from it. Thus he says most excellently that matter alone is the root of individuation, even though matter marked by quantity is its principle. For by this it is understood that nothing really distinct from matter itself is, at least directly, the root of such individuation. How this is consistent with quantity itself being in a certain way reduced to the first root, or individuation of material substance being attributed to it insofar as it is and is divided by the ultimate division from any other, will be explained below at num. 91 and 92, as cited above.

By this, too, the answer to the second confirmation is clear. For once the aforesaid supposition is made, namely, that matter marked by quantity is understood as matter radically containing this quantity and not that one, and consequently thus taken is the first root of individuation—which we shall show to be true in dub. 5—it is most easily reconciled how, even if matter marked by quantity in this sense is the principle of individuation, this does not prevent substance from being individuated through itself as through the first root, that is, as through something of its own kind, as has been explained. All accidents, however, are individuated through something extrinsic to their proper genus, namely, through a subject; although between quantity taken according to its formal being and the other accidents there is, as will be explained in the following disputation, such a disparity, as noted.

62 To the second, although matter taken in itself and precisely speaking, that is, insofar as it is not marked by this quantity rather than that one, is the first part of the substantial composite according to its species and considered in the abstract, it is nevertheless not a part of it as it is, this and individual, except insofar as it has being this and is marked in some way through quantity, for the reasons stated. Accordingly, in accordance with these points, the antecedent must be conceded and the consequent denied. Its proof convinces of nothing once we have posited what we have just said, as will be clear to the reader.

To the third, the antecedent must be conceded, provided the due proportion between the extremes mentioned there is preserved. The consequent must then be denied. In answer to its proof, it must be said that there is a disparity between the reasons. For form, of itself and taken precisely, is determined to confer this specification rather than that one, because it is naturally able to confer only one and the same specification. Matter, however, if taken in itself and precisely speaking, does not have sufficient determination to confer this individuation rather than that one, because as taken it can be found in several individuals. Thus it must in some way be determined and marked through quantity in order to be the principle and root of this individuation rather than that one.

63 To the fourth, once the antecedent is granted, the consequent must be denied. In answer to its proof, the antecedent must be denied. For the reason on which generic unity of material substance is taken from matter alone as from the first root (as was meanwhile explained by our Complutensians in Logic, disput. 5, num. 75 and thereafter) is not that this unity is material insofar as it denotes precisely a thing standing in the place of matter and potency; rather, it is because this is the unity of metaphysical potency, which is of itself indifferent but is contracted and determined through this specific difference rather than that one. Thus, it does not demand matter determined in some way through this quantity rather than that one. Individual unity, however, is the unity of a material thing ultimately determined and divided by the ultimate division. Hence it is no wonder that it demands as its first root not matter that is indifferent and undetermined, or matter taken in itself and precisely as stated above, but that very matter insofar as it is in some way marked and determined by quantity. By this, what suffices for the other points brought in the same argument is clear.

To the confirmation, the antecedent must be conceded if incommunicability is understood negatively, but not if it is understood positively. For the incommunicability spoken of in the antecedent, being the same as numerical unity and the individuation of something said to be incommunicable, means that matter, which according to itself and with the precision already stated is only one by negative unity, must likewise be incommunicable in the same way, namely, by negative incommunicability. The consequent must then be denied. For what is most powerful in the individual as such is not negative incommunicability but positive incommunicability. Therefore, positive incommunicability cannot proceed from matter as from the first root and principle unless matter is itself presupposed to be one by positive unity and positive incommunicability, and consequently to be in some way marked by quantity.

64 To the fifth, what will be said in dub. 5 will give the answer. For now, however, the antecedent must be denied, at least as regards its final part. In answer to the proof, it must be said that, although this quantity rather than that one cannot actually be received except in singular matter, and neither common matter but only singular matter has a connection with this quantity and not that one, or precontains this quantity rather than that one, nevertheless a difference intervenes here. For matter insofar as it actually receives quantity is presupposed to be singular and individual; but it does not become singular through the aforesaid reception actually exercised. Rather, it becomes singular through having the connection explained below at num. 116, or through precontaining this quantity rather than that one by the mode of a first root. It is not presupposed to be singular and individual. Consequently, it is shown to be, not presupposed to be, the first root of individuation. Thus matter taken in itself and precisely speaking, that is, insofar as we abstract from its being in some way marked by quantity, can never be positively singular or the first root of individuation.

The last argument asks us to explain by which of the three modes in which, in the explanation of the title of this difficulty, we said matter can be marked by quantity, it must be marked in order to be the first root of individuation. But since this must be explained exactly, several difficulties must be touched upon whose exact resolution is not without considerable difficulty. We shall therefore discuss in the three following difficulties by which of the three aforesaid modes matter is marked by quantity in order to be the first and sufficient root of the individuation both of the substantial form and of the whole composite; and consequently in order that, in a proportionate manner, it be positively this and individual.