Cursus Theologicus, Tomus I: In Primam Partem

From an exact understanding of this difficulty, and from its resolution, almost everything that we have said about the individuation of material substance depends, together with many other things that are customarily said on Thomas’s way in very serious difficulties; and therefore, both because of what has recently been said and because of that reason, we raise this difficulty in detail.

§ I. Opinion denying it.

19 The negative position is defended by Durandus; Aureolus in Capreolus, In 2, dist. 3, q. 1, a. 2; Scotus, q. 4; Suárez, disp. 5 of his Metaphysics; and others. The principal foundation of this opinion, however, is what was touched on above concerning other things: whatever can be reduced to this form, namely, that quantity is not more being from itself than many other accidents, therefore will not be more individuated from itself than they are. The antecedent seems clear. Rather, accidents are more perfect from themselves than quantity, and have more being from themselves than quantity: because being is the root of perfection, and whatever is more being from itself is also more being from itself. The consequence is likewise evident. For each thing is one in whatever real unity it possesses insofar as it is being; therefore, what does not have more being from itself than other things will not be more one from itself by real, namely individual, unity than they are.

The same opinion is proved secondly. Substantial form does not in any way have being individuated from itself as from the first root, as was established in the preceding disputation, dub. 1; much less therefore will quantity have it. The consequence is evident. Then, because substantial form is nobler than quantity, and so, this nobility notwithstanding, it could not be raised above matter so as to be individuated from itself in some way as from the first root, but only from matter, much less can this befitting quantity. Then also: because substantial form is not individuated from itself as from the first root, because it is a form receivable in matter, since this form is common from itself and communicable to several, as we said in the preceding difficulty; but quantity too is a form receivable in a subject; therefore, and so on.

20 Thirdly. For either this belongs to quantity because it is an accident, or because it is such an accident; but by neither of these modes: therefore by none. The antecedent, as to the first part, requires no proof; otherwise all accidents would be individuated from themselves in the same way, the contrary of which we proved in the preceding difficulty. As to the second part, however, it is proved. Since quantity, insofar as it is an accident with a specific character, says that it is the extension of substance, and insofar as it is an accident with numerical character, it imports this extension and not that one, with respect to this substance and not with respect to that one; therefore, according to either reason, it takes its whole being from the substance that it regards as its first root: since for this reason other accidents cannot be individuated from themselves as from the first root, because, in order to be these, they cannot fail to regard their determinate subject.

Finally. Since otherwise there would be no inconvenience in the fact that, at least supernaturally, two quantities could exist simultaneously in the same subject; but this cannot be admitted, as will be evident from what we shall say in no. 57; therefore, and so on. The consequence is evident. For if quantity is individuated from itself, and its numerical unity is not derived from the unity of the subject, there is no reason why, when only one subject exists, two quantities could not supernaturally exist there: for in that event nothing would oppose this except the impenetrability of one quantity with another. Yet that opposition exists only with respect to God’s ordained power, not with respect to absolute and supernatural power, as is evident from what was said in the Physics, disp. 19, no. 56, by our Complutensian College.

§ II. The true opinion of Aristotle and D. Thomas.

21 Nevertheless, it must be said that this is peculiar to quantity among all other accidents, and among all other forms receivable in matter: that it is individuated from itself in some way as from the first root. This is Aristotle’s view in the places cited in the preceding disputation. For precisely because quantity is quantity, in the way there indicated, the root of the individuation of material substance, it must itself be in some way individuated from itself, as was there explained and as we shall say with the Divine Thomas.

The same was taught by D. Thomas, Opusculum 70, q. 4, a. 2, on the third, in these words: The reason of an individual is that it is intrinsically indivisible and divided from others by the last division; but no accident has in itself a proper reason of division except quantity; whence dimensions have in themselves a certain reason of individuation according to a determinate position, since position is the difference of quantity, and thus it has a double reason of individuation: one from the subject, as every other accident; and another from itself insofar as it has position, on account of which, abstracted from sensible matter, we imagine this line and this circle.

22 The same Saintly Doctor maintains this very thing in 3 part., q. 11, a. 2, where also, from the fact that quantity is the root of the individuation of other forms, though in the way explained above, he concludes that it is in some way individuated from itself; and therefore it is not individuated from the subject according to the reason previously stated. Thus, after saying that this belongs to the reason of an individual, so that it cannot exist in several, he immediately adds: This happens in two ways: in one way, because it is not naturally able to be in anything, and in this way immaterial forms that subsist separately through themselves are also individuated through themselves. In the other way, because a substantial or accidental form is indeed naturally able to be in something, but not in several: as this whiteness which is in this body. As to the first, then, matter is the principle of individuation of all forms inhering in it: because forms of this kind, insofar as they are from themselves, are naturally able to be in something as in a subject, from which any one of them is received in matter, which is not in another, already the form itself thus existing cannot be in another. As to the second, it must be said that quantitative dimension is the principle of individuation: for something is naturally one only by this, that it is intrinsically indivisible and divided from all others; division, however, occurs in substance by reason of quantity, as is said in the first book of the Physics; and therefore quantitative dimension itself is a certain principle of individuation for forms of this kind, insofar as forms of the same species are numerically different in different parts of matter. Whence quantitative dimension itself has a certain individuation in itself; so that we can imagine several lines of the same species differing in position, according to what falls under the reason of this quantity: for it belongs to dimension to be quantity having position.

23 The Holy Preceptor finally asserted this very thing, 4 contra Gentes, ch. 65, in 4, dist. 12, q. 1, a. 1, q. 2, and Quodlibet 7, a. 10, in these words: Quantity is individuated not only from the subject, as other accidents, but also from position, which belongs to the reason of quantitative dimension itself, which is quantity having position; and therefore it is possible to imagine two separated lines, of the same species, numerically different, according to their different positions. Otherwise a line would not be divisible by its very reason as such: for a line is divided only into lines; but it is impossible to imagine several whitenesses of the same species without a subject; and thus it is clear that whiteness is individuated only from the subject.

Whence the Holy Doctor is followed by Capreolus in 2, dist. 3, q. 1, a. 3; Cajetan, 1 part., q. 29, a. 1; Ferrara, 4 contra Gentes, ch. 65; Báñez, De Generatione 1, ch. 5, q. 3, a. 8, in the first solution to the third; González, 1 p., disp. 23, no. 13; and many other Thomists.

§ III. The opinion of D. Thomas is explained and proved.

24 Nevertheless, because this assertion needs explanation owing to the word “in some way” contained in it, it must first be explained before it is proved. For, as is commonly said in the matter of the Trinity, q. 40, a. 2, and especially in the school of D. Thomas, a divine relation, for example Fatherhood, considered according to its ultimate reason, can be divided into two unequal concepts: into itself insofar as it has the reason of a hypostatic form; and into itself insofar as it expresses being toward, namely toward the Son. According to the former reason it exercises a function which according to the latter it cannot exercise: for, the person of the Father being constituted by divine Fatherhood according to an analogy with the constitution of created persons (which constitution is what we are discussing now), the person of the Father is constituted through divine Fatherhood considered according to its quasi-atomic reason as the being of the first person, insofar as the said Fatherhood has the reason of a hypostatic form, but not according to what it expresses as being toward, namely toward the Son, because that function and that unequal concept of referring the Father to the Son is conceived in some way as later than the active and passive generation of the Son; and the reason of the person of the Father, already constituted, must in some way be conceived as prior itself to the active generation of the Son: since actions or productions belong either to supposita or to persons already constituted; and therefore that relation cannot constitute the Father in the way stated, but can well refer the same Father, already constituted, to the Son.

25 Thus, quantity considered not according to the common reason of an accident, but according to its own proper reason, can be divided into two unequal concepts: first, into itself as extension, and this extension of this substance and not another, and consequently as expressing this relation to this substance rather than that one; and then also into itself insofar as it expresses that it has a determinate position arising from the partial positions of its parts; and consequently insofar as those parts are so coordinated with it that they preserve the reason of matter, or material principle, with respect to it; and therefore it consists of them as from its own matter, not from just any matter, but a matter which gives it that, by reason of those very parts, it has a peculiar position or situation. And although quantity thus taken cannot altogether be separated from the order to the subject, nevertheless, when it is considered under this explicit and unequal reason, it is concerned (at least in the first and proper sense) not with that order, but with the order which the aforesaid parts have to that total quantity, and with quantity itself insofar as it precisely expresses the being of a certain thing having the condition and nature of possessing the aforesaid parts and being coordinated with it in the aforesaid way; and it is not concerned (at least in the first and proper sense) with whether the same quantity, as it consists from those parts, expresses a relation to this substance rather than that one.

What therefore, in one assertion with the Holy Doctor, we wish to say is that quantity has this peculiarity among other accidents and any forms receivable in matter: that, divided in some way into two unequal concepts of itself, it has in some way being individuated from the subject and in some way individuated from itself, as from the first root. The former belongs to it according to the first concept just reviewed; the latter, however, belongs to it according to the second. And therefore D. Thomas, in the places cited for this assertion, used such a sequence of words that this itself is clearly denoted, as will be evident to one considering it.

26 Thus the assertion, explained as to what it indicates, namely that quantity, insofar as it expresses the reason of extension and of this extension of substance, and consequently according to that first unequal concept, is individuated from the subject as from the first root, is established by what was said in the preceding difficulty. For, considered according to this reason, it is considered by the mode of form, but not of just any form, but of a form communicable to its subject no less than other accidents; and therefore it cannot be individuated from anywhere else than from its subject, as from the first root, as is evident from the same statements.

As to the second part, however, it must be proved by no other reason than that which the Holy Doctor supplied in the cited testimonies; and this can be proposed in the following form. Since quantity has from itself, as from the first root, a being divisible into several parts of the same reason, or into several entitative parts differing only numerically, therefore it has from itself, as from the first root, being individuated in some way. The antecedent is established by what our Complutensian College said in the Logic, disp. 13, no. 30 and following, and in the De Generatione, disp. 5, no. 32 and following, where they show how it belongs to quantity, insofar as it is quantity, to have entitative parts such that it has them only by itself or by its reason. The consequence is proved. Then because quantity has from itself parts of the same reason, or differing only numerically, it also has from itself whence it is numerically one. Then also: because it has the aforesaid parts, it certainly has them according to a distinct position, and they can thus be distinguished from one another numerically from that distinct situation and position; likewise, one quantity can differ numerically from another by the determinate situation and position that it has. And therefore, if two lines separated from every subject were given, they could be understood and be numerically different, because one would have a situation distinct from the other.

§ IV. Objections of opponents against the reasoning of D. Thomas.

27 Nevertheless, opponents first object against this reasoning that it is incorrectly inferred from the fact that quantity has from itself parts of the same reason that it is in some way individuated from itself and is the first root of its own individuation; therefore, and so on. The antecedent is proved. For all this belongs to its specific concept, as distinguished from its individuation and root; and therefore all quantities agree specifically in this, that they have parts of the same reason; therefore on this ground quantity cannot be individuated from itself, nor be the root of its individuation and of purely individual distinction, since whatever belongs to the specific concept of a form, as distinguished from its individuation, cannot thereby be individuated or be the root of unity and purely individual distinction.

28 This is confirmed firstly. For from the fact that a vague individual cannot be from itself a determinate individual, and singular in the strict sense, but only by reason of something else, namely a first root, since it is said to possess from itself the reason of the singular taken in the common sense, follows only that quantity has those different parts by numerical diversity taken in the common sense, since all quantities agree in this; therefore, from its having parts in this way, it cannot be inferred that it is individuated from itself by the determinate individuation in question.

This is confirmed secondly. For otherwise, in quantity the specific unity would not yet be distinguished virtually, or with a foundation in the thing, from numerical unity, nor could two quantities be distinguished merely numerically; but this is plainly false; therefore, and so on. The consequence is proved. For therefore, in the Angels the specific unity of anything is not distinguished from its numerical unity, nor can they be distinguished from one another merely numerically, because they are certain forms individuated from themselves, as we indicated in the preceding disputation, no. 17, and as we shall say at greater length from D. Thomas in the treatise on the Angels; therefore, if quantity is individuated from itself, that specific unity cannot be virtually distinguished in it from numerical unity, nor will it be numerically distinguishable from another quantity of the same species.

29 Secondly, they object. For whatever belongs to quantity, and to it according to what belongs to it as such, whether it is to have from itself entitative parts or any other intrinsic reason of quantity, can be only the proper reason of such a form and directed to the line of form; therefore, on that very ground it will be unsuitable that quantity should be individuated from itself, or be the root of individuation, by that reason. The antecedent seems certain. For since quantity, according to its higher reason, is a certain form, it cannot, according to its peculiar constitutive reason, import anything that is not the proper reason of such a form and directed to the line of form. For example, because substantial form, such as a lion’s, according to its higher reason, has the reason of form, it therefore cannot, according to its peculiar reason fitting it, import anything that is not the proper reason of such a form and directed to the line of form. The consequence is proved. For, as is evident from the preceding disputation, the substantial form of a lion, as such, according to no one of its reasons can be from itself, as from the first root, individuated, because whatever belongs to it according to this reason can be only the proper reason of such a form.

30 Thirdly. For the reason of the whole integral and of its parts is far different from the reason of the universal whole, such as the atomic species and its subjective parts, namely individuals; therefore, from the fact that quantity is from itself a certain integral whole consisting in integral parts, it is incorrectly inferred that it also has from itself a foundation for the reason of a universal whole, namely the atomic species, and can at the same time, without anything else, be divided into different subjective parts contained under the said whole. The consequence seems certain. For from the fact that something has the property of one whole, it does not follow that it will have from itself the property of another whole of a different reason. The antecedent, however, is proved. Since an integral whole is of such a condition that it must really be distinguished from its parts, whereas the universal whole is not, and therefore it cannot be predicated of its part, but this is false: Half a forearm is a forearm; but the universal whole is so; and therefore this proposition is true: This quantity here is a quantity; therefore, and so on.

Fourthly. From the fact that quantity enjoys parts having diverse positions, and consequently that diverse parts of the same quantity and diverse total quantities can be distinguished from one another, just as diverse lines, it is incorrectly inferred that quantity is in some way the root of its own individuation; therefore, and so on. The antecedent seems certain. For since position belongs to a distinct category, it cannot be inferred from it that quantity is individuated from itself but from something else, and consequently that something else is the root of its individuation.

§ V. Solution of objections against the reasoning of D. Thomas.

31 To the first, the antecedent must be denied. In proving it, the antecedent must be distinguished. If its meaning is that that whole, taken in the common sense, belongs to the specific concept of quantity, it must be granted; but otherwise, if its meaning is that that whole, taken in particular and altogether determinately, refers to the specific concept of the same quantity, the consequent must be denied in the same proportional way. For although quantity cannot be the first root of its own individuation precisely because it has parts of the same reason in the common sense, it can nevertheless be so because it has those parts in particular and altogether determinately.

Thus quantity and the other accidents agree in some respects with regard to individuation and differ in others. They agree because, just as whiteness is individuated proximately and intrinsically by that same thing by which it has its species, but taken in a particular way, and therefore only a certain individual difference virtually distinct from its specification is added to it, namely that it is this whiteness and not that one, so too is it with quantity. And therefore only an individual difference is added to it in the same way, namely that it is this quantity and not that one, and consequently it has these parts and not those.

32 But they differ, because the fact that whiteness is this whiteness, and that its individual difference arises from another thing, namely from the subject, as from a first root: and therefore the aforesaid individual difference is not the first root of its proper function; rather, the subject is that which, in the first and proper sense, is the first source and root of it. In quantity, however, its being this quantity and not that one arises in some way from the quantity itself, as from the first root; and thus that same individual difference, considered physically, is at least in the proper sense the first root of its proper function, constituting quantity in the being of this quantity.

And the reason is this. For just as, because matter, not indeed according to itself (for that belongs to the specific concept of the entire substantial composite, as our Complutensians indicated in the Physics, disp. 6, no. 8), but insofar as it in some way imports quantity in the common sense, is the first root of individuation, so the same matter, insofar as it imports the same quantity taken vaguely in the same way, must be the first root of that same individuation considered vaguely; otherwise matter itself, insofar as it brings the same quantity to be this and not that, could not be the first root of this completely determinate individuation. Likewise, since quantity itself, by reason of its specific difference, while connoting its subject by the common reason of subject, is the first root of having parts that differ only numerically, it must, by reason of its individual difference taken in the same vague way and under the connotation of the subject taken in the same way, also be the first root of having those same parts numerically distinct. Finally, by reason of its individual difference considered altogether in a particular way, while connoting this subject and not that one considered altogether determinately, it will be the first reason for having these parts and not those, and for their being diverse by this numerical diversity and not that one; and consequently it will also be the first root of this, namely that the quantity is this and not that. And therefore, precisely because the aforesaid quantity connotes the aforesaid subject, nothing will be lacking for it to exercise, in some respect, the office of being the root of its own individuation and purely individual distinction.

33 Therefore, just as it is not removed from prime matter that it is the first root of the individuation of the composite, although it requires something connotated, namely that it was disposed by these dispositions and not those, and consequently those accepted in this numerical composite and not that one, so likewise we must philosophize in the present case (preserving, however, the proportion already indicated).

It is added that, precisely because matter, as presupposing this quantity and not that one, connotes only the aforesaid dispositions, and is therefore the first root of the individuation of material substance, quantity itself, considered according to its formal being, can also, while connotating the same dispositions, become in some way, for the reason stated, the root of its own individuation.

34 From this, the first confirmation is sufficiently established. For it proves only that a vague individual cannot be a determinate individual unless something virtually distinct from it is superadded, namely a certain individual and marked difference; not that this difference must be derived from something else as from a first root, but from that very line (in the way recently explained) from which the individual difference, taken in the common sense, is derived: as we say concerning the individuation of the entire substantial composite and of accidents. Hence this confirmation serves us rather than harms us.

The second confirmation is also evident from what has been said: the consequence must be denied, and the reasons are unequal. For Angels are subsistent forms, irreceivable in another as in a subject; and therefore they can be individuated neither from a subject as from a first root nor from it as from what is connoted, and consequently cannot have a purely individual distinction; but quantity is otherwise: insofar as it is from itself, it is in some way individuated, connoting its subject, as was explained.

35 To the second, the antecedent must be granted, taking the line of form to mean that it has from itself a multiplicity of entitative parts, of the same specific reason, diverse however according to number, or seeking a distinct position in its whole. Then the consequence must be denied. Its proof is evident from what was said. For the proper reason of a lion’s form considered in itself does not belong to the line of a form having from itself the aforesaid parts, as quantity does; and therefore it cannot, according to any of its reasons, be the first root of its own individuation.

Thus quantity is distinguished from other forms in that, since it has from itself entitative parts of the same reason, or parts precisely diverse according to number, it must have from itself whence it can be distinguished specifically and numerically. Numerically, indeed, because the aforesaid parts, as they dispose it, have themselves by the mode of matter with respect to it, and consequently there is in it something by the mode of a material principle, from which, as from a first root, its numerical unity and purely individual distinction, in the way stated, are derived. Most especially, because such parts are not just any parts, but parts having a distinct position or situation, and consequently are of such a condition that although they are of the same reason or species, they are nevertheless distinguished in some way; and thus by this reason, as we have already noted, they can be in some way the first root of the aforesaid individuation.

Likewise it must have from itself whence it can be distinguished specifically, namely insofar as it is a form directly belonging to its own category, by reason of which it has more sufficiently the formal character from which its specification is derived.

Nevertheless, since other forms do not have from themselves the aforesaid distinction of parts, and consequently do not belong of themselves to the line of a form having those parts, there is not in them a sufficient root from which, as from a first principle, their specific and individual unity can be taken.

36 To the third, although those two wholes are distinct, they are nevertheless so joined together that that accident which has from itself that entitative totality can, from itself and in the stated way, be divided by the division of the universal whole into its subjective parts; so that, without anything else belonging to a third category and being directly imported, the aforesaid division can occur (as is evident from the statements made for the assertion), although other accidents cannot according to any of their reasons be thus divided by the division of the universal whole into subjective parts; rather, they have them from their subjects as from first roots.

To the last, the antecedent must be denied. For in this reasoning we are not speaking of positions formally taken and belonging to the category of position, but of position insofar as it is the difference of quantity, as is said to consist in parts having position, which otherwise are best explained a posteriori by the fact that they have diverse positions. This solution is taken from D. Thomas, Opusculum 70, q. 4, a. 2, in the solution to the third, and elsewhere often.

37 It makes no difference if one urges that quantity at least thus becomes, through its parts, virtually possessing distinct positions directed to the peculiar category of position, in some way the first root of the individuation of that quantity, and thus that the whole matter must be reduced, as it were, to a first root in the category of position; since quantity can be numerically distinguished from another quantity only if it establishes distinct positions, as was urged.

The answer is given by denying the consequence. In proving it, the antecedent must be denied. For although the same quantity has a distinct position of its parts with respect to itself, and also a distinct position of them with respect to place, or a distinct position belonging to the category of position, and the former reason demands the latter and establishes it, just as it demands and establishes other properties or affections of quantity, nevertheless quantity is not in some way the first root of its own individuation because it specially virtually possesses the aforesaid positions; but rather insofar as, per se and formally, it has a distinct position of its parts with respect to itself. For since these positions do not have from themselves a distinction of entitative parts, or of the same reason, even with respect to place, since they enjoy only the category of quantity, it follows that they cannot be in some way the first root of its own individuation; and consequently neither can quantity, insofar as it virtually possesses them as it were in a root, be in some way the first source of its own individuation; rather, conversely, the positions themselves, having parts of the same reason, or diverse only numerically, are in some way individuated from it by reason of quantity. Although, because the distinct position of parts with respect to the whole is very clearly known through distinct positions, it can for that reason be best explained through them.

§ VI. Corollaries worthy of notice.

38 From all these things it is first inferred, with Nazarius, 1 part., q. 3, a. 2, sole controversy, and very many other serious Thomists, that some (though few) do not philosophize according to the mind of D. Thomas, who reduce the root of the individuation of material substance both to matter and to substantial form, each indeed as the first root in its own genus, without mentioning quantity: so that matter, connoting form, is the first root of individuation in the genus of material cause; whereas form, connoting matter, has that same office in the genus of formal cause; and, comparison being made between the two, no resolution is made into either as into a root absolutely and simply prior, since matter is this and the root of individuation because it regards this form; and conversely form is this because it regards this matter; so that neither has its being as this by reason of being determined by quantity.

The reason for this corollary is deduced from what has been said. For precisely because quantity has from itself entitative parts, and consequently is from itself, as from a first root, individuated in the stated way, prime matter, for example, cannot be individuated on Thomas’s way, and consequently cannot be the first root of individuation unless, in the way recounted in the preceding disputation from no. 34 through no. 36, it is determined by quantity. For, as the Holy Doctor concludes excellently, Opusculum 70 on Boethius, De Trinitate, q. 4, a. 2 on the third, from the fact that quantity has from itself parts of the same reason, and thus is from itself in some way individuated, it is rightly inferred that matter individuates other forms because, in the way explained above, they are subject to that form, namely quantity, which has from itself the reason of individuation.

39 It is added that, as is evident from the preceding disputation, no. 9 and following, substantial form on Thomas’s way cannot be the first root of individuation. Because, as we shall explain more fully from the same source, unity and distinction arising from substantial form, as from a first root, and consequently from it, at least considered directly, are specific unity and distinction. From this, and from what was said in the preceding disputation, a stronger confirmation of the same corollary is deduced. For precisely because form is not individuated from itself, nor is the root of individuation, and matter considered in itself and precisely cannot have this, since under this consideration it belongs only to the concept of the species, it follows that matter, insofar as it presupposes something else, must be the first root of individuation; and consequently insofar as it presupposes this quantity: since no other thing’s presupposition in matter is better adapted to this function than that of quantity, which from itself and in the way explained is individuated.

40 Secondly, it is inferred that one cannot proceed so completely, following the traces of the Angelic Doctor in this matter of the principle of the individuation of material substance and of quantity, nor so defend to the letter the reasons by which the Holy Doctor is led, those who ascribe to material substance its own proper entitative parts and their distinction with respect to itself, such that they do not arise from quantity, as from a form inhering and intrinsically constituting the same substance in the reason of the entitative whole consisting of the aforesaid parts. For they cannot so completely defend that quantity, in the way explained, is in some way the reason of its own individuation, and that matter determined by quantity is the first root of individuation.

And the reason is this. For, as our Complutensian College excellently teaches in De Generatione, disp. 5, from no. 39 through 42, precisely because material substance would have from itself proper entitative parts of the same reason, and consequently diverse only numerically, the first root of having them would not be quantity, as is evident from the very terms; but rather quantity would have them by reason of substance, as the first root of the same; because in that event material substance would have parts of the same reason prior to quantity. And the reason why quantity and the other material accidents would have them would be because material substance, and prime matter, from which, as from the first principle from which quantity flows, they receive them, would have them prior to quantity. And thus neither would quantity be from itself the first root of its own individuation, nor would material substance be individuated in prime matter determined by quantity. For the strongest reason and foundation on which the Angelic Doctor relies continually to assert that quantity is individuated from itself in the way stated, and that the first root of the individuation of material substance is prime matter determined by quantity, and not merely prime matter, is precisely that quantity has from itself, as from a first root, parts of the same reason, as is evident from the places cited in no. 22, from what the Holy Doctor taught in 4 contra Gentes, ch. 65, and from the reason we deduced from them in favor of our assertion.

41 It is added that D. Thomas is constant in this: that he ascribes to quantity in a proper way that it is individuated from itself in the stated way, but not to the other accidents, as is evident from the places recently cited. But if material substance had entitative parts from itself, then the other material accidents would also enjoy those parts from themselves, as is commonly taught by all those who ascribe to material substance its own proper entitative parts belonging to it from itself; so that one part of the aforesaid accidents could be received in one part of substance and quantity, and another in another, so that (as they themselves say) a material accident would not inhere indivisibly, that is, by inhering according to itself as a whole in the whole substance and quantity, and according to itself as a whole in any part of each and indivisible in both; and consequently the aforesaid accidents would have from themselves, no less than quantity, individuation in some way. For on the way of the Holy Doctor the sole foundation whereby quantity has this peculiarity, namely that it is individuated from itself in some way, is that it has from itself parts of the same reason, or (which comes to the same for the present) that it has diverse partial positions, since position is the difference of quantity, as is evident from all the places in which the Holy Doctor treats this matter.

From all these things it follows that it makes no difference if one says that not just any entitative parts, but specifically entitative parts belonging to the genus of quantity, can be the first root of individuation; and therefore D. Thomas mentioned none except entitative parts having a distinct position. For these alone are both entitative and quantitative parts; whence it is rightly said that these parts, being variously situated (or seeking distinct positions, in which numerical distinction especially shines), are the first root of individuation, and not other parts.

42 It is therefore evident from what has been said that this makes no difference. First, because D. Thomas, wishing to explain why it belongs to quantity alone among material forms to be individuated from itself by reason of its parts, mentioned entitative parts having a distinct position, which belongs to the reason of quantity. For according to his opinion, nothing other than quantity can in any way have entitative parts and their distinction; but whatever enjoys them must receive them from quantity, as from a formal cause and inhering principle, as our Complutensian College has shown at length from the same Holy Doctor in De Generatione, disp. 5, no. 32 and following. Then also: because, as we said from D. Thomas, Quodlibet 7, a. 10, and 4 contra Gentes, ch. 65, this position and their diversity is not position and diversity of the category of position, but position and diverse position of parts in the whole. It is evident, however, that if substance had from itself entitative parts composing one and the same entitative and substantial whole, then the aforesaid parts would have position in the whole; otherwise they would not compose it, and precisely because they would be distinct with respect to themselves and to the whole, they could not fail to have a distinct position or union both among themselves and with respect to the same whole.

43 Finally. Because the Angelic Doctor, 4 contra Gentes, ch. 65, concludes precisely from the fact that quantity enjoys parts having position in the whole that it is individuated from itself, since it is repugnant for something to have parts of the same species and thereby not to be an individual from itself or by the force of its proper line. Thus, after he said, Quantity has this peculiarity among the other accidents, that it is individuated according to itself¹, and that therefore this is so because position, which is the order of parts in the whole, is included in its reason; for it is quantity having position, he immediately, in order to give the reason for this, attended precisely to the diversity of parts of the same species, and therefore added only: Wherever the diversity of parts of the same species is understood, individuation must necessarily be understood: for things of one species are not multiplied except according to the individual; and hence many whitenesses cannot be apprehended except according as they are in different subjects (understand actually or in aptitude), but many lines can be apprehended even if they are considered in themselves.

Whence, for him, to enjoy parts having diverse position is not indeed of the genus and category of position, but, as he says, to have parts of the same species having position precisely in the whole, or (which is the same) to place themselves in it through a numerically distinct communication both with respect to the whole and with respect to one another. This is strictly the same as having parts precisely of the same species; otherwise, since being individuated from oneself belongs to the reason of a form having parts of the same species, he would attend only to the immediately related words and would not give a sufficient reason why quantity, enjoying parts having position, is individuated from itself.

And certainly the Angelic Doctor rightly attended only to this, namely that quantity precisely has parts of the same species, and consequently parts diverse only numerically, in order that it might be sufficiently inferred from this that it is in some way individuated from itself: for, as we showed in no. 32, what is numerically one in the first sense, and vaguely one numerically, and finally altogether determinately one numerically, must arise from the same real principle and first root. It is evident, however, that precisely because something is conceived as having parts in the first sense which are distinct and at the same time of the same species, and consequently distinguishable only numerically, it is conceived as numerically one in the first sense, and as the root of its numerical unity in the first sense; otherwise it would not have from itself parts distinct only numerically in the first sense; therefore that same reality will be precisely that by which, because the individual exists from a part of the thing, the determinate individual and the root of its individuation exists.

44 Thus, what this solution adduces in its own favor, namely that numerical distinction shines most in parts seeking a distinct position of the category of position, and consequently that only these parts can be the first roots of its individuation, is of no help to it. For by the same reasoning it would prove against its own authors that quantity alone has entitative parts, but not substance from itself and by the force of its proper line: for only the parts of quantity seek those distinct positions in which the distinction of entitative parts shines most. It is added that the aforesaid positions, as category and genus of position, neither according to themselves nor as presupposed, can be the root of individuation, as we said in no. 36. And therefore, from the fact that quantity seeks them, it cannot have this special property, namely that it is the root of its own individuation.

Hence also remains refuted another solution, which could be offered against our corollary by the reasons adduced, namely that quantity is individuated by reason of its parts from its own reason, even if substance has entitative parts from itself, because although substance does not have them from quantity as from what is received, it nevertheless has them from that same quantity as from what is presupposed at the root; and thus the fact that it is individuated by reason of its parts does not prevent it from being in some way individuated by quantity as by a first root, and quantity itself from being the first root of its own individuation.

45 Therefore this solution collapses from what has been said. First, because if quantity were repugnant, the possibility of material substance would nevertheless remain; nevertheless the aforesaid substance in the opinion of the opponents would have entitative parts of the same reason: for in their opinion, precisely because it would not be spiritual, it would not be intrinsically indivisible. Then also: because other material accidents do not presuppose quantity intrinsically; yet they have parts of the same reason, as the opponents admit; therefore it is a sign that substance does not have entitative parts from itself because it would presuppose quantity intrinsically: for it has those parts from itself no less than the other material accidents. Then, next (which follows from the preceding): because whatever belongs to things of diverse categories does not belong to them by a peculiar reason of any one of those categories, but by a reason common analogically to all of them, as is evident from themselves and from induction; therefore, since this—namely, having proper parts of the same reason—belongs both to material substance and, according to the opponents, to quantity and the other material accidents, the consequence follows that it does not belong to one of them by the reason of another, but by some general reason, and therefore whatever has the aforesaid material entity also enjoys entitative parts from itself.

Finally: because just as it would follow that matter, as presupposing quantity, is the first root of the individuation of material substance; if it had from itself, according to its species or quasi-species, and according to what it formally expresses, a foundation from which it would be the first root of the aforesaid individuation, as is evident from what we said in the preceding disputation, dub. 2 and 5; so, because material substance according to its essence and according to what it expresses, obtains whence it has entitative parts of the same reason, namely the reason of a material thing as distinguished from a spiritual thing, it follows that it also implies having the aforesaid parts from quantity itself, virtually or radically presupposed, but precisely from what it expresses from itself, namely the reason of a material thing; and therefore whatever is material must, on the contrary opinion, enjoy proper entitative parts.

46 It is added that, precisely because having proper parts, or parts of the same reason, or entitative parts, belongs to substance and quantity by reason of a material thing, it cannot but belong to them by reason of matter, which is the first root of materiality. Therefore, since the being material of matter is found prior in the genus of substance according to its (let us say thus) formal or expressed character, than according to its presupposing being material as such among the other genera, it follows that parts are found prior in the genus of substance, if it has them in this genus as its own proper parts, than in the genus of quantity.

Finally, it is added that, when a comparison is made between the entitative parts of substance and quantity, insofar as they precisely say parts of the same reason and are in some way mutually distinct, namely numerically, without considering whether they are or are not impenetrable with respect to place, the parts of substance are from themselves nobler and more perfect than the parts of quantity; therefore there is no reason why the latter should belong to substance from quantity, as virtually presupposed, but from the force of its essence and of what it expresses, according to which it otherwise virtually presupposes the aforesaid parts.

§ VII. The arguments proposed for the first opinion are satisfied.

47 To the first, the antecedent should be passed over and the consequence denied. In proving it, the antecedent must be distinguished. If its meaning is that each thing is one proximately and immediately insofar as it is being, it must be granted; and consequently, whatever has more being, or is nobler in the reason of being, will also be more one proximately and immediately numerically, that is, it will have a somewhat nobler numerical unity. If, however, its meaning is that whatever has more being will have more fundamental unity, to the point that it does not suppose something else as the first root of its numerical unity, it must be denied: because this mode of being more one numerically does not follow from nobility merely insofar as it is nobler. And therefore, although substantial form is nobler than matter, it is nevertheless not in this way more one than matter, as is evident from what was said in the preceding disputation, dub. 1 and 2; but the conclusion follows with respect to a peculiar mode of being, namely being that is from itself the first subject, or is a form not receivable in a subject, or finally has from itself and by the force of its proper line entitative parts of the same reason and species, which therefore have from within themselves a difference among themselves solely numerically.

48 To the second, the antecedent being granted, the consequence must be denied. From what was recently said, it is clear that being an individual from oneself as from the first root does not follow from being nobler, but from a peculiar mode or reason of having being by one of the modes recently recounted. As to the second proof, however, the major proposition must be distinguished: Because it is a form receivable in matter, in any sense, must be denied; because it is a form receivable in matter, in such a way that it does not have from itself and from its proper line any intrinsic material principle composing it and belonging to it by the mode of matter, must be granted. The minor proposition must likewise be distinguished in the same proportional way. For although quantity is from itself a form receivable in a subject, it nevertheless has as predicate both a material principle, namely entitative parts of the same reason; and although a form is common insofar as it is receivable in this respect, if it nevertheless has from itself entitative parts which are compared by the mode of matter with respect to it, and which further connotate this subject rather than that one, it has from itself, directly and according to the reason already stated, a kind of individuation, as was explained.

Whence that greatest principle taken from D. Thomas in the work cited above, namely that a form receivable in a subject is not individuated from itself as from a first root, is understood to concern an individuation that proceeds adequately and solely from it as from a first root. This does not belong to quantity, because quantity is from itself, as from a first root, singular only in a certain way and in the sense explained. Or it can be understood to concern an individuation that in some way also proceeds from the aforesaid form as from a first root, without connotating this determinate subject rather than that one; otherwise, if such a form had in itself a sufficient material principle and connotated the aforesaid subject, [the principle would apply].

49 To the third, the major proposition must be granted as to its second part and in the sense explained, and the minor must be denied as to that same part. In proving it, the antecedent must be distinguished. If its meaning is that the adequate reason of quantity, insofar as it is such by a specific or numerical character, is to be from itself an extension, or this extension of substance, or of this substance, insofar as this precisely signifies per se and directly a relation to substance or to this substance, it must be denied; otherwise, if its meaning is that the relation already stated and explained is only an unequal reason of the same quantity insofar as it is such by a specific or numerical character, it must be granted. Then the consequence must be denied if it is understood to concern either reason according to what it is adequately said, and not only according to the unequal reason recently stated. In proving it, the antecedent must be distinguished in the same proportional way. For therefore other accidents are not individuated from themselves as quantity is, because their adequate reason, insofar as they are these things, is per se and directly in relation to their subject; but this does not belong to quantity, as we said in no. 25.

These matters are explained. For quantity, insofar as it is this thing, is distinguished from other accidents, insofar as they too are these things, in that the whole reason of these things, insofar as they are these, does not express a relation to something else from which they are intrinsically and really composed, such as a material principle, but only to the subject; and therefore they do not have being individuated from themselves, as from a first root, but from the subject. But the whole reason of quantity, insofar as it is this thing, is not only to regard the subject, but also, as regards a material principle, in such a way that it does not regard something else from which it is composed as the principle of its materiality. For since it consists from itself and intrinsically from parts of the same reason, and consequently numerically diverse, and having a distinct position in the whole, which are compared by the mode of matter with respect to it, it follows that beyond the unequal reason of regarding the subject, it also has this other unequal reason through which it regards the aforesaid parts by the mode of a material principle. And although this relation, as we noted above, cannot altogether be separated from the relation to the subject, nevertheless, when it is conceived unequally under this explicit and unequal reason, it is concerned in the first and proper sense not directly with that order, but with that which the aforesaid quantity imports to its parts as the principle of its materiality. And therefore quantity can be in some way individuated from itself, and in some way from the subject: from itself in a certain way insofar as it regards its parts and the parts compatible with it, as its matter—these parts and not those—while connotating the altogether determinate subject; from the subject, however, in a certain way as from a first root, insofar as, according to another unequal concept, it must still according to its ultimate reason express per se and directly the relation of extending this substance and not that one, and consequently expresses explicitly and directly a relation to this subject.

Whence the other accidents seek their subject only once for their own individuation, namely in order to influence it by the mode of a first root; but quantity demands it once by the mode of a first root and again by the mode of the connotated. For since quantity is in some way individuated by the subject and in some way by itself, as from a first root, the subject must concur once by the mode of a first root and once by the mode of the connotated; and therefore, unless the aforesaid connotated [subject] is posited, quantity cannot exercise the office of being in some way the root of its own individuation with respect to that unequal reason according to which it is itself individuated.

50 We have said that, when quantity is conceived unequally under the explicit and unequal reason under which it is individuated from itself, it is not concerned expressly, per se, and directly with the order to the subject, because although quantity can be expressed and conceived unequally as a certain thing consisting in its parts, as from a matter from which it is composed, without expressly conceiving a relation to the subject as to the matter in which it is received or from which it is produced, as will be evident to the observer, it nevertheless cannot altogether be separated from such a relation, but must still then implicitly and obliquely involve that relation and the subject. For just as Fatherhood, constituting the first divine person by analogy with the constitution of a created person, does not expressly express another concept of being toward, namely expressly regarding the Son, it nevertheless always implicitly expresses an order to him, so that by none of its unequal reasons can it be altogether separated from him.

From this it is also more clearly understood why D. Thomas, in the final testimony adduced for the assertion, established a distinction between two quantities and two whitenesses: the former can be imagined separated from subjects, of one species and numerically distinct, whereas two whitenesses cannot. For his meaning is not that neither whitenesses nor quantities can be separated in fact from the subject by divine power, as is evident from what was said in the preceding disputation, no. 87; but that, two quantities being conceived without their subject being expressly conceived, and without an order to it, and so in some way separated from it, both actually and in aptitude, they can by reason of their eminent reason, which this possession gives them, be conceived expressly as precisely distinct according to number, because they are conceived with the foundation and root, already stated and explained, of their own individuation and numerical distinction, and are in the same proportional way separated from subjects; whereas, two whitenesses being conceived without their subjects, actually and in aptitude, it is impossible to imagine them as two of the same species and distinct according to number: for they have their individuation from the relation to the subject alone. But another explanation of this testimony is also to be found, as we gave it in the preceding disputation, no. 87 and following.