Cursus Theologicus, Tomus I: In Primam Partem

1 Once the individuation of material substance, and its root, have been explained, the mind is immediately prompted to inquire into the principle of the individuation of its accidents: and as, in the disputation concerning the first root of the individuation of the entire substantial composite, it is not expressly and formally discussed whether substance itself is in very truth and intrinsically individual, because this is sufficiently evident; nor whether it is the metaphysical principle by which substances are rendered individual, because, as is certain and admitted by all, metaphysical individual differences must be given, at least distinguished in reason from specific differences, which in this order are the principle of those same substances in their individual being and which constitute them in the being of such substances; but only concerning the first principle and physical root of the aforesaid individuation, into which all the other things are resolved: so, namely, that we take the individuation of the accidents to be, on the part of the thing, individual and to have its own metaphysical principle, that is, its own metaphysical individual differences, through which they are constituted in this order. And therefore we institute this disputation only concerning the first principle and the physical foundation of that same individuation. Wherefore, since this is clear from what was said in the preceding disputation, num. 1, and as Suarez most rightly points out, disput. 5 of his Metaphysics, sect. 7, num. 1, there is for us, as regards the present controversy, no controversy with Scotus, who thought that this disputation should be brought to a close by his haecceities, which are nothing else than metaphysical individual differences. For we, since we admit those same individual differences, proceed further, and investigate their physical root.

Whether the subject is the first root and principle of the individuation of accidents, and of their pure individual distinction? The decision of this difficulty follows almost entirely from what we have said in the preceding disputation, difficulties 1 and 2. However, so that the mind of St. Thomas may be made more evident and a fuller answer may be given to certain objections that press their adversaries, we therefore raise this difficulty separately.

§ I. The negative position is proposed.

2 The negative position is defended by Durandus in the place cited above, and by Suarez, Metaphysics, his disputation 5, section 7, and by many others. From this they think that the a priori reason, and the first root of the individuation of an accident, is the accident itself as it is such an entity in act, or aptitude.

Suarez reduces the foundations of this position to this form in the same place, no. 4. First, because each thing is formally and intrinsically one in number (which is the foundation of unity, or of what he calls the one) by that through which it is an entity in act in the nature of things, or apt to become such: because every such entity is singular; but every thing is intrinsically and formally such an entity in act through its own entity; therefore it is singular and individual through that same thing; therefore accidents have this as well.

And this is confirmed. Because the subject cannot be the principle individuating accidents; therefore it can only be an intrinsic principle of this kind belonging to the accidents themselves. The antecedent is clear: because in the first place the subject cannot be called an intrinsic principle of the individuation of an accident, as though it intrinsically and per se composed the accident; because we are not now speaking of the composite of subject and accident, but of the accidental form itself: which plainly is not intrinsically composed from the subject itself; nor can the subject in this way be its intrinsic principle. Again, the subject cannot be called the principle individuating an accident, as the relational terminus, or aptitude, of such an accident to inform such a subject: because with respect to the same subject, two accidents numerically distinct can have an aptitude to inform it; therefore those aptitudes cannot be distinguished numerically from the subject; therefore they are from themselves.

3 Secondly, this seems to be established most strongly from certain accidents which, according to their own condition, subsist in a subject but refer it, or somehow lead it, to something else: such as relations, acts, habits, and the like. For if an accident is said to be individuated by the subject because it naturally looks to it, why should these accidents not rather be said to be individuated by the ultimate terms to which they naturally look, especially since they take their essential specific reasons from them?

Thirdly, because it is said without foundation that this accident has a natural coadaptation and relation to this subject alone. For although perhaps it can come to be in that subject alone through natural causes, nevertheless it is in itself apt to inform any subject capable of such an accident: just as conversely it can happen that this subject naturally has, for example, only this whiteness or this quantity; and yet its capacity is not thereby understood to be so limited and determined from itself to this accident that it is not sufficient in itself to receive similar accidents.

4 Fourthly, this position might be urged from the fact that otherwise all accidents which succeed one another in the same subject would at least successively be numerically the same; and thus heat that is now in water and perishes, and heat that will afterward be introduced into it, would not be distinguished in number, which is certainly contrary to the common opinion of the philosophers. The consequence is proved. First, because where there is the same root and the same reason of at least successive individuation, individuation must also be the same in the same way. Then also: because things having the same form at least successively cannot fail to have the same specific unity at least in the same way; since the form just mentioned is the first root of specific unity; therefore, if the subject is the first root of the individuation of accidents, the consequence will be that accidents having the same subject at least successively will likewise be numerically the same.

Finally, because if accidents were individuated by their subjects, two inconveniences would follow. The first is that quantity could not be individuated from itself, but from the subject, since it is a true accident no less than the other accidents; yet this cannot be reconciled with what we said in the preceding disputation: for material substance is individuated by matter designated by quantity, because quantity is individuated among material things from itself; and so whatever among those things is individual must either be quantity or in some way participate quantity. The second is that two accidents differing only numerically could not exist at the same time in the same subject, as is evident from itself and will be clearer from what is said at no. 57: just as matter designated by quantity is the root of the individuation of substantial form; therefore two forms cannot exist at the same time in the same matter; yet this is false, since several visible species of different colors exist at the same time in the same pupil; and so on.

§ II. According to the mind of Aristotle and St. Thomas the difficulty is decided.

5 Nevertheless, it must be said that the first root and principle of the individuation and pure individual distinction of accidents is the subject itself, taken formally; and consequently that accidents having a formally different subject are numerically different, just as if they had the same subject taken in the said way, they would not be numerically distinct. Thus Aristotle, in the places cited in the preceding disputation, difficulties 1 and 2, and Metaphysics V, text 15, where St. Thomas also says, in First Part, q. 29, a. 1: Accidents are individuated through the subject: for this whiteness is said to be such insofar as it is in this subject; and q. 39, a. 3, where, speaking of unity and individual multiplicity, he says: But accidents, just as they have being in a subject, so they receive unity and multiplicity from the subject; and in opusculum 29, where he says: But it must be noted that accidents are not individuated through prime matter, but through their proper subject, which is being in act, [through which] they are individuated: as substantial forms also are individuated through prime matter, which is their subject.

The same is taught by the Holy Doctor: then in Third Part, q. 77, a. 2, saying: Since the subject is the principle of the individuation of accidents, what is posited as the subject of some accidents must in some way be a principle of individuation. Then also in many other places listed in the golden table under the word accidens, no. 24, where all Thomists defend this opinion in common; and therefore it would be superfluous to cite them in particular.

6 The most powerful reason for this assertion, however, is none other than those which we brought forward in the preceding disputation, difficulty 1. For as those arguments prove that the individuation of substantial form, and of the composite constituted through it, must be taken from matter designated by quantity, as from the first root, because purely individual distinction is material distinction, and therefore is taken from matter; so for the same reason, the individuation and purely individual distinction of accidents, since it is material, cannot fail to be taken from their matter, namely from the subject taken formally, as from the first root; otherwise, as we expounded there in reasons 1 and 2, such a distinction, precisely because it would be formal and proceed from form as such, would be specific and not purely individual.

This can also be explained and confirmed from what we touched on from St. Thomas in the preceding disputation. For accidents have from the subject their individual being in themselves by the ultimate division, or being that is incommunicable to another, as to the subject of inferiority and predication; and they are also thereby distinguished from other accidents of the same species; therefore they will also receive individuation from that same subject, as from their proper principle.

7 The consequence is evident. The antecedent, however, as regards the first part, is proved and explained. Because accidents, as such, are acts and forms, and thus are communicable from themselves to another, as to a subject of inherence; and therefore, according to this reason taken most formally, they cannot found that negation which is proper to an individual, namely, that it cannot be in another, something in some way distinct from it on the part of the thing conceived, as in a subject of inferiority and predication; because this reason presupposes that the thing which grounds it, considered as its foundation, has in some way not to be received in another, as in a subject of inherence or information, as we said from no. 53 through no. 61 of the preceding disputation and shall touch on below. But precisely because the said accidents are connaturally, whether in act or by aptitude, in this subject rather than that one, according to the common course of their order, they are altogether irreceivable, at least connaturally, in another subject of inherence; and thus, according to this sole reason (with the qualification concerning quantity to be explained in the following difficulty), they are incommunicable to another in some way distinct from them, in the way in which a universal is communicated to another in some way different from itself, as to a subject of inferiority and predication.

From this also the same antecedent is sufficiently established as regards the second part. First, because, as we expounded in the preceding disputation, no. 79 and following, precisely by that through which something is incommunicable to another, in the way just indicated, as by a principle and first root sufficient in itself for such individuation, it must in fact be different from every other thing of the same species. Then also: because in the common notion of accident the subject is posited in common by way of a difference: as when we say, Evenness is the curvature of the nose, as our Complutensians explain at length in Logic, disputation 5, q. 2, so if an accident were to be defined in the singular, its subject in the singular would have to be posited by way of a difference: as if we should say, This evenness is this curvature of this nose; therefore the sign is that the first root of the individuation of the same, and of the division of being, is their subject insofar as the same subject is also, by the ultimate division, distinct from every other, according to which relation we are speaking of it here.

§ III. An objection is noted, and its solution.

8 But you will object that this does not fit well with what was said in the preceding disputation concerning the individuation of material substance. For if substance, as individual and divided by the ultimate division from every other thing, is the first root of the individuation of accidents, and this [substance] is individual by reason of matter designated by quantity, as by the first root, the consequence will be that matter itself designated [by quantity] ought rather to be called the first root of the individuation of those accidents, according to the dictum: Because of which each such thing, and that more.

It will be answered that this objection is intended to refute the first principle in itself insufficient for the individuation of accidents; but not the first principle in itself sufficient, of which we are speaking here, about which the place is St. Thomas's opusculum on the principle of individuation, when he denied to the aforementioned principle the reason of prime matter and granted it to the subject of those accidents. For since accidents are second forms, and as such must be individuated by a subject, they must presuppose as the first root of their own individuation a subject at least including form, namely substantial form, through which they are first in act simpliciter; since being according to what, which is to be supplied by accidental form, cannot be of that kind unless being simpliciter proceeding from substantial form is presupposed; otherwise it would truly be being simpliciter and substantial, as our Complutensians teach very well in the book On Generation, disputation 2, no. 78.

9 Nor does it matter if, against this solution, you urge that a sufficient reason is given from prime matter designated by quantity why these accidents rather than those ought to be given: so that the entire individuation of them is resolved into that same matter as into a sufficient root; and so on. The antecedent is proved. For from the fact that this matter designated by this quantity is given, this substantial form must be given, and not that one; and this composite, not that one; and ultimately these accidents, not those. Hence, if it is asked why these accidents are given, it will be answered that this happened because this composite is given, which is their subject, and not another; and therefore this composite, and not another, is given, and consequently these accidents, and not those, because this matter designated [by quantity], and not that one, is presupposed; and therefore, that being presupposed, other accidents cannot naturally speaking be received in the same composite for the time being, and therefore not in the same [composite] taken formally, as we shall explain below; and so on.

It will be answered that the antecedent is true if it is understood as a sufficient reason within the order of inference, or a sufficient reason based on the goodness and infallibility of the consequence, but not as a sufficient reason within the order of reality, or based on the sufficiency of the antecedent in the reality of the thing. And in answer to the proof, the antecedent will be distinguished in the same proportional way, and the consequence denied.

10 This is explained. For just as, from the denial of efficacious assistance toward an act falling under a precept, a sufficient reason is given within the order of inference for the sin committed by the person to whom that assistance is denied: since it is deduced by the best consequence that he would sin if such assistance were once denied him; nevertheless, it cannot from this be given as a sufficient reason in the reality of the thing, or based on the sufficiency of the antecedent in the reality of the thing, namely on the denial of the said assistance; indeed, not any reason that could in this order be in some way the root of sin formally taken, from the fact that God is incapable of this concurrence. Thus, from the positing of matter designated by quantity, a sufficient reason is given within the order of inference, or a sufficient reason based on the goodness of the consequence: for (at least speaking naturally) it is deduced by a good consequence that if prime matter is designated by this quantity, and not that one, these accidents, and not those, will be given in the composite; nevertheless, a sufficient reason is not posited within the order of reality, or based on the sufficiency of the antecedent alone in the reality of the thing, for the reason touched on in the preceding number.

Therefore, just as that sin cannot follow unless a creature acts and it is attributed to it, as the first principle and source of the sin, so this accident, and not that one, cannot be given unless its subject, namely the whole composite, is given; and that, in the reality of the thing, as a principle sufficient in itself, is attributed to be the first root of its individuation. And just as the denial of efficacious assistance has a connection sufficient for that goodness of consequence concerning sin, because when God denies assistance, the creature immediately fails through its own fault, and not through a defect in God who gives sufficient assistance, so that connection will be sufficient for the goodness of the consequence by which, from the positing of matter designated [by quantity], it is rightly inferred that these numerical accidents, and not those, ought to be given in the composite: namely, the connection between this principle insufficient in itself in the reality of the thing and the other principle, from which the whole sufficient principle, namely the entire composite, will be constituted.

11 Add that it is not improbable that the prior objection and its reply can be answered differently from the fact that, at least very probably, prime matter designated by quantity is the first principle by which, and the first root in this order, of the individuation of accidents, but not the first principle which; for we are speaking here of the first principle which, not of the first principle by which. For in things having a first principle which in fact distinct from the principle by which, as happens here, when their principle is investigated absolutely, recourse is had to the principle which, not to the principle by which. As in efficient causes, when we speak absolutely of the principle and cause of an action proceeding from them, recourse is usually had with greater reason to the principle of acting which than to the principle by which. Therefore it is commonly said that actions are those of supposita, not of forms: because the former are the principle which, while the latter are the principle by which, of the same actions.

§ IV. Solution of the arguments of the first position.

12 The first [argument] is clear from what was said in the preceding disputation, concerning how it proves that accidents are individuated most proximately through their own entities, such as these: because they are individuated from the fact that they look to this subject, formally taken, and not to another; and this regard is not really distinguished from their entity; nevertheless, they are not individuated by themselves, as by the first and radical principle: rather, from the fact that the subject is this [subject], it follows that the accidents are these; and from the fact that the said accidents are numerically such, and numerically distinct only by the said relation, it follows very well that the subject is the first root of such individuation and distinction. As is commonly said in the analogous case of substantial form: which is proximately this form, with respect to matter designated [by quantity], but radically with respect to the same prime matter designated by quantity. For from the fact that matter is this matter, it follows a priori that the form will be this form; and from the fact that this matter, and not that one, is looked to by this form, it is collected a priori that such a form is this form numerically, and that matter also, considered by way of the terminus inspected in itself, is the first root of such individuation, as we said in difficulties 1 and 2 of the preceding disputation.

In confirmation, the antecedent must be denied. And in answer to the proof, having granted the antecedent as regards its first part, it must be denied as regards its second part, according to what we have just said. Nor does the opposite prove the objection: for it is true only when speaking of the same subject materially and taken in the reality of the thing, because this can be looked to by several numerically different accidents; but not of the same subject formally, and within the line of the subject formally taken; and consequently, as it connotes in the being of the subject this time rather than that one, etc. For a subject taken in this way is looked to by one and the same numerical accident; and thus, however many accidents there are, there correspond to them so many subjects inspected by themselves, which can be the same materially and in the reality of the thing, but not formally and in the being of the subject, as we shall explain more fully from no. 15 through no. 18.

13 To the second [argument], it will be answered that accidents which do not subsist in a subject, but somehow refer it to something extrinsic, such as natural powers and operative habits, take their individuation from the subject, although they receive their specific reason from those extrinsic terms. The reason for this disparity is clear from what was said at nos. 5 and 6 of this difficulty and in the preceding disputation, no. 12 and following. For the said extrinsic terms are compared by way of an extrinsic formal cause with respect to those same accidents, taken according to their species; and thus they are fit to give them a species, which can arise from a formal cause, whether intrinsic or extrinsic; but not to give them individuation, whose first and most powerful root must, in the genus of a material cause, concur with them; and therefore such individuation is best given to the subject of the accidents, as to the first source and origin of it.

14 To the third [argument], the antecedent must be denied. And in answer to the proof, it must be said that although we grant that this numerical accident naturally, or according to the common course of its order, looks to this numerical subject formally taken, and can be received by divine power in another numerical subject; nevertheless, not in such a way that the said accident has a connatural aptitude, or one according to the common course of its order, to be received in this subject: and thus, even while existing in an extraneous subject, it always looks to, and always seeks, a connatural subject, or that which according to the common course of its order is at least owed to it in some way; and from this relation it immediately receives its individuation, and remotely, as from the first root, it takes it from the subject.

We have said that it always seeks a connatural subject, or that which according to the common course of its order is at least owed to it in some way, so that a distinction of what is owed is established between accidents of the natural and supernatural orders. For to the former a connatural subject which can be assigned; but not so to the latter; although in reality they at least in some way require, according to the common course of their order, a peculiar subject which; and therefore charity received in Michael under this number cannot, according to the common course of its supernatural order, be received in Gabriel.

15 As to what is added there, namely, that this numerical subject does not naturally look to this numerical accident alone, but can connaturally receive several and different accidents, and consequently conversely this numerical accident can be connaturally received in different subjects, is clear from what was said in the preceding disputation. For although the antecedent can be true of the same subject materially and taken in the reality of the thing, and in the way just mentioned elsewhere; nevertheless, not of the same subject formally and accepted in the being of the subject, and as it connotes this difference of time rather than that one, etc. For according to this reason, subject and accident are mutually adapted and measured so that neither this subject can be naturally terminated toward another accident, nor this accident toward another subject: as we said in the analogous case when comparing matter designated by this quantity with substantial form, and as will be clearer from what is said in the three numbers immediately following.

But since it is settled that the subject, taken in the reality of the thing and materially, and the accident itself considered in this same order, do not have the said mutual commensurability: because this numerical subject, so taken, has from its peculiar reason greater amplitude and indifference. This is sufficiently collected a posteriori from experience, namely, that the same subject materially, at least successively, can naturally receive several numerically different accidents; whereas the same numerical accident, even materially accepted, cannot be received according to the common course, even successively, in different subjects.

16 The consequence must be denied in answer to the fourth [argument]. And in answer to the first proof, it must be said that it is true of the same root formally and taken in the being of a root; but not of the same root materially and accepted in the reality of the thing, as happens here. From this, in answer to the second proof, it is clear that if it were possible for the same form in species, materially and accepted in the reality of the thing, successively to inform, so nevertheless that it would be different in species in the being of the form and of the root of specific unity, then it would not give the same specific unity successively either. And so nothing is proved against us from this: for, when several numerically different accidents are received successively in the same subject materially and taken in the reality of the thing, we give several numerical subjects formally, accepted in the being of the root of their individuation.

This is explained. For numerical unity of an accident requires not only that it be in this subject, materially and accepted in the reality of the thing, but also identity of time: no otherwise, proportion being preserved, than is desired for the numerical unity of motion, according to the doctrine of Aristotle commonly accepted and taught by our Complutensian College in Physics, disputation 23, no. 22, the unity of the terminus and of the same time; and thus, when time varies, the individuation of the accident is inferred to vary, and although the subject may be the same in the reality of the thing, it is not the same when formally taken in the being of the subject. Because the very subject in the reality of the thing varies formally in the being of the subject insofar as it underlies different circumstances of time. And thus, as often as Peter's only whiteness ceases and Peter becomes white again, so often whiteness varies and another whiteness numerically is produced anew and successively. For although Peter remains the same in the reality of the thing, he does not remain the same in the being of the subject formally taken, or in the being of the right of such a subject: because he underlies or connotes a different circumstance of time.

17 This can be further elucidated by the example of a surface with respect to place, together with the relation of distance from the center of the earth and the poles of the world. Although these may not often vary in the reality of the thing, as if a located body were moved around with the same surface in the reality of the thing, nevertheless they often vary in the being of the material reason of place formally taken, as happens in the example just given; and consequently place itself varies, because the said surface underlies different relations of distance, and it, insofar as it underlies such a distance, is said to be the material reason of place in the most formal sense. Thus, for the present, proportion being preserved, it must be philosophized: although, as will be evident to the observer, there intervenes a difference between the example offered and the matter under discussion.

Nor does it follow from what was said in the preceding disputation, no. 134, that the individuation of accidents must be reduced, as to its first root, to time itself: because, as we said in the analogous case of quantity concerning the individuation of substance, time concurs only by way of connoting something extrinsic; the subject, however, although it is not included directly in the accident itself, is nevertheless that which directly individuates the accident in the being of a root. For this office does not require being intrinsically and essentially included in it; it is enough that it be the first material root of the accident itself, irreceivable in another, as in a prior subject; and that it be of such a condition that, according to this reason, it is intrinsically, that is, by the reception of the accident itself, unifiable with it; and these two things accord to the subject of accidents, not to time, as is evident from itself.

18 This itself can also be explained, and at the same time a certain objection that might have been made here can be solved, by the example of the efficient cause of this numerical accident, say of this numerical heat produced by this fire, which cannot be produced by another fire, according to what our Complutensians teach in Physics, disputation 15, no. 50. For although precisely because it is produced by that numerical fire, it cannot fail to be distinguished from another heat produced by another fire, nevertheless neither of these fires concurs in the genus of a material cause, but of an efficient cause, and therefore altogether extrinsically. For this reason, and for other reasons which will be obvious to each from what has just been said and will be touched on in this same disputation, we reduce the individuation of the said heat, considered in the said way, not to the producing fire, but to the receiving subject, as to its first root. For here we are not speaking of any root at all, namely an altogether extrinsic root by relation to which individuation is not taken; but of a root in some way intrinsic, and therefore of that by relation to which individuation is taken.

Finally, it must be said that [this argument] touches on a twofold difficulty: namely, whether quantity has this peculiar property among the other accidents, and whether the substantial forms that can be received in matter are in some way individuated from itself; and whether two accidents differing only numerically can exist at the same time in the same subject. But since each of these difficulties is sufficiently grave in itself, and several things are needed for its decision, as will be clear from what follows, we shall give each of them a separate doubt.

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.

51 The particle “essentially repugns” has deliberately been placed in the title so that it is clear that the question is not concerned merely with repugnance in relation to God's ordinary power, but also with absolute power. But another particle has been added, namely “to a merely numerical distinction of accidents,” so that the title is to be understood universally concerning all accidents that differ only in number precisely insofar as they are such, and not merely peculiarly concerning some of them considered according to their peculiar reason.

§ I. The position that denies it.

52 The position that denies the thesis is held by Aureolus in 1, dist. 7, quaest. 2, art. 1; Scotus, as reported by Capreolus, ibidem, art. 2, and by Caietanus, 3. part., quaest. 35, art. 5; Suarez, 1. tom. of his Metaphys., disput. 5, sect. 8; and others whom he reports there.

This is proved first. For one and the same efficient cause can elicit several actions at once that differ only numerically, as when fire heats several logs simultaneously; likewise, the same end (provided that this is said in its proper sense) then gives finality to those actions simultaneously; and finally, the same substantial form can inform at once, at least supernaturally, a twofold matter differing only numerically, because the substantial form, considered in itself, does not regard this matter more than that matter; and therefore, by God's absolute power, it can be present in both simultaneously. Thus, for the same reason, the same material cause of accidents, namely the subject, can receive at once two accidents differing only numerically; and consequently there will be no essential repugnance to their purely individual distinction from the fact that they are received simultaneously in the same subject. This last consequence clearly follows from the preceding one. The first, however, follows from the parity of reason between its consequent and its antecedent: the material cause is not of lesser power in its own genus than the other causes in theirs; therefore, if those causes can at least supernaturally produce several effects simultaneously that differ only in number, the material cause will also be able to produce them simultaneously, or (which is equivalent for the present purpose) to receive them simultaneously.

53 This is proved secondly by several examples belonging to the order of knowability. For visible species representing two whites that differ only numerically cannot be distinguished further than by number: their objects, from which they derive their unity and distinction, are distinguished only individually, yet the species are simultaneously in the same eye, and therefore both whites can be seen simultaneously through visions differing only numerically. Likewise, the said species are simultaneously in the same part of the medium through which they are conveyed from the object to the eye; consequently, when the eye is applied to any part of the medium, it is affected through the species of each white, which could not happen unless each species were present in every part of that same medium.

Again, innumerable species of many and diverse individuals differing only numerically are preserved in the imagination, and several of them are ordinarily perceived by the same imagination at once, although the said species and these actions of the imagination must, for the reason just noted, be distinguished only numerically; then, once the intellect has cognized one singular through a species abstracted from the phantasms, another intelligible species is produced in it representing that same singular, as our Complutensian College says in disput. 18, numero 99, in lib. de Anima. Accordingly, when another singular is afterward cognized through that former species abstracted from the phantasms, a new species is also produced in the same intellect representing this same singular, while it is simultaneously in the intellect together with the preexisting species representing the former singular, and differs from it only numerically. Finally, the same intellect is accustomed to understand several things differing only in number, and consequently through intellections differing only numerically, as when it cognizes Peter and John simultaneously.

54 This is confirmed. Although accidents having the same function, such as two whitenesses, cannot be simultaneously present in the same subject by God's ordinary power, because when one of them performs that function, the other is superfluous for its performance, and nature abhors superfluity; nevertheless, whenever accidents differing only numerically differ in function and office, and what is performed by one of them cannot be caused by the other, they can be simultaneously present in the same subject, since none of them is superfluous. Yet all the accidents mentioned in the preceding argument, although differing only numerically, simultaneously differ in function and office. Consequently, the species of one white represents only that white and not another; likewise, its vision, as such, is only the perception of itself and not of another, and so of the rest. Thus, they can well be simultaneously and naturally present in the same subject. Likewise, any other accidents can supernaturally be found simultaneously in the same subject even if they do not differ in function and office, because they may be placed there by God for other reasons and have no contrariety or opposition among themselves, as is evident in the case of two whitenesses.

55 This is proved thirdly by other examples belonging to the entitative and natural order. For several lights differing only numerically can be present simultaneously in the same medium, as when a twofold luminous object illuminates the same medium from either side. The sign of this is that, if an opaque body is placed between one light and another, two shadows are caused; yet this would not happen, and only one shadow would appear, if a light numerically different from the other were not produced there. Similarly, if Peter has one relation of paternity to his first son and afterward has a second son, he is referred to that second son by a new relation of paternity, existing simultaneously with the former relation. Indeed, precisely because each is a son, the relation cannot fail to refer simultaneously to each; and precisely because the said relation is of such a condition that it is founded on a distinct having begotten, namely this second son and not another, it cannot fail to be distinct from the preexisting relation of paternity founded on a distinct having begotten, namely the first son and not another. Above all, because otherwise the same relation could perish and not perish simultaneously, as when the first son dies while the second remains: the relation to the first would perish while the relation to the second would remain, whereas on the contrary position the relation would be the same in relation to each.

56 Fourthly. For a subject can receive at once several accidents distinct in number which are otherwise also different in species; therefore, it can likewise receive at once several accidents differing only numerically. The antecedent is evident of itself. The consequence, however, is proved thus: whether the individual unities of whiteness and blackness are joined simultaneously to the specific unities and differences of those same things, or are not joined to them, they do not change in the being of individual unities. Consequently, through that very individual difference by which this whiteness differs individually from this blackness, it can also be distinguished numerically from another whiteness. Thus, just as a subject can receive at once several accidents differing numerically, which are otherwise distinguished by species, and can consequently be the simultaneous root of their individual being, so too it can receive those accidents and be the root of their singular being even if they differ only numerically.

§ II. The position of Aristotle and D. Thomas is preferred.

57 It must nevertheless be said that it essentially repugns to the individuation of accidents, insofar as several accidents differing only numerically, whatever they may be, are received simultaneously in the same subject, and consequently that this cannot be done by God's absolute power. This assertion is gathered from Arist., 5 Metaphys., text. 15, where, after setting out the various ways in which things are said to differ in species, he adduces in the fifth place the specific distinction of several accidents precisely insofar as they are simultaneously in the same subject; and therefore he concludes: “And whatever things have a difference in the same substance.” D. Thom. explains this testimony ibidem, lect. 12, in these words: “Here he shows in how many ways things are said to differ in species, etc. And the fifth mode is when some accidents are in the same subject and nevertheless differ from one another, because it is impossible for several accidents of one species to be in the same subject.”

The Holy Doctor teaches the same thing in 3. part., quaest. 35, art. 5, where, from the fact that several accidents differing only numerically cannot be simultaneously in the same subject, he proves that several paternities of the same kind cannot be simultaneously in one father; and thus he says: “Because several forms of the same species cannot simultaneously be in the same subject, it is not possible for several paternities to be in one who is the father of several sons by natural generation; otherwise it would be so if he were the father of one by natural generation and of another by adoption.”

58 He also taught this in 4, dist. 12, quaest. 1, art. 1, q. 3, where, arguing against those who said that after the consecration of the bread, its dimensions and the other accidents were founded in the air as in a subject, and consequently that the dimensions of the air and of the consecrated bread, ceasing to exist, were received simultaneously as in a subject in the air itself, he says: “Since all dimensions are of the same species, whatever matter they are in, because matter does not enter into their definition, if the dimensions of the bread are again in the air as in a subject, it follows that two accidents of the same species are in the same subject, which is a contradiction to their being simultaneous, because the number of accidents of the same species is derived only from the subject. Hence, if the subject is one, it follows that those accidents are several, and not several.”

Therefore the disciples of the Holy Doctor follow him: Capreol. in 1, dist. 7, quaest. 2, art. 3; Caietan., 3 part., quaest. 35, art. 5; Hervaeus quodlib. 3, quaest. 9; Palud. in 3, dist. 8, quaest. 2; Flandria, 5 Metaphysic.; Soncin., 7 Metaphysic., quaest. 4; Navarrete, Nazar., Gonzal.; and many others.

59 The fundamental reason for the assertion is none other than the reason adduced by D. Thomas in the places cited, namely: if two accidents differing only numerically could be simultaneously in the same subject, they would be two and yet not two: they would indeed be two, as is supposed, but they would not be two, because they would be distinguished neither essentially nor formally—otherwise they would not be of the same species—nor numerically, since the first principle and root of a purely numerical distinction is the subject. Thus, if the subject were not multiplied in the event in which this occurred, those accidents could not be multiplied numerically. Just as two things cannot be distinguished essentially and specifically unless the first principle and root of that distinction, namely form, is essentially multiplied, because it universally repugns that two things should be distinguished in any way without a proportional multiplication of the diverse principles and roots causing such a distinction.

§ III. Two solutions of the opponents and their refutation.

60 The opponents first meet this argument by saying that it does not demonstrate the thesis universally concerning all accidents, but only at most concerning accidents connatural to some subject, not concerning others that would be connatural to other subjects and would be supernaturally united and received simultaneously in another: for example, if two whitenesses, one connatural to Peter and the other to Paul, were supernaturally received simultaneously in John in a manner beyond nature. For these could be distinguished most perfectly from one another numerically, even if they were simultaneously in the aforementioned subject, because they would not be individuated or distinguished by it, but by their proper subjects, in which they seek to be connatural, and each would always bear a relation to them as principles of individuation and distinction.

61 But against this. Although we grant that a whiteness connatural to Peter can be supernaturally received in John, as many hold probably, nevertheless this cannot occur unless, on the part of John and of its union with the whiteness, there corresponded to it that proper and peculiar mode of union and reception which is proper to John; not, indeed, those modes by which it can be connatural in Peter, but those by which it ought to be connatural in John. Consequently, if a twofold whiteness were to be posited simultaneously in him, it could not fail to be received on John's part through unions and receptions connatural to him, each of which would be individuated by him. Thus, if these cannot be multiplied simultaneously in the same subject, neither could those whitenesses be received simultaneously in it; but it repugns for those receptions, insofar as they hold from John's part, to be simultaneously in the same subject and to be multiplied numerically. Therefore, it will also repugn for those two whitenesses to be subjected simultaneously in John.

The consequence seems certain, especially because otherwise those whitenesses received in John would be two, as supposed, and yet not two, since it repugns for whitenesses to be received as two and for their reception to be one. The minor premise, however, follows clearly enough from the reason of D. Thomas and from what this solution admits: those receptions, insofar as they hold from John's part, would be of the modes that are connaturally individuated by John, and consequently, the unity of the subject and its simultaneity in him not being multiplied, they cannot be multiplied numerically.

The major premise is proved from the peculiar nature of a mode, universally accepted by philosophers. For although a form having its own true entity, insofar as it is distinguished from a mode, can be separated from its subject by divine power and (as we now admit according to the probable opinion of many) received in another subject, a mode cannot. First, because it belongs to the essence of a mode actually to modify the thing of which it is the mode. Second, because, as philosophers commonly hold, this is the point distinguishing a properly entitative distinction from a modal distinction: in the former, either extreme can be separated (so far as the force of the distinction is concerned) and exist without the other; in the latter, however, this is not so. Consequently, it repugns for Peter's session to exist except in Peter. Therefore, it also repugns for those whitenesses to be received in John through modes of union connatural to Peter or Paul; but they must necessarily be united through unions or receptions connatural to John. Thus, if these repugn to being multiplied simultaneously in the same subject, in the same way it follows that the said whitenesses are received, since they cannot be received without modes of union and reception in a subject.

62 Furthermore. Although it is probable, as our Complutensian College touches on in lib. de Generat., disput. ultima, num. 15, that Peter's whiteness can be supernaturally received in John, the opposite is more probable; therefore, the reason of D. Thomas concerning these accidents will not remain infirm. The consequence is sufficiently clear.

The antecedent is proved from what our Complutensian College teaches in lib. Physic., disput. 15, num. 50. For as not every efficient cause—for example, not every fire—can produce every other fire, but a certain infinite collection of individuals in a syncategorematic way must be designated for each fire, which that fire can produce; and therefore it even repugns by divine power that one fire produce another fire by its native power, unless it belongs to those contained in the collection corresponding to it, as is shown more broadly in the cited place. Similarly, distinct collections must be designated for each subject, beginning in potency in a syncategorematic way with diverse accidents, so that none of them can receive an accident by its native power, or by reason of its entity, unless it belongs to those contained in the series or collection corresponding to it. For just as an efficient cause by the force of its power or entity cannot extend beyond its adequate object, so neither can the material cause by the force of its native power and entity extend beyond its own; because in every genus of cause there must be a complete commensurability between cause and object.

63 Second, others answer that the Holy Doctor's reason proves the point at most concerning absolute, not relative, accidents: since these do not regard anything other than the subject, it is necessary that, precisely because they are simultaneously in one and the same subject, they have nothing from which they can be distinguished. Yet these, however simultaneously they may be in the same subject, regard diverse terms, and hence they can be distinguished by reason of the said term considered by itself.

Yet this solution does not diminish the force of the Angelic Doctor's reason, but remains sufficiently refuted by what we have adduced from the same author in this disputation, no. 6, and in the preceding [disputation], no. 12. Numerical distinction, being material, must be derived from the part of the subject and of those things which hold from its part, not from the part of form; otherwise it would be formal and specific. But terms considered by themselves, as pertaining to relative accidents distinct from the subjects in which they are received, concur in the genus of a cause formally extrinsic to their being, and do not hold from the part of the subject but rather from the part of those same accidents. Therefore numerical distinction of them cannot be derived from the terms.

§ IV. The opponents' final solution and its refutation.

64 Others object that the force of the Holy Doctor's reason does not refute the claim when the two accidents naturally seek to be at different times. For since the unity of an accident requires not only unity of subject but also unity of time, the said accidents can be distinguished from one another from a different time considered naturally, or, better said, from the same subject connoting that different time. Above all, because according to our position, the same subject under a different time is the same only in the being of the thing, but diverse formally in the being of the subject; and thus the multiplicity of those accidents existing simultaneously in it can be derived from this.

But against this. For it repugns that one and the same subject entirely, and by the same formally considered power in the being of the thing, should connote those diverse times simultaneously in the solution just proposed, and should become formally multiple in the reason of the subject, since time concurs toward individuation only as connoted by the subject.

65 The reason for this essential repugnance is as follows. Since one and the same subject entirely in the being of an entity should connote those diverse times simultaneously and become multiple in the reason of the subject, this exceeds its natural power, so that by the force of its own natural entity it cannot have this property. But nothing can be added to it that would make it capable of connoting those distinct times simultaneously and becoming multiple in the reason of the subject; therefore, by no means can it connote them even supernaturally and become multiple.

The major premise seems certain. For if the same subject in the being of the thing could, by its own power, connote those diverse times simultaneously and become multiple in the reason of the subject, without exceeding its natural power, there would be no reason why the subject's power—for example, its power to be heated, namely with six degrees—should be fulfilled naturally by one heat of six degrees, so that it could not simultaneously receive another altogether similar heat naturally. For it could by its own power connote those two times simultaneously and become multiple in the reason of the subject; and consequently, by reason of that other power formally considered, it would naturally become capable of receiving another heat simultaneously in the same subject, as we shall explain more fully below. Above all, since neither of those heats is intrinsically incompossible with the other, and the multitude and abundance of heats would not be superfluous but could in some way contribute to more vigorous action, just as a multiplicity of matter contributes to that end. Yet this is repugnant to evident experience and philosophical reason, as is clear from what the Complutensian College says in lib. de Generat., disput. 8, num. 5, and subsequently. Therefore, and so forth.

The minor premise is also clear. For the subject can connote those two times simultaneously and become multiple only by reason of its natural entity, since it must connote them and become multiple by that by which it is the root of individuation; but by its natural entity it has the being of that root. Therefore, whatever is added to it beyond its intrinsic natural entity does not make it more capable of connoting those two times simultaneously and becoming multiple in the reason of the subject than if nothing were added to it.

66 This is confirmed and explained. For among the other reasons why the same prime matter in the being of an entity cannot simultaneously become multiple in the reason of the subject with respect to several substantial forms received simultaneously in it, one is this: prime matter, as this singular matter, cannot naturally be one and the same in the being of an entity and become formally multiple in the reason of the subject, and consequently neither can it supernaturally do so. And thus it cannot receive those forms simultaneously, as our Complutensian College teaches in lib. Physic., disp. 4, num. 66, because matter receives form only by the display of its own natural entity. Therefore, if naturally, so far as the force of its natural entity is concerned, it cannot receive those forms simultaneously and become multiple in view of this, neither can it do so supernaturally. Thus, since this same reason urges in the present case, the same must be affirmed in proportion.

67 It makes no difference if you object that a certain subject can supernaturally receive an accident once corrupted, such as sight, and can therefore connote simultaneously the present time in which the subject exists and the past time in which that accident naturally existed, to which it has a natural relation. Therefore, it is not inconvenient that the same subject in the being of the thing should be simultaneously multiple formally in the being of the subject; and consequently that it should receive simultaneously several accidents differing only numerically, even if these are individuated by their subject.

For the answer is made by granting the antecedent and denying the consequence. The reason for the disparity is twofold. First, because in that event one of these times is connoted by the subject considered in the being of the thing; the other, however, only by the same subject formally considered in the being of the subject, so that it has the character of such only insofar as it is subject to the aforesaid time. Consequently, such a subject remains the same in whatever time it exists, provided that it connotes that time, formerly past, though not as past. But for the same subject to receive simultaneously two accidents differing only numerically, and to be the root of their diversity, it is required that in the reason of the subject it connote diverse times simultaneously: for the subject is not formally multiplied in the being of the subject unless it connotes the aforesaid times, and a subject not formally multiplied in the being of the subject cannot sustain a multiplicity according to the number of the aforesaid accidents in it, as is clear from what has been said.

68 We have said that when a subject receives supernaturally an accident once corrupted, it formally connotes only one time in the being of the subject, namely the time formerly past; it does not connote that time as past, because although the subject, insofar as the force of its natural entity is concerned, regards it in the former way, it does not regard it in the latter way, namely as past. For as by the force of its natural entity it does not regard sight as restored, but regards the sight that has been restored, and consequently does not regard by the force of that same entity the sight as formerly extinguished and afterward recovered, so also it does not connote that time as past, although it connotes the same time that is past. Yet this suffices for that very accident once extinguished to be received by it. For that time does not concur toward individuation because it is past; otherwise, while it was present, it could not have concurred toward the individuation of the number of the accident that was extinguished and is afterward reproduced. Instead, it acts according to that numerical entity which formerly was past. By this, too, a certain tacit objection that could have arisen here remains resolved.

69 The second reason for the disparity, by which the preceding [reason] is further illustrated, is this. Although something supernatural is required on the part of the principle for the reception of an accident once corrupted, because in natural causes there is not sufficient power to make a return from privation to habit, or to reproduce what has once been corrupted, nevertheless, on the part of the subject considered according to its entity, the power that it has of itself and naturally is sufficient for receiving it. For sight, for example, acquired supernaturally and produced naturally, if considered by itself, is altogether of the same reason; thus, precisely considered from the part of the subject and of the accidental form, or of the time, it requires no greater power than the natural power of the same subject, nor does the subject exercise a double or greater influx than it would if the accident were produced naturally. Accordingly, just as the aforesaid subject, insofar as the force of its natural entity is concerned, has (in the manner indicated) the power to receive all and every sight corresponding to it—not indeed so as to receive all or any of them simultaneously, but only successively—so, in the same proportional manner, by the force of that same natural entity, it has the power to connote all those times in which they are naturally to be received. Thus, although it may regard them simultaneously as properly connoted, it cannot regard them as simultaneous, but only as successively connotable. Just as, for two contraries in the highest degree to be simultaneously in the same subject, something supernatural is required on the part of the principle, this does not occur because the subject, insofar as it is its own power, lacks sufficient natural power to receive either, or because a double influx, greater than that necessary for naturally receiving two accidents different in species but compatible with one another, is demanded from it; rather, this alone repugns because of the incompossibility between them, insofar as they hold from their own part. Therefore, when supernatural power overcomes and defeats that incompossibility, one and the same subject can simultaneously subsist under those two mutually contrary accidents possessing the highest degree of intensity.

70 Furthermore, insofar as the subject is considered according to its own nature and native power, it cannot receive a twofold accident differing only numerically or become naturally multiple; and finally, it cannot, by the force of its own natural entity, exercise that double influx, as has been said. Thus, even if something supernatural is posited on the part of the principle, or even if divine power is posited, it cannot be done.

We have said, in order thus to dispel another tacit objection, that the subject, with the limitation aforesaid—namely, insofar as it is considered precisely on the part of the subject and of the accidental form, or of the time—has sufficient natural power to receive an accident once corrupted and to connote the aforesaid time, because, considering everything and in the composite sense of the pastness of such an accident or time, it does not have an absolute and simple connatural power to receive that accident and connote that past time. This natural power, understood in the manner indicated, regards the efficient cause as operating according to the ordinary course; it does not regard it as operating on the part of the principle in a supernatural mode of operation, as our Complutensian College says in lib. Physic., disp. 3, num. 93. Nevertheless, even supernaturally and by a supernatural mode of operation, the efficient cause could not introduce the aforesaid natural accident into the subject unless, with the mode and limitation indicated, the subject had sufficient power from the force of its natural entity to receive it.

71 It makes no difference if you press from this direction that, if a subject can supernaturally receive a past accident, although it does not have the power and capacity, absolutely and simply considered natural, to receive it in that way, then for the same reason it can receive simultaneously through divine power two accidents differing only numerically, although it does not have natural power to receive them in that way.

For the answer follows from what has been said. In order for a subject to receive an accident as past through divine power, nothing further is required on the part of the subject than is required for receiving it absolutely; only something on the part of the efficient principle and mode of producing it is required. But in order for it to receive at once two accidents differing only numerically, the proper entity of the subject is not sufficient. For otherwise it could naturally have a whiteness, for example, which according to the ordinary course is to be had today, and, retaining that one, receive tomorrow another whiteness which according to the same course was then to be produced; and consequently, naturally speaking, it would connote simultaneously on the following day the present time as such, and simultaneously the past time in which the prior whiteness began to exist; and consequently, naturally speaking, and according to the same numerical receptive power, it would also be multiple in the reason of the subject. For, as we touched on in no. 65, there would be no reason why something supernatural should be required on the part of the efficient cause, as is required for the restoration and reproduction of the same accident; rather, all the conditions required for such reproduction would be naturally possible, as will be evident to the one considering the matter.

§ V. The arguments of the first position are answered.

72 To the first [argument], granting the antecedent concerning the efficient and final causes, it must be denied concerning the formal cause, as is clear from what N. Complutens. says in lib. Phys., disp. 4, num. 61; for the formal cause also causes by reason of its intrinsic natural or native entity, just as the material cause does. Therefore, here too, the reason that we touched on against prime matter in no. 66 urges. Nor does its opposite proof establish the contrary, as is clear from what has been said. The consequence must therefore also be denied.

The reason for the disparity is derived from what has been said. For that numerical diversity of effects is not taken from the other causes, namely from the efficient and final causes, as from the first root and in a sense intrinsic principle; indeed, it is not even taken from the first source, namely the formal cause; but it is taken from the subject. Thus, it does not require a multiple efficient cause, for example formally considered; but it does require a subject formally accepted as multiple, so that into it the said numerical distinction of the effects may simultaneously be poured. Therefore, since the corresponding subject cannot be formally, though badly, multiple simultaneously, as has been shown, it follows that that numerical distinction cannot be derived simultaneously from it into the said accidents. The proof of the consequence adduced there establishes no further point: each cause must be powerful in its own genus, according to the nature of that proper genus. But the nature of the proper genus of the material cause demands this multiplicity in order to produce effects distinct in number; the nature of the proper genus of a cause, for example the efficient cause as such, does not, because their numerical distinction is not taken through relation to it.

73 To the second, it is answered, with Caietanus, in the cited 3. part., question, that all those accidents are distinguished by species. Because the specification and nature of the visible species representing this particular white consists in representing it insofar as it is also this [object], so that it is essentially commensurated to represent it and not another, numerically different object. Consequently, the aforesaid white, insofar as it is this [object], enters into the formal object of that same species; and consequently, the aforesaid species, being distinct by formal objects, are distinguished not only numerically but also by species. And although the aforesaid singulars are distinct in the being of the thing only numerically, they are nevertheless distinguished essentially in the being of the sensible object that seeks and desires for itself that visible species having the aforesaid essence commensurated with itself and not with another. The same must be said, in proportion, of the other examples there enumerated (if it is true that all those accidents can be simultaneously in the same subject).

74 This is explained further. For the objects of sight, for example, can be taken in two ways. First, in the being of the thing: thus this white and that white are of the same species. Second, in the being of the sensible object: thus they are of diverse reasons and are distinguished by species. First, for the reason just stated, because the essence of that species also consists in the representation of the individual difference of the object; for, as our Complutensian College says in lib. de Anima, disp. 9, num. 24, and disp. 18, num. 104, sense differs from intellect in this: the former has a singular for its object, whereas the latter has the universal. Second, because, just as in the being of nature only those things are said to be of one species in which whatever has one essentially has another essentially, so in representation only those things will be said to be of the same species or essence in which whatever represents one according to its atomic reason and the same formality represents that very same other in the manner stated. And such are the two visible species that are sent from the same white toward a double eye; consequently, these will be of the same species, because they do not differ in representation. But two species that are sent from two individuals necessarily differ in representation, because one of them, according to its atomic reason and exactly the same formality, represents this particular white, reaching as far as its numerical being; the other represents another in the same way. Therefore, whatever one represents according to the same atomic formality, the other cannot represent.

It is therefore also clear with respect to the other examples contained there. For although the visions of two whites are not formally representative of them, as will be clear from what we shall say in the following treatise, disput. 2, no. 215, and afterward, nevertheless they are specified by intentional species, the means through which they are elicited. Thus, when these are essentially multiplied, the visions themselves cannot fail to be essentially multiplied. The same must be said in proportion concerning the several intellections that concern several individuals differing only numerically. For these either arise through means that are essentially and really distinct, or through one means that is really one in species but, considering everything it connotes, is eminently several (as is clear from what the Complutensian College says in lib. de Anima, disp. 18, quaest. 6, et disp. 21, quaest. 6); consequently, it specifies them according to their diverse formal reasons. Capreolus may also be consulted on this at the place cited.

75 To the confirmation, the antecedent must be denied concerning the second part, concerning those accidents there recounted and distinguished in function and office. Because that same distinction in function and office is material and numerical; and therefore it cannot come from anywhere except the subject, yet it could not originate from the subject if those accidents were received simultaneously in it, as has been shown.

Moreover, there is no accident, however similar to another, that is not distinguished from it in function and office. For one whiteness, for example, which appeared not to be distinguished in this way from another whiteness, is in fact distinguished from it: the function and office of that whiteness is not just to make the subject white in any way, but to be determinately white as what it is and not through something else. Thus, just as this diversity of function and office does not entail that two whitenesses can be received simultaneously, because this entire diversity does not exceed the force of a material and numerical diversity, so too any other diversity in function and office, provided that it entails only a diversity contained within the latitude of material and numerical diversity, will not be sufficient for the said accidents to be received simultaneously in the same subject.

76 To the third, the first of its examples is established by what our Complutensian College says in lib. Physic., disp. 15, num. 42 et 43. The second is clear from what they assert in Log., disp. 14, num. 92 et 93. For the formal terminus of this paternity is not this son because he is here, but because he is the son of this father; and the reason grounding it is not this, namely “has begotten,” because he is this son, for example, the firstborn, but because he is “having begotten” by this father, whether this numerical son or another is produced through that act of “having begotten.” Consequently, the very same paternity can extend to any son whatever, provided that he was begotten by this father; and when one of two already-begotten sons dies, the relation does not perish with respect to the one who remains, because its formal terminus remains the same. Thus, it does not follow that the same relation can perish and not perish simultaneously; rather, by connoting the generation and existence of the first son, it terminates with respect to him; and by connoting the generation and existence of the second son, together with the corruption of the preexisting relation, the same paternity, without any change in itself and solely through the change of the diverse connotes that are inadequately connotated by it, can extend to the second son and not terminate with respect to the first.

77 To the last, it is answered that the reason is disparate. For the subject individuates accidents distinct in species through diverse powers formally considered in the being of the thing, so that one formal power in the being of an entity corresponds to all whitenesses, and another to all blackness, and so of the rest. Consequently, it is not surprising that, existing at the same time, they can receive those accidents simultaneously in a subject diverse formally (even in the being of the thing) and distinguish them from one another numerically.

The reason why the aforesaid powers, formally and as stated, must be given is this: since the subject, insofar as it is the principle of individuation, regards only the individuation itself and the purely individual distinction of accidents, it follows that through one formally considered power (even in the being of the thing) it regards only accidents of the same species, and through another it regards those which, when compared with one another, are not distinguished by species. Whether the aforesaid powers, distinct in the being of an entity, can be distinguished simultaneously from the nature of the thing apart from the intellect, or only virtually, is another question to be discussed elsewhere, God willing.