Disputationes metaphysicae

1. That accidents differing only in number are in the same subject can happen in two ways, namely at the same time or only successively; and each has been placed in controversy, and in the present section we treat only the former.

The first opinion is treated

2. In which there is the first opinion, which denies that not only accidents of the same species, but also of diverse species, if they are contained under the same proximate genus, can be at the same time in the same subject. See St. Thomas, I, q. 85, a. 1, where: It is impossible (he says) that the same subject be perfected at the same time by several forms of one genus and of diverse species, as it is impossible that the same body according to the same part be at the same time coloured with diverse colours or figured with diverse figures. But in De veritate, q. 8, a. 14, he declares this of forms existing in perfect act. Which exposition the Thomists commonly embrace, and so they solve the arguments about several intelligible or sensible species contained under the same proximate genus (such as are the species of man and horse) existing at the same time in the same power, and about two sciences, for example, or two moral or theological virtues, which, since they differ in species and are contained under the same proximate genus, can be at the same time in the same power, even with perfect intension; for these and similar things they say are at the same time only in incomplete act, because they are at the same time only in first act or in habit, not in second act.

3. But in truth it is difficult to sustain this opinion in that generality simply and absolutely. First, because no sufficient reason for it can be given; for, as Scotus well objects, In I, dist. 3, q. 6, § Ad quaestionem igitur, in the examples which St. Thomas brought forward above, those accidents differing in species cannot be at the same time for this reason, that they include some opposition in order to the subject; for two colours are always opposed, either as extreme contraries, or as extreme and intermediate, or as approaching more to one of the extremes; figures too include repugnance in site, or in straightness and obliquity, or in some similar thing; but it is not necessary that all accidents differing in species have an opposition of this kind with respect to the subject. Next, Durandus, In II, dist. 3, q. 8, urges not badly the argument about intelligible species (although he himself uses it badly to deny intelligible species); he argues, then, that, although the intellect does not actually understand, several species are perfect and complete as regards the act of informing; for actual operation matters nothing to the complete being of a form. Cajetan answers, I, q. 85, a. 4, that this is true of species in real being, but not in intelligible being. But, to omit that this is a certain begging of the question in the question which he disputes there, namely whether the intellect can have several acts of understanding at the same time, because, as he himself expounds, that intelligible being is nothing other than that it actually moves the power to actual consideration; to omit this (I say), for the question with which we are here dealing it is enough that two accidents according to their real being have at the same time a complete act of informing in the same subject. And the same argument can be made of the habits of the moral virtues or of the sciences, in which that distinction of real or intelligible being has no place. And from these the argument can be extended also to acts; for it will not be repugnant that they be at the same time, as far as depends on themselves or on the receptive power, if there is not lacking an active power which can effect them at the same time, because in the rest there is no greater repugnance between acts than between habits of the same genus, if otherwise they are not contrary.

4. And so too is solved the reason which St. Thomas indicates in the said De veritate, q. 8, namely, that acts of the same genus regard the same power and terminate it; but the same power cannot at the same time be terminated by several acts. For the answer is that this is true in acts adequate to the same power, but not in inadequate ones; as in the present case one species or one habit is not the adequate first act of the intellect, because it does not perfect it in order to its adequate object; and therefore several can be in it at the same time, even if they are of the same genus, until they integrally and adequately perfect it. And the same will have to be said of any accidental forms whatever. As, for example, heat and dryness, although perhaps they agree in proximate genus, can be at the same time in the same fire, because neither of those qualities per se fills the natural capacity of fire, neither the passive, which it has by reason of matter, nor in a certain way the active, which it has by reason of form through natural emanation. That proposition of St. Thomas, then, in order to be true in some sense, is to be understood of forms which completely and adequately actuate the potency of the subject in such a genus or notion, as will be more evident from what is to be said. For this opinion which has hitherto been treated is not founded on the individuation of accidents, and so did not pertain to the present question; yet it had necessarily to be set out first, both for the completion of the doctrine and also because it throws light on what we shall say.

The second opinion

5. The second opinion, then, is also extreme, that no accidents at all of the same species can be at the same time in the same subject. Which is thought to be Aristotle’s, Metaphysics V, c. 10, text 15, saying that those accidents differ in species which, being in the same substance, have a difference. Where St. Thomas, lect. 12, gives the general reason of that assertion, because it is impossible that several accidents of the same species be in the same subject. He teaches the same, III, q. 35, a. 5, where also he does not admit several relations diverse only in number in the same father with respect to several sons, nor in the same son with respect to father and mother. And so Capreolus generally defends this opinion, In I, dist. 7, q. 2; Cajetan, III, q. 35, a. 5; Hervaeus, Quodlibet III, q. 9, and In III, dist. 8, q. 1; there Paludanus, q. 2; Soncinas, Metaphysics VII, q. 4, where he adduces several reasons. But the chief is taken from individuation; for distinction in forms is only either formal, which is specific, or material from the subject, which is numerical, from Aristotle, Metaphysics III, c. 3; Book V, c. 6; therefore, where neither of these intervenes, there cannot be distinction; therefore, where there is the specific unity of an accident in the same subject, there cannot be numerical plurality. It is confirmed, because otherwise, by the reason by which two accidents diverse only in number could be at the same time in the same subject, they could also be multiplied to infinity, because there is no greater reason for one multitude than for another; whence it is inferred that there are infinite relations in the same subject, and other similar inconveniences.

6. But it is also difficult to sustain this opinion in this whole generality without any exception, on account of various examples in which it plainly seems to fail, which we shall bring forward immediately. And therefore, although none of the authors simply teaches the extremely contrary opinion, namely that any accidents whatever differing only in number, of whatever species they are, can be at the same time in the same subject—for this is openly repugnant not only to Aristotle and all philosophers, but also to experience itself, as was touched upon above and will be more fully evident from what is to be said—nevertheless several apply exceptions and limitations to the aforesaid opinion; but because it is difficult to choose a middle way and give its reason, therefore in making this exception they do not agree among themselves.

The third opinion

7. The third opinion, then, is that of the Thomists, who distinguish accidents in complete or incomplete act; for in the former way they deny that accidents differing only in number can be at the same time in one subject, on account of the reasons given and the authority of Aristotle and St. Thomas, whom they so expound. But in the latter way they admit it. So Cajetan, I, q. 95, a. 4. More clearly Capreolus, In II, dist. 3, q. 2, on the arguments against the ninth conclusion; Javellus, Metaphysics V, q. 16. Who seem to have taken this from St. Thomas, De veritate, q. 8, a. 14, and seem to have been led chiefly by the argument of intentional species; because they cannot deny that several differing only in number can be in the same subject, namely in the same intellect, or in the same phantasy, or in the same medium according to the same part.

8. But first of all this distinction is not sufficient, for we shall show below that not only these intentional accidents but also several others according to their whole complete being can be at the same time in the same subject. Next, about these intentional accidents the argument made above returns, namely for what reason they are said to be incompletely in the subject: whether because they do not effect, or because they do not fully inform; this latter is false, because they are in it according to their whole being; therefore they inform; but the former seems irrelevant, because the complete being of an accident does not consist in effecting but in informing. Finally there is added that, if these accidents cannot be in the same subject on account of individuation, then the same will hold whether they are in actual operation or not; because before they operate they have their individuation from the subject; therefore either that reason is not fitting, or it equally proves that these accidents cannot be distinguished in number in the same subject even while they do not operate.

The fourth opinion

9. The fourth opinion is that proper accidents, or those which flow intrinsically from the subject, cannot be several differing only in number in the same subject; but those which are common accidents can be at the same time. So Jandun, Metaphysics V, q. 36. The reason of the former part is that nature abhors superfluity; whence, since the proper accident is intrinsic to the nature, and one suffices for the function and end of the nature, it is not multiplied. And hence is taken the reason of the other part; for, since the common accident often comes from without and per accidens, it is not repugnant that it be multiplied in the same subject; and so it happens that several heatings are made at the same time in the same wood by diverse fires.

10. But this opinion, although it is true as regards the former part¹, is not universally true as regards the latter, because neither several whitenesses nor several heats can be at the same time in the same subject, although these are common accidents. Nor is what is said of several heatings true, for when two fires heat the same wood according to the same part, as they effect one heat, so also one heating, which is from each partially and from both together as from the total cause. Moreover, if that rule were generally true, it would follow that two sciences of the same species and in order to the same object, and similarly two temperances diverse only in number, could be at the same time in the same subject, which is not probable. Finally there stands in the way a general reason, because even in extraneous and accidental changes the extrinsic agent intends to assimilate the patient to itself; whence, if it finds it similar, it does not act on it again; otherwise, after it had once assimilated it to itself, it would act on it again and again, and so the action would proceed to infinity, at least as regards the multiplication of accidental forms. And by the same reason things altogether similar in the same accident would change each other mutually, and would multiply similar accidents in themselves. Indeed by the same or greater reason the same thing would act on itself, by producing in itself through one accident another similar one, or, if it already had two, it would effect a third, and so to infinity; all of which are plainly false and absurd. Whence it is gathered that also in these accidental changes the principle of them on the side of the subject is the privation of a similar form; and therefore a change of this kind does not tend to multiplying an accident of the same species in the same subject.

The fifth opinion

11. The fifth opinion distinguishes accidents which are made through proper motion or which are made without motion; and of the former it denies that they can be at the same time in the same subject, on account of the reason adduced, that motion comes about from contrary to contrary; but of the latter it affirms that accidents diverse only in number can be at the same time in the same subject. Fonseca reports this opinion, Book V, c. 10, q. 1, sect. 1, and it is wont to be attributed to Scotus, Gabriel, Durandus and others, In III, dist. 8; yet Durandus there, q. 3, says nothing of this, but rather in the solution ad 1, in absolute accidents, admits only that those which are of the same species can be in the same supposit according to one part and another; but in relative ones according to one foundation and another. But Gabriel there, a. 3, dub. 1, applies no distinction, but simply denies that it is repugnant that two accidents differing only in number be in the same subject. And Scotus speaks almost in the same way there, sole question. He indicates, however, that through the operation of a natural agent the multiplication of qualities of the same notion in the same subject does not come about; because the natural agent intends to perfect an imperfect pre-existing form; and therefore it does not induce an altogether other form, but some degree or as it were part which it unites to the pre-existing one in order to perfect it. In which he indicates that distinction of accidents which are made through motion or without it. Which Antonius Andreae also indicates, Metaphysics V, q. 8. For he says that relative accidents differing only in number can be in the same subject; but of absolute ones he subdistinguishes, for some are educed from the potency of the subject, and these are not multiplied in number in the same subject; but others are not educed, and these can be multiplied. And of this kind he thinks is light, about which the students of perspective contend that from two luminous bodies two lights are produced in the same part of the subject, because they make two shadows, and because, one luminous body being taken away, some light in the air is corrupted and some remains.

12. All accidents inhering in a subject are educed from its potency.—But these things are partly false, partly do not satisfy. And, to begin from this last, it is false that there are some accidents in a subject which, in the way in which they are made in it, are not educed from its potency,² because all depend on the subject in becoming and in being; and specially of light it is evident that it is educed from the potency of the subject; for it is not created, nor made only in the subject, but from the subject, the air, for example, concurring in the genus of material cause to its effecting. It is also false that lights are multiplied in number in the same subject; nor is there any experience by which this could be proved; for experience only teaches that, other things being equal, two luminous bodies act more in the same part than one only; but this is not on account of the multiplication of lights, but on account of the greater intension of the same light; from which it comes about that, one agent being taken away, or in that part to which the action of one reaches and not of the other, the effect appears less, not because one light is corrupted and the other remains, but because the same becomes and is preserved more remiss. And hence it is also that sometimes two shadows result, because a shadow is nothing other than the lack or diminution of light; and it often happens that, one body being interposed between two luminous bodies distant from each other, in one place it impedes the action of one, and in another distant place the action of the other, but in the intermediate place the action of neither is impeded; and thence it comes about that several shadows appear. And hence the first distinction about accidents which are made through motion or without it is easily refuted; for, if motion is taken rigorously for successive motion which comes about from a contrary, it is evident from the example of light that the latter part is false; for light is not made through motion, but through instantaneous change, nor is it made from a contrary positive term, but from a privative one, and yet it cannot be multiplied in the same subject. Likewise that distinction seems very per accidens; for what does it matter to this numerical distinction or identity of accidents that they are made through motion or through change? Because the distinction of accidents is not taken thence, but either from themselves or from the subject. But if the subject is in potency only to one heat which comes about successively, why will it not also be said to be in potency only to one light, although it comes about all at once? Or conversely, if it is in potency to several lights, why will it not be in potency to several heats? But if it is said that in those things which come about successively the agent does not intend to induce a new accident but to perfect the pre-existing one, the same will be said of light and of any other similar quality, which, as it comes about in an instant from the opposite privation, so also can be intensified in an instant from the privation of so much intension. Whence here too there has place the reason touched upon above from Scotus, that not only successive motion but every natural action of an agent is in order to render the patient similar to itself; and therefore it does not act on what is similar, but requires in the patient privation as the principle of its action; when, therefore, light is in the air as four, and a new luminous body is applied, it will not act on the air in so far as it is similar to itself in four degrees, but rather in so far as it is dissimilar in further degrees; the reason, therefore, of accidents which come about through change or through motion is the same.

13. But if motion in that distinction is not taken in that rigour, but as it comprehends change, so that the sense is that those accidents which come about per se through proper action are not multiplied in the subject according to number, but others are multiplied, then too the distinction can be attacked: first, because it is given through things which are very extrinsic and per accidens to the numerical distinction of accidents. Secondly, because neither part seems to be constant; for sensible species come about through proper action, and yet are multiplied in number in the same part of the medium; sound too seems to come about per se by proper action, and yet is multiplied in number in the same subject, as experience seems to prove; for we hear a harmony of several voices at the same time and through the same medium, which could not come about unless the sounds were diverse. But conversely figure does not come about per se primarily through motion, and yet cannot be multiplied in number in the same subject; and the same is true in all similar absolute ones, because they cannot be multiplied through the change of something extrinsic, as relative ones can; and therefore, as they do not come about per se, so neither can they be multiplied per se in the same subject; nor even concomitantly, since that form which comes about per se and upon which they follow is not multiplied in number in the same subject.

14. Relative accidents can be multiplied under the same species in the same subject, yet not all.—Moreover, the distinction of absolute and relative does not satisfy in every respect; for, if relatives are taken rigorously for relatives according to being and predicamental ones, it is indeed true that these can sometimes be multiplied in number in the same subject, as we shall say in treating of relations; but this is not universally true; for the relation of the creature cannot be multiplied in the same subject. But the other part, about absolute ones, is less universal, as is evident from the examples adduced of species and of sounds and similar things. Fonseca uses another distinction, in the place cited above, sect. 3, which in great part coincides with the aforesaid. And in sum he says that of accidents naturally acquired through motion, or through change conjoined to motion, there cannot be several of the same species in the same subject, and of these he explains in the fourth place the saying of Aristotle, which in this sense he understands to be universally and without exception true. But he adds subsequently that of accidents which are not intensified and remitted, whether they are acquired through motion or change conjoined to motion or in another way, it is necessary that there be very many of the same species in the same subject. Whence he seems to limit the former opinion to those accidents which are intensified and remitted; and so the former opinion is not altogether general, as he indicates in the fourth conclusion. But not even with that limitation does this opinion seem universally true, because intentional species can be intensified and remitted, and nevertheless are multiplied in the same subject; it is also probable that sound is remitted and intensified, which nevertheless he himself says is multiplied in the same subject. What he also adds in the same place, that in order to the absolute power of God there cannot be in the same subject several accidents distinct in number when they are such that by their nature they coalesce into one more intense in number, is difficult to believe, as I shall immediately declare more fully.

Resolution of the question as regards the mode in which several similar accidents can be at the same time in the same subject

15. In so great a variety of opinions, then, it is difficult to prescribe some certain rule in this matter and to assign its true reason. Two things, however, seem to me certain in this matter. One is that this universal negative proposition, that several accidents of the same species cannot be in the same subject, cannot be verified absolutely and simply, or without some limitation. Which the examples of intentional species and of relations prove to me most of all, supposing that they are something real distinct from the nature of the thing from absolute things. But the example adduced of sound is not so convincing, both because it is not certain that sound comes about per se primarily through that motion or action; and most of all because it is not sufficiently established that the several sounds which are heard are in the same part of the subject; for they always come about in the beginning in distinct places and there are properly perceived; but when they reach the hearing, or the part of the medium near the hearing, perhaps they no longer reach it according to real being but only according to intentional being. Other examples are wont to be adduced of the continuities and durations of two motions which can come about at the same time in the same thing; as, for example, the same wood can at the same time be heated and dried, which two motions, although they are diverse in species, nevertheless their continuities and durations seem to differ only in number. But these examples do not greatly compel, both because it is very probable that neither is duration an accident or mode distinct from the nature of the thing from the existence of the enduring thing, nor intrinsic or entitative continuity from the continuous thing itself; and also because, even if we admit such accidents, they are not in the mobile immediately, but by means of the motion which they affect; and therefore they are not properly in the same subject according to the same. Nevertheless the former examples suffice, to which can be added that the same power can have at the same time several acts distinct in number, although perhaps not altogether similar or supremely perfect, as if the will or appetite at the same time loves two men by diverse acts; or if the blessed (as many wish) at the same time love God necessarily and freely from charity.

16. Of which accidents it is to be judged that they can coexist in one subject, of which not.—Secondly, it is certain that it cannot naturally happen in every species of accidents that several which differ only in number be at the same time in the same subject. This is evident of all the properties which belong from within, such as are quantity, which belongs from within by reason of matter, the connatural powers or faculties which in each thing flow from the form, and in the same part of the subject are never multiplied within the same species, as is sufficiently evident by induction. Likewise of real and absolute qualities, either the first, by which matter is disposed, or the second, which result from these, as can also be proved by experience; for the instance which is wont to be adduced of the degrees of intension is not to the point; for these do not properly differ in number, of which elsewhere. The same, finally, is more probable of light and similar things. But what general rule is to be handed down, or what reason of the difference to be assigned, I find nothing which satisfies me in every respect. We can, however, explain it in this way. Some accidents so differ only in number that, besides the distinction of entities, in all the rest they have a certain likeness and agreement, namely in the function or offices to which they are destined, and in whatever relationship they express, such as are two heats, two whitenesses and the like. But there are others which, although they agree in the specific notion and under it differ only in number, nevertheless do not have so great a likeness among themselves, but differ either in function or in relationship. As, for example, two visible species of Peter differ in number in the former way. But two visible species of Peter and of Paul differ in number in this latter way; for they are not as similar among themselves as those two; for they have diverse transcendental relationships to objects and are ordered to diverse functions.

17. I say, then, thirdly, that accidents of the former kind cannot be multiplied in number in the same subject, but those which are of the latter kind can be multiplied. And each can be proved by induction and by the examples adduced. For altogether absolute accidents are never multiplied in number in the same subject for this reason, that they are similar in the former way; but respective accidents, whether by predicamental or transcendental respect, can be multiplied, because with specific unity they can have some dissimilitude, as it were material, on whose occasion they can be multiplied; whence it comes about that with respect to the same thing they can never be multiplied; and therefore the relation of the creature cannot be multiplied, because its term can only be one, and with respect to the same term relations cannot be multiplied. Therefore too, although we grant that the relations to father and mother are several and diverse only in number, nevertheless the relation to the father cannot be multiplied in the same son. But the reason of the difference between the two kinds of accidents can be assigned sufficiently probably from what has been said. First, from the final cause, because when accidents are altogether similar, their multiplication in the same subject would be superfluous and idle, which nature abhors; but when they are in some way diverse, or are ordered to diverse ends, as is evident in intentional species, or result from things ordered to diverse ends and thence participate diverse relationships, as happens in relations, then the numerical multiplication is not superfluous nor beyond an end consonant with nature.

18. Secondly, on the side of the agent, because, when accidents are altogether similar, no agent per se intends either their plurality or to induce another into a subject already having another altogether similar, because the agent only intends to render the patient similar to itself, which it sufficiently attains through only one form of this kind. But when the accidents are not similar in the aforesaid way, this reason ceases and the subject needs a greater assimilation; and therefore the agent also procures it. As, for example, although the medium, having received the species of Peter, is intentionally similar to him, it is not sufficiently similar to Paul, and therefore there remains in Paul the power of inducing a species by which he may render it similar to himself, and so of the others.

19. Whence, thirdly, a reason is given from the capacity of the subject; for just as prime matter, although it is indifferent to all substantial forms, nevertheless does not have the capacity to have all at the same time, nor several, because it is sufficiently actuated by one form, so also the subject of accidents, although per se primarily it is capable of some species of accident, and consequently is indifferent to any individual of it, is nevertheless not capable of receiving at the same time all or several individuals of such a species, in so far as in them the specific notion is found in the same way, because such a capacity is sufficiently actuated by one form of such a species; and this happens when the individual forms are altogether similar and of the same notion and relationship; but when the accidents are dissimilar and have various relationships, then one does not suffice to fill the capacity of the subject, and therefore it can happen that they are multiplied in the same subject until they altogether fill its capacity. As the intellective power, in so far as it is capable of natural science of God or of man, is sufficiently disposed in first act by one science in number of metaphysics or of philosophy, and therefore no longer remains capable of another similar science; yet the same intellective faculty, as it is capable of actual knowledge of men, is not fully actuated by one act by which it knows Peter or Paul, nor by one intelligible species; and therefore it is capable of several, until its faculty is sufficiently completed, because those several do not actuate it altogether in the same way, but in order to diverse things. Whence it finally comes about that, of the distinctions brought forward above, that one which distinguishes between absolute and respective comes nearest to the truth; for absolute ones are not multiplied, because they are always altogether similar; but respective ones, either according to being or according to expression, or by predicamental relation or transcendental relationship, can be multiplied when they regard diverse terms or are ordered to diverse functions, on account of the dissimilitude which they have in themselves, because none of them fully actuates the subject, as has been declared. And according to these things is to be explained the place of Aristotle in Metaphysics V. For it is not necessary that that indication of specific diversity be altogether universal of all accidents, but of those which in the individual are perfectly similar.

A formal answer to the question as it pertains to individuation

20. From these things is gathered the formal answer to the present question, on account of which all these things have been said, namely, that it does not come per se from individuation that some accidents diverse only in number cannot be at the same time in the same subject. For, although they were in it at the same time, they could very well be understood as distinct in number by reason of their entities, as those things are distinguished which can be at the same time, as has been said, or as those are distinguished which are successively in the same subject, as will be said immediately. But that some cannot be in it comes from the natural incapacity of the subject and the adequation which is found between its receptive potency and such an act, and consequently from the defect of a natural agent which could effect that multiplication.

21. Whence I further infer that by absolute power it is not repugnant that several accidents differing only in number, even if they are altogether similar, be placed at the same time in the same subject; because it is not repugnant from their individuation and distinction, and God can operate in the subject beyond its natural capacity; and if God willed to do this for the showing of his power, it would not be altogether superfluous. This, however, some limit to those accidents which are not intensified nor remitted; for of those which receive intension they think it impossible even by absolute power that several differing only in number be placed in the same subject without their composing one intense quality, if each of them inheres in the subject, because by this very fact they are necessarily united among themselves into one more intense; because two degrees of heat require no other union in order to compose one intense heat except that they be in the same subject. Whence, if one of them inheres in the subject and the other does not inhere but is sustained by the same subject in another way without inherence, then it will not be repugnant that they be at the same time, or rather be sustained at the same time by the same subject, because then they do not have among themselves the union necessary to compose one more intense quality; and in this opinion Giles is cited, In I, dist. 17, In II, dist. 1, q. 2, a. 1; but there he says nothing.

22. This opinion, however, seems to suppose false principles about the intension of qualities. The first, that intension comes about through the addition or aggregation of several degrees of the same quality altogether similar among themselves. The second, that those degrees have no union among themselves, either in some common and real positive term, or by another genus of union after the manner of act and potency, but are only united in the subject and in the same part of the subject, if it has parts. The third, that those degrees do not regard the subject in any order, but all equally immediately, so that there is no order among them of first, second and third degree, except perhaps in the order of generation and production; but if they come about at the same time, all are equally first. From which doctrine it excellently follows that God cannot multiply degrees of heat inhering in the same subject without their making one more intense; because such intension is nothing other than the aggregation of several similar degrees in the same subject; but without these principles I do not see on what foundation that limitation can rest, as I shall immediately show; indeed that opinion so explained does not properly limit that God can³ place any intensible qualities whatever diverse only in number in the same subject, but adds that, by the very fact that he places them, they will necessarily effect one more intense.

23. That doctrine of intension, however, involves some repugnance, which, since it is foreign to this place, cannot be professedly declared, but is nevertheless briefly indicated. For either those degrees of which an intense quality is said to be composed, for example eight degrees of heat, are indivisible in themselves, or each has its own breadth of intension and remission: the first cannot be said, first, because otherwise intension could not be a continuous motion; for each of those degrees would necessarily have to be acquired whole at once, otherwise it would not be indivisible; therefore the whole intension would have to come about through momentary and indivisible changes; therefore not by continuous succession, which is both against sense and experience and against reason, because as long as the natural agent overcomes the patient there is no reason why it should interrupt the action; otherwise it would not be in its power afterwards to repeat it, nor could a philosophical reason be given why it should effect it now rather than before or afterwards. Secondly, because otherwise the degrees of heat would in no way make one heat per se, but would be united merely per accidens in the same subject, as whiteness and sweetness; but this is not enough for them to effect one individual of heat, any more than if God placed two intellects in the same soul. Indeed, if this sufficed for intension, no reason could be given why, if God placed two intellects in the same soul, they would not effect one more intense; for if you say that intellects are not qualities which are apt to coalesce into one more intense, against this is the fact that according to that opinion, in order that qualities can coalesce into one more intense, nothing else is required except that, since they are altogether of the same notion, they can be united in the same subject; but intellects will have this at least in order to the divine power. Thirdly, many absurdities follow from that opinion, namely that a remiss quality could intensify another equal or even more intense one by effecting as many degrees as it has in itself; or, if likeness stands in the way, it follows that a more intense quality cannot intensify a more remiss one, because they are altogether similar in form. It follows also that no natural reason can be given why, when a form is remitted, one degree rather than another is cast off, and other similar things which it would be long to pursue. It must necessarily be said, then, that in those degrees of intension of heat, for example, which we divide in the mind, there is a breadth according to which there can be continuous intension or remission in them, which breadth must necessarily be divisible to infinity; otherwise by reason of them continuous alteration could not come about, because continuous motion must necessarily be divisible to infinity; whence consequently it is also necessary that these degrees be joined among themselves by some common term, because otherwise neither continuity nor true real union can be conceived between them, without which that breadth cannot be understood; because if two degrees are not united among themselves in this way, then neither in one degree will its two parts or halves (so to speak) be united among themselves; because the whole quality is composed of several degrees just as each degree is composed of two or three equal parts; but these cannot be understood without the said union, any more than a continuum divided into its every part can be understood.

24. From these contrary principles about intension, however, it plainly follows that God can place in the same subject several intensible qualities differing only in number which do not effect one more intense, as, for example, two heats as eight, because he can place them inhering in the subject and not having among themselves any union per se, but only per accidens by reason of the subject, which is not enough for intension. Nor can any new implication of contradiction be brought forward in this; and so the doctors more frequently think, In I Sent., dist. 17, where Gregory, q. 5; Ockham, q. 7; Giles, Quodlibet IV, q. 1, where he adduces a not contemptible conjecture: because God can intimately place two quantities differing only in number in the same site, their distinction being preserved and without any real union between them by reason of which they would effect one greater quantity; why, then, could he not place two whitenesses in the same subject, their distinction being preserved and without a union by reason of which they would compose one more intense?