Disputationes metaphysicae

1. In any composition whatever something is as matter and something as form.—Since the distinction of form into physical and metaphysical is very common, and all the things which we have hitherto said apply to physical form, it seems to be a metaphysical business to say something also of metaphysical form, which, the things which we have said being supposed, can be briefly dispatched, because this is called form only through analogy and as it were a certain metaphor. It is to be noticed, then, from what was said above, that besides physical composition from matter and form there is another which imitates it, yet of itself abstracts from true matter, and therefore is named metaphysical. But this is twofold, as regards the present point: one from nature and supposit, the other from genus and difference; I omit that which is from being and essence, because it is more obscure and, as regards the present point, no special notion of form intervenes in it, as will be evident from what is to be said. Next it is to be considered that in every composition, in order that one be understood to arise from many, something is always considered as matter and something as form, both because composition from matter and form is the first real composition and most of all proper and per se, and therefore through a certain analogy to it every other composition is declared; and also because matter is something formless and imperfect and a certain inchoation and as it were foundation of nature; but form is as it were the beauty and perfection and consummation of nature; but in every composition there is something as it were potential, which is the foundation and inchoation of the thing, and something which is the term or consummation of the thing, and therefore something is always considered as matter and something as form. Which is so true that even in composition from integrating parts, which seems most of all material, one part is always considered as matter and another as form, which will appear more clearly in heterogeneous things, as in man the head is as it were the form of the other parts; and in artificial things the roof, for example, is as it were the form of the building; according to which analogy the theologians also distinguish the matters and forms of the sacraments. And in homogeneous things, where that diverse relationship cannot be distinguished between the parts on account of their likeness and uniformity, all the parts are said to be the matter of the whole, but the composite is compared as form to the individual parts. In all which no special causality intervenes, but union alone with analogy and proportion to matter and form.

2. From these, then, it is understood that metaphysical form in general is called that which in metaphysical composition essentially constitutes the thing itself, or completes or actuates the essence of the thing; nor can this form so taken in common be described otherwise. But there is a difference between the two metaphysical compositions said above, that the former, namely from nature and supposit, is a composition of the thing (we are speaking of creatures), that is, of those things which in the thing itself are in some way actually distinguished, as are nature and subsistence, of which we shall treat diffusely below; but the latter is a composition of reason, because its extremes are not actually distinguished in the thing but by reason only, as was seen above. There is also another difference, that in the former composition one extreme is the whole essence of the thing, but the other does not pertain intrinsically to the essence, but is a term or mode of the essence; but in the other composition each extreme is essential and neither expresses the whole essence of the thing explicitly or actually, although it can confusedly include it whole. Whence it comes about that the former is also wont to be called total form, real and most properly metaphysical; but the latter is rather form according to reason, and therefore can be called not only metaphysical but also logical.

The essence of metaphysical form is shown

3. Metaphysical form is the whole essence of the thing.—It must be said, then, first, that properly metaphysical form, which is the form of the whole, is nothing other than the whole essence of the substantial thing, which we also call the integral nature of the thing, which is not called form because it specially exercises the proper causality of form, but because it essentially constitutes the thing through itself. I declare and prove the individual parts; for in man, for example, this form of the whole is said to be humanity, which, since it consists of the matter and form of man, expresses the whole essence of man; for that which man adds to humanity is not of the essence of man, as we shall say below treating of subsistence, and in the mystery of the Incarnation is briefly evident; for in Christ there is the whole essence of man, although there is not created human subsistence. Moreover, this form of the whole is found not only in material things but also in spiritual ones; indeed not only in created things but also in God himself it is considered by us; for we conceive the Deity as the form essentially constituting God and any divine supposit whatever, in so far as he is this God; although it is proper that in the thing itself it is not distinguished from that of whose essence it is; in which it falls short of that notion of form which essence has in created things, because that does not pertain to perfection simply, but includes imperfection; therefore this form in immaterial things can be nothing other than their essence. But in material things this form of the whole differs from the physical and partial form, as is evident from the common use of these words, and from the very distinction of physical form from metaphysical; but it does not differ except because the form of the whole expresses the whole nature composed of matter and form, but the physical form only expresses the formal part; therefore this metaphysical form also in these things expresses their whole essence. Because, as we shall show below in the disputation on material substance, matter too is of the essence of this substance, and so the nature composed of matter and form is its whole essence; and so the first part of the conclusion is evident.

4. Metaphysical form is marked by the name of nature.—But that this metaphysical form is wont to be most properly called by the name of nature is evident, first, from usage; for so we attribute also to God the divine nature, to the intelligences the angelic, to men the human, and so of the other things. Next, in this way we distinguish nature from supposit, either from the nature of the thing, as in created substances, or by reason only, as in the divine; and in this way we say that in God the nature does not generate, but the supposit, and that the divine Word assumed a nature, not a human person. Likewise, each thing through its nature has that it is such and that it is essentially distinguished from others; therefore the nature of a substantial thing adequately (so to speak) is the total form itself by which it is essentially such. Finally nature, as is commonly thought, expresses order to operation, in which alone it differs from essence, that the name of essence was taken from order to being, but the name of nature was taken from order to operation; for nature was so called as it were making something be born; whence nature is said not to be idle, and to be the artificer of things, and to make nothing in vain, etc. Whence the theologians too say that faculties and operations are multiplied when natures are multiplied. But the first and adequate principal principle of operations in each thing is its essence; which in immaterial things is manifest; but in material things the form seems to be the principle of operating, which is the formal and active principle; yet, because matter too in its genus concurs in some way, especially to natural and intrinsic motions or acts, therefore I said that the adequate first and radical principle is the essence of each thing; therefore the essence itself and the form of the whole is the same as the nature of each thing.

5. The etymology of the name “nature” and its various significates.—I know that Aristotle, Metaphysics V, c. 4, assigns various significations of this name nature and among them places in the last place that by which it signifies the substance or essence of the thing, which he says is a transference from another signification by which nature signifies the form which is the term of generation. And in Physics II, c. 1, he restricts the notion of nature to the first intrinsic principle of motion only, and thence natural being is wont to be said of material substances only. I judge, however, that these are to be understood of this word nature as regards its imposition, but not as regards the thing signified; for these are wont to be very distinct in these analogous names, as St. Thomas rightly noted, I, q. 13, a. 6. As regards the imposition of the word, then, it is likely that this word first signified other things which Aristotle numbers there, as, for example, natural generation and especially the rise or birth of living things; for nature is so called as it were nascitura, and thence the word could be derived to signifying the intrinsic principles of the thing generated, namely matter and form. Or, as St. Thomas says, I, q. 29, a. 1, ad 4, because the birth of living things is from an intrinsic principle, therefore this word was derived to signifying the first intrinsic principle of motion, which is matter and form. And because through the form the essence of the thing is completed, finally that word was derived to signifying the essence of the thing. And because the ancient philosophers who disputed of nature did not know other substances except material ones, therefore they attributed nature to them alone and thence they peculiarly obtained the name of natural beings.

6. But if we regard the thing signified and speak of this word metaphysically rather than physically, this word absolutely and principally signifies the essence simply and integral of each thing, as it is signified after the manner of total form. And in immaterial things it is simple; but in material things it is composed of matter and form, because neither matter nor form is the integral nature of the thing, but partial; but the integral nature of the thing is composed of both; and therefore it is deservedly called metaphysically the total form. But accidents, as they do not have essence simply, so neither nature except with an addition, namely accidental nature, and more properly they are said to be according to nature, or against or beyond nature. Wherefore in accidents, as will be seen below, this notion of total form of which we are now treating does not properly have place (I speak according to the thing, whatever may be the case with our possible mode of conceiving); and the reason is that an accident is a form as it were partial and physical, whence in itself it is an incomplete nature and so imperfect that it does not make one per se but per accidens with its subject; and thence it comes about that from both one integral nature and form of the whole does not result, as from matter and substantial form.

7. Whether metaphysical form exercises any causality.—The last part of the conclusion finally can easily be proved from all that has been said, for first of all, since this form of the whole in material things includes prime matter itself, it cannot exercise proper formal causality, which consists in actuating some subject. Likewise in immaterial things, since the whole essence is simple and abstracting from every receptive thing, it cannot be called form on account of proper formal causality. And, if it is permitted to argue from theology, the humanity of Christ is the metaphysical form of this man Christ and yet is not a true form of the divine Word, having true causality into him, by reason of which it would be said formally to constitute this man. And the argument can be extended to any nature whatever with respect to its proper supposit; for the nature is compared either to the subsistence itself or to the composite of nature and subsistence. With respect to subsistence the nature does not have formal causality, but rather as it were material (I omit active, of which afterwards), because proper subsistence is not compared to the nature as its subject, but as its term. Whence rather subsistence is in some way the act of the nature than conversely. Likewise, because subsistence is a mode of the nature, whence it affects and in some way actuates it; according to this comparison, then, the nature does not exercise the causality of form. Whence in the said example of the mystery of the Incarnation the theologians say that the humanity is not only not compared to the Word as its form, but rather that the Word is related as form in so far as it in some way perfects and actuates the humanity, although no proper and true causality intervenes there.

8. And hence it further comes about that also with respect to the whole composite or supposit the integral nature is not called total form on account of the true and proper causality of form; because this causality is never with respect to the composite unless it is first and immediately exercised about some subject from which and the form the composite results. If, then, the total nature does not exercise formal causality about the other extreme of this composition, neither can it exercise it about the whole composite. It remains, therefore, that the integral nature is called form only because it is the whole quiddity, notion or essence intrinsically constituting the supposit in such genus or species. Which constitution is not through a causality in some way distinct from the nature itself, but is through the intrinsic actuality and entity of the total nature itself. And on account of this too this form is called metaphysical and not physical.

9. Whence too it is understood in passing that no proper matter corresponds to this form, because, as has been said, it is not called form because it informs some subject; but, if we speak generally, only the supposit corresponds to this nature as essentially constituted through it. But in material things the integral nature can be compared, as total form, to the partial natures of which it is composed; for, although one of them is form, nevertheless, in so far as both matter and form are a certain incomplete part and of itself imperfect, it can be compared as matter to the whole composite nature, and this as something whole and complete is compared to the parts as form; for the whole is related as form with respect to the parts, on the testimony of Aristotle, Physics II, text 31, although there he speaks chiefly of the integral whole with respect to its parts.

10. Metaphysical forms are single in individual composites.—Finally it is understood from what has been said that this form can only be one with respect to the same thing; it is evident, because it expresses the whole nature of the thing; but this in one thing can only be one. Nor does it matter that according to reason the specific and generic form of the whole can be distinguished in the same thing, as humanity, animality, etc.; for, if these are taken with respect to the same thing, they are not several forms in the thing, but one and the same diversely conceived; and in so far as it is conceived as several according to reason, it is not taken with respect to one but to several, even according to reason; for animality is not the total form of man, but of animal as such; and so, proportion being kept, the form of the whole is only one with respect to the same thing.

11. A doubt is met.—One can only doubt about the conclusion posited; for the total form, if it is the form of the supposit, does not only include the essential principles, but also the individuating principles, which are not of the essence of the thing, because the total form and integral nature of Peter is not only humanity, but this humanity; therefore it is false that this form only includes the whole essence of the thing. Next it follows that existence is not included in this form, because this too is not of the essence. But the consequent appears false; for, if it does not include existence, how does it really constitute? To these it must be said that this form is to be taken with proportion with respect to that which is constituted through it, and so it always expresses the integral and only nature and essence of it. For, if it is compared to the common species precisely taken, it includes only the specific essential principles, and humanity expresses the total form of man. But if it is compared to a determinate individual, so it includes the individual and particular essential principles, which, although they are not of the essence of the thing absolutely speaking, because in this word a certain prescission of the mind is included, are nevertheless of the essence of the individual as it is individual, as was declared above in treating of the principle of individuation. One must speak similarly of existence; for, although this is not absolutely of the essence of the created or creatable thing, it is nevertheless of its essence as existing or as constituted in the notion of actual entity; and therefore, although this form includes only the essence of the thing, nevertheless, in order that it constitute it actually, it includes existence, not only as a necessary extrinsic or concomitant condition, but also as intrinsically constituting the actual entity of the nature itself, through which it formally constitutes such a substance or substantial individual.

What logical form is

12. I say, secondly: metaphysical form according to reason (which is also called logical) is chiefly wont to be said of the essential difference; yet according to some respect it is attributed also to the genus, and also to the definition; whence this form does not have proper real causality, but of reason only, and a proportional matter corresponds to it. This whole assertion is most clear and is evident from the common use of speaking, the things being supposed which were said above of the thing itself in treating of universals, where we declared how genus and difference are compared among themselves and whence they are taken. Where among other things we said with Aristotle, Metaphysics VII, texts 42 and 43, that from genus and difference there arises one per se, because they are proximately compared among themselves as potency and act of the same genus and per se ordered among themselves, where St. Thomas, lect. 12, part. 5, declares that genus and difference are not compared as potency and act distinct in the thing, but because they express the same essence as determinable or after the manner of its determination. From which it is understood that the difference imitates form in the notion of actuating, terminating and distinguishing, and therefore that it is that to which this notion of metaphysical form belongs first; but the genus in comparison with it has the notion of matter, because it is something potential, actuable and indifferent to many, until through the difference it is understood to be contracted and determined; whence too it comes about that the difference of itself is more perfect than the genus, because that which within the same genus is related as act is more perfect than that which is related as potency. Whence too in the place cited above we said that the difference is taken from a nobler principle; in this, then, there is also proportion between form and difference, that, as form is more perfect than matter, so difference than genus. Again, as matter and form are really distinguished, so that neither one is the other nor intrinsically includes the other, so also genus and difference are separated by concepts, according to which they are so distinguished that neither in the concept of the genus is the difference actually included, nor in the concept of the difference the genus; otherwise it would not be a proper metaphysical composition, nor would they be compared as proper act and potency, because it is of the notion of these that they do not include each other; and this Aristotle taught, Metaphysics VII, above, Book III, text 10, and Topics VI, c. 3.

13. From which too it comes about that, as it does not belong to matter per se and necessarily that it be under this or that determinate form, so the genus per se and necessarily does not require determinately any one of the differences, although it necessarily requires some in confusion, as matter requires form. But in this is to be noticed a difference between matter and form on the one side, and genus and difference on the other, that, although matter naturally cannot be without some form, absolutely nevertheless it does not imply a contradiction that it be so preserved, and similarly form sometimes can not depend on matter even naturally, and that which so depends can nevertheless supernaturally be preserved without matter; but genus and difference are so per se conjoined that it is altogether repugnant either that the genus subsist without all differences, or the difference outside the genus which it actuates. And the reason is clear, because genus and difference are not distinguished in the thing, but express the same essence as determinable and determining, and therefore it is not wonderful that they cannot be separated in the thing in the said way. Likewise, because in the thing there cannot be anything which does not have a determinate essence and consequently constituted in some proper and ultimate species, in which it is necessary that both the common or generic and the proper predicates be included; these, therefore, cannot so precisely and abstractly subsist as they are conceived.

14. How genus and difference are understood to be united.—From which another difference is further understood, namely that between genus and difference there does not intervene a mediating union distinct from them, even according to the true reason of conceiving, as between matter and form we were saying above that there intervenes a mode of union distinct in the thing from them, because actual union between them is not of their intrinsic notion, indeed is separable from them, and therefore it is necessary that it mediate between them and be distinguished from them. But genus and difference are so per se united (or rather are one in the thing, although they are distinguished by reason) that they are altogether inseparable according to the thing and in a certain way according to reason; for, although by a prescissive concept the difference can be understood without the genus, nevertheless it cannot be conceived negatively as existing without the genus, or not actuating the genus. And therefore, just as in real modes, which are only modally distinguished from the things which they modify, we say that they are not united to those things through a distinct union but through themselves, so with much greater reason the difference is to be conceived as an essential mode of the species and through itself contracting and actuating the genus without another intermediate union.

15. The difference does not cause really.—Finally from these it is understood that the difference, in so far as it is called form, does not have proper real causality, because real causality is only between those things which are distinguished in the thing itself, or at least it is necessary that there intervene some real influx and causality distinct from the nature of the thing from the cause itself or the effect; but here none of these intervenes, because neither is the difference distinct in the thing from the species, nor from the genus as it is contracted through it. Nor yet does there intervene there some causality distinct from the difference itself. This, then, is only a certain constitution according to reason and our mode of conceiving, which only through analogy and proportion to the real cause is called form or formal causality. And the same is to be understood of the genus, in so far as the notion or causality of matter is attributed to it. Nor does it matter that the thing constituted of these is often a true and real essence, as man or horse; for, although such essence in itself is real, nevertheless as so composed it is not a being of the thing but of reason, since the composition itself is only of reason.

16. How the genus is predicated of the whole species.—But someone will object: for, if the difference is compared to the genus as form, and the genus to the difference as matter, then each is compared to the species or the thing defined as part to whole; therefore neither will be able absolutely and in recto to be predicated of the species, because the part, although it can be predicated obliquely or denominatively of the whole, cannot nevertheless absolutely and in recto; for we do not say: man is matter, but has matter, or is material; these expressions, therefore, will be false: man is animal, and similar ones. This objection has only been proposed in order to declare the other part of the conclusion, by which we were saying that both the genus with respect to the species and the definition with respect to the thing defined are wont to be called metaphysical form. The common distinction, then, is that the genus (and the same holds proportionally of the difference) can be considered in two ways: either precisely, as it expresses such a grade and as it were stops in it of itself; and in this sense it is a part, and as such also is not predicated of the whole, because it would give this sense, that man, for example, is animal precisely and solitarily and abstractly taken, or is not more than animal, which sense is plainly false. And the genus under this consideration is compared as matter to the difference, and conversely the difference as form to the genus. And so the things which have hitherto been said proceed. And in the same sense to the objection the whole which is inferred in it is conceded, namely that genus and difference are parts, and as such are not predicated; nor are they only parts, but are also called elements by Aristotle,¹ especially the differences and the highest genera, on account of their simplicity, and because in them the ultimate resolution in metaphysics comes about, as is evident from Posterior Analytics II, c. 14. But in another way the genus is considered as a whole, which they call potential or confused, because it confusedly expresses the whole quiddity of the species, and in this way it is excellently predicated of the species or the thing defined, because it is no longer predicated as a part, but as a whole; and this is the common sense of this expression; for when it is said man is animal, nothing is excluded from man, but it is affirmed that the same supposit which is man is also animal; or that man, by the same form and essence by which he is man, is also animal; but each of these is true. The genus, then, in so far as it can be predicated of the species, as something superior to it and as it were containing it, is said in some way to have the notion of form with respect to it; and conversely the inferiors, in so far as they are subjected to the superiors and in a certain way sustain them in themselves, have a certain notion of matter. And by a similar or greater reason the species is compared as form to the individuals, but these as matter.

17. And in this sense I understand Aristotle, Metaphysics V, c. 2, when he reduces each part of the definition to the formal cause; for, as regards the genus, I think it is to be understood not formally as it is a part, but as it is a certain whole, as I have explained. But the whole definition, because it declares the whole essence and is the proper notion of the thing defined itself and is most properly predicated of it, can therefore also be called metaphysical form, although it is not composite. And so it is easy to explain all similar expressions, which only consist in a certain analogy and transference.

18. The difference between metaphysical and physical form.—There only remains a brief doubt to be dispatched, which arises from a difference to be noted between this metaphysical form and the physical, that the substantial physical form is not multiplied in the same composite, as we said above; but this form can be multiplied; for both the genera of the same thing can be several, and the differences similarly; indeed even the definition, although it seems to contain and explain the whole essence of the thing, can nevertheless be manifold, as is evident from Posterior Analytics I, c. 7, and Book II, cc. 8 and 12, and De Anima II, c. 7. But the reason of the difference is easy, because physical forms really distinct are so compared that each constitutes a perfect and consummated species of substance, and their composition would have to be real and physical, and therefore they are repugnant in the same substance properly and per se one. But this metaphysical form, namely the difference, neither makes a real composition nor is distinguished from another difference except through the prescission and abstraction of the mind; but our mind can prescind and abstract the same thing in various ways, and therefore can conceive in the same thing several predicates of genus and difference; wherefore the multitude of essential differences does not stand in the way of the unity and composition per se from genus and difference.

Whether there is a process to infinity in essential predicates

19. But from this difference a difficulty at once arises; for it follows that there can be given a process to infinity in these metaphysical formal and material causes, that is, in quidditative predicates. But the consequent is against Aristotle, Metaphysics II, c. 1, where he thought it better known that there cannot be given a process to infinity in the parts of the definition, which are genus and difference, than in the forms themselves; and therefore from the negation of infinite predicates he proves the negation of infinite forms. But the sequel is proved, because it is no more repugnant that there be given two differences in one thing than three or four, and so of any number whatever; therefore in this number one can proceed to infinity. Especially because this number of predicates does not arise from things or distinct modes which are on the side of the thing in one and the same substance, but from our concepts with some foundation in the thing; but we can prescind and abstract in infinite ways, and in things there is a foundation for this to be done by us on account of the various agreements and dissimilitudes which one thing has with others, in which agreements these abstractions are founded. And the difficulty urges most of all if one species is compared not only to the other species made, but to all possible ones, which can be multiplied to infinity and in infinite ways.

20. Some reasons which are wont to be adduced for the conclusion are shown inefficacious.—Nevertheless it must be said absolutely with Aristotle that also in these formal causes there is not given a process to infinity. So teach all the interpreters, who adduce various reasons. The first is that otherwise the thing constituted would be infinitely perfect, because any predicate whatever adds some perfection. But perhaps the consequence will be denied, because one finite perfection can be the foundation of infinite concepts, which, although they express perfections distinct by reason, do not increase perfection in the thing. The second reason is that, if these differences are infinite, the properties too which follow upon them will be infinite. But it will be answered that from the generic and specific difference properties distinct in the thing do not always follow, as is evident in these predicates: substance, spiritual, of Gabriel, etc.; but it is enough that the properties too correspond proportionately according to universal or special notions, as was also touched upon above.

21. The true reason of the conclusion.—The third and most probable reason is that it is necessary that there be given a supreme genus which is as it were the prime matter of this composition and a specific and lowest difference which is as it were the ultimate form; therefore the intermediate forms too are necessarily in a finite and determinate number. The major is proved by Aristotle because in these quidditative predicates one is always prior to another, that is, more universal and extending to more; but it is not prior except because it approaches more to that which is first; therefore it is necessary that there be given also some supreme genus. Next this is evident by experience, running through all the predicaments, and especially in substance, which, as it immediately signifies complete substance, is the supreme genus; for nothing more universal with respect to substances can be thought; but I suppose that being is not a genus, although, even if it were a genus, nothing would stand in the way, for it would be the supreme; and so we have what we intend. And so too nothing will stand in the way if anyone contends that this resolution must be made as far as transcendental predicates, because, although this were true, one would stop at some last. And the reason is that in all things or substances there is given some first or least essential agreement according to which can be abstracted either a transcendental predicate or a supreme genus. But the minor is proved from the very constitution of the ultimate species, because there cannot be any thing which is not constituted in some ultimate species; otherwise it would not have a determinate essence, nor one diverse from the other determinate species; but the ultimate species must be constituted through some ultimate difference. Nor do I now dispute whether this ultimate difference is simple or coalescing from many, of which each is common, as Porphyry seems to have signified, in the chapter on Difference; and Aristotle not a little favours it, Topics I, c. 3, and Book VI, cc. 3 and 4, and Posterior Analytics II, c. 14; for this matters nothing at present, because one must necessarily stop at differences which are not actuated by others, although perhaps two or three of these agree to constitute the ultimate species; for now the reason made only proceeds of subordinated differences. But the first consequence seems self-evident, because between the extremes first and last there cannot be given infinite intermediates, as we said above of forms; for the reason made there proceeds equally here.

22. Objections against the aforesaid reason.—But this reason can be weakened in two ways: first by saying that, although predicates per se subordinated in one line after the manner of act and potency are finite, nevertheless those not subordinated or in diverse lines can be multiplied to infinity, as if someone said that there are given several supreme genera; or that to the constitution of the ultimate species several differences agree not subordinated among themselves, and these can be multiplied to infinity; or that one and the same genus, whether proximate or remote, can at the same time be contracted by several differences which are not altogether repugnant among themselves nor subordinated among themselves; as, for example, animal according to the ancient philosophers is contracted through rational and through mortal, which agree in man, in others are separated; and substance could be immediately divided through living and through corporeal, which agree in some substances, in others are separated. From which too it seems to follow that between the differences themselves there is a certain circle, and they are compared in turn and mutually as potency and act; for, if substance is immediately divided into living and not living, again living substance could be divided into incorporeal and corporeal; but, if conversely substance is divided into corporeal and incorporeal, corporeal will be divided into living and not living. But if this is not inconvenient, because they are reflections of the intellect, for the same cause that multiplication of predicates to infinity will not be absurd. The other evasion can be that, although there is given a supreme genus and a lowest difference, it is not repugnant that between them several intermediate predicates can be prescinded or distinguished by the intellect to infinity, as between the extreme points of a line there are given infinite parts or points; for, as these are infinite in potency, so those predicates, as they are in the thing, can be called several only in potency, because in the thing they are not actually many unless they are distinguished by the intellect; and therefore, although the intellect can distinguish more and more to infinity, it does not follow that in the thing they are infinite except in potency. From which too it comes about that those predicates which we actually distinguish are always finite, both because we cannot form except finite concepts of things, and also because all the agreements and differences of any species whatever to the others which have been made are in a certain and determinate number, even if with respect to possible things they can perhaps be multiplied to infinity. And so one could interpret Aristotle of the differences or essential predicates which in fact are abstracted or can be abstracted through human discourse or knowledge.

23. They are solved.—A saying of Aristotle is explained.—But nevertheless I judge the reason made to be efficacious and that it simply cannot come about that the predicates be multiplied to infinity. And first of all I take it that with respect to any thing whatever there is given only one supreme genus or predicate and one ultimate difference. And the former part indeed has been sufficiently proved both by reason and by usage or experience; but of the latter it has been doubted by some, yet to me it seems equally certain. First indeed, because the difference is taken from the form; but every form diverse in species from another has some essential grade proper to itself and not common to others; therefore from that there can be taken a difference altogether proper and common to no other. Secondly, because the ultimate species cannot be constituted by the conjunction alone of two common differences, because each of those differences constitutes a subaltern and generic species; but the ultimate species is not an aggregate of two subaltern species, otherwise neither would it be one proper and special essence, nor would it be one metaphysical composite constituted of proper act and proper potency. As, for example, in that example of man, if rational and mortal were taken as subaltern and common differences, man would never be constituted from their aggregation; but rational is to be taken as it is proper to man, that is, as it includes discourse or aptitude for it; and in this way rational will be the simple difference proper to man, but mortal is of itself a subaltern and common difference, not indeed to other users of reason, for there is no rational or intellectual mortal besides man, but to other sentient or living things. So, then, it happens in all species of things. And this is what Aristotle said, Metaphysics VII, text 43, that one must proceed in the division of common differences until one arrives at the indifferent ones, that is, at the ultimate and altogether proper differences, as St. Thomas and all expound; and then (says Aristotle) there will be as many species as differences. For each individual difference (adds St. Thomas) will constitute one most special species.

24. The intermediate differences are enclosed in a finite number.—But, this principle being posited, that the intermediate differences can only be in a finite number is declared in this way. And first, if the differential grades were distinct in the thing itself, it is evident that they could only be finite, because they would be actually several; therefore finite or infinite, but in a finite thing there cannot be infinite grades of distinct perfections; they will therefore be finite. All the more because those grades are not understood to be communicating among themselves, as proportional parts, but altogether co-distinct and indivisible; nor yet are they so compared to the thing as points to the line, which are so indivisible that they do not increase the quantity of the line; but each difference adds a certain grade and as it were a determinate part of perfection, from the conjunction of which parts arises the integral perfection of the species, which, since it is finite, can only arise from finite as it were parts. Whence, just as in the intensive breadth of a finite quality only finite degrees not communicating among themselves can be distinguished, from the conjunction of which arises the whole finite intension of the quality, in the same way one must philosophize proportionately in the differential grades. But although these grades according to the truer opinion are not actually distinguished in the thing, nevertheless the discourse made has the same force in order to the distinction and conception of our mind, because even as distinct by reason they are conceived as not communicating among themselves, if the grades themselves are taken precisely and formally, as they must be taken. For one subaltern difference does not include another, because neither is the inferior of the concept of the superior nor conversely; the intermediate differential grades, therefore, are altogether co-distinct and not communicating among themselves; therefore on this side their distinction, even if it is according to reason, cannot proceed to infinity nor can it be compared with the division of the parts of the continuum. But from elsewhere any of those grades whatever is indivisible according to concept; for any difference whatever, whether generic or specific, is indivisible, and is so indivisible that it increases essentially the perfection of the thing in order to the concept of the mind; therefore also in order to the concept of the mind a finite essence cannot be divided or constituted through such differences except finite in number, which, since they are indivisible, one cannot proceed to infinity in their division.

25. And so the consequence made in the third reason remains efficacious; and the objection insinuated in the second evasion ceases, because in a finite thing there cannot be contained, even in potency, infinite things not communicating among themselves and increasing the perfection or quantity of the thing. Wherefore, if once all the differences are conceived and distinguished by reason which can be founded in the essence of the thing, their number cannot be increased, either with respect to existing or to possible things; for through them it agrees or differs with all, both those which are and those which can be.

26. And thence too the former objection is easily excluded, for in whatever way differences are multiplied, and whether they are subordinated among themselves or not, they can only be in a finite number on account of the said cause; namely because a finite perfection cannot even by the mind be divided into several as it were parts not communicating among themselves except only in a finite number. But it is more probable that all the differences which agree to the constitution of one essence are in some way subordinated among themselves as potency and act; otherwise they could not constitute one per se. Nor yet is it likely that in this a circle is committed, since the relationships of act and potency are so opposed among themselves.

27. Wherefore, although the same genus is divided by us in various ways, it is nevertheless not always divided through the proper and immediate differences by which it is proximately contracted and actuated; and therefore it can sometimes happen that two differences are compared among themselves as act and potency. As in the example posited, although substance can be divided through corporeal and incorporeal, living and not living, the former division is always immediate and proximate; a sign of which is that it is taken as it were from the intrinsic principles and absolute entity of the thing, but the latter is taken in order to operation; and therefore the difference of the living, as it is in corporeal things, is always compared as act and not as potency to the corporeal grade. And although that difference is found also in incorporeal things, it is nevertheless found in a far diverse way, because incorporeal substance is (so to speak) totally living, that is, lives by reason of its whole substance, but corporeal by reason of a part; in which special way it seems to be taken when it is posited as a difference of body. And although we grant that there can be given a common difference of the living abstracting from those two modes, thence at most it comes about that some genera not placed subalternately have a common difference, which perhaps is not inconvenient; for so Aristotle thought, Topics VI, of which elsewhere.

28. Another reason of Aristotle for the conclusion.—So, then, the third reason remains sufficiently declared and confirmed; and the first too receives strength from the aforesaid discourse. But the second, if it is understood not of properties in rigour, as they express faculties of operating or some other thing distinct from substance, but of any mode of being or operating whatever, can be defended, because these genera and differences are most of all distinguished by us through order to some property of this kind. Finally Aristotle adds another reason, namely that, if in these differences there were a process to infinity, the thing could never be sufficiently distinctly known or defined by us, because knowledge or altogether distinct definition begins from the supreme genus and through the addition of all the differences arrives at the last; which could not come about if those were infinite. Which has place most of all in human knowledge, which proceeds little by little from one to another, in which way it is impossible to traverse infinity successively by numbering, as is evident from Physics III, c. 7, and is sufficiently self-evident.