Disputationes metaphysicae

1. The first opinion.—The first opinion is that one adds over being a certain positive accident, distinct from the nature of the thing from being, yet per se consequent upon and concomitant with every being. So Avicenna thought, Metaphysics III, c. 2, and Book VII, c. 1; for in the former place he calls one an accident and something accompanying the essence, but in the latter place he says that it is not absolutely the same as being. And Scotus seems to have followed this opinion, Metaphysics IV, q. 2, and In II, dist. 3, q. 2; Antonius Andreae, Metaphysics IV, q. 3, who teaches that one adds over being something positive distinct from being from the nature of the thing. But this opinion, as regards the distinction from the nature of the thing between being and that which one adds over being, has been sufficiently rejected in the preceding disputation, and it is plainly repugnant to Aristotle, Metaphysics IV, cc. 2 and 5, and will be further refuted from what follows.

The opinion is proposed that the notion of one is positive

2. Whence the second opinion can be that one adds over being a certain positive property, distinct from being not really, or from the nature of the thing, but by reason alone, in the way in which wisdom or justice is said to add something to God and to be a positive attribute of his, distinct from him by reason alone. St. Bonaventure seems to hold this opinion, In I, dist. 23, a. 1, q. 1, where he says that one in God expresses something positive, but in the creature sometimes something privative, sometimes positive. Whence he says that, although the mode of signifying or explaining unity is after the manner of a negation, because simple things are not conceived and explained by us except through negation, nevertheless as regards the thing signified and understood it is something positive. Alexander of Hales indicates the same, I p., q. 13, membs. 1 and 2; Soto, on the Logic, chapter on Property, q. 2, ad 2; and it can be persuaded, first, because by the opinion of all one adds indivision over being; but indivision, although it is signified after the manner of a negation, is nevertheless in truth not a negation, but a positive notion; therefore. The major is evident from the very exposition of the word; for that is called one which is undivided in itself. Likewise from its opposite, namely multitude; for those things are called many which are divided among themselves; therefore that is called one which is undivided in itself. Likewise it is evident from the proportion to quantitative unity; for those quantities are called several which are divided, but that one which is not divided; just as, therefore, quantity is one through the indivision of quantity, so entity is one through the indivision of entity. The minor is proved, first, because division is a negation; therefore indivision, although it has the form of a negation, is nevertheless in the thing not a negation, but rather an affirmation. The consequence is proved, because two negations (as they say) affirm, and because in the thing itself a negation is never immediately destroyed by a negation; for no such opposition is found in things; it is taken away, therefore, by an opposed positive form. But the antecedent, namely that division expresses a negation, is St. Thomas’s, De potentia, q. 9, a. 7, saying that multitude includes a negation, namely the division of one from another. And I, q. 11, a. 2, ad 4, he says that we apprehend division in so far as we apprehend that this being is not that; and Soncinas says the same, Metaphysics X, q. 4. Nor can we conceive division otherwise.

3. Secondly, this can be explained by reason in this way, because in those things which are one through composition, unity arises through the union of many, which union is something positive in them, as we shall see afterwards; but conversely several things are by this very fact many, and not one, that they lack union; division, therefore, formally expresses only the lack of union; it consists, therefore, in a negation; but conversely indivision expresses the lack of division, which is to deny the lack of union; but this is to posit union, which is something positive. And consequently, in those things which are one not through the union of many, but through simple entities, unity expresses a positive perfection consisting in a certain integrity of the thing, which is a higher and more eminent perfection than union, although it is explained by us through negation on account of its simplicity. Whence a twofold confirmation is taken. The first, because negation as such does not admit of more and less; but one or unity admits of more and less; for that is more one which is one through a simple entity than that which is one through the composition of many, and the further one departs from unity, the greater the composition, or the less the union; it is therefore a sign that unity adds something positive. The second confirmation is that negation expresses no perfection, but unity expresses perfection; for in God it pertains to his greatest perfection that he is only one, and that he is most of all one, and that in him all things which are not opposed are altogether one. And in the angels it is judged to pertain to their perfection that in each species there is only one; and the mode of their unity, namely through such simplicity, also pertains to their perfection; and the same holds proportionately in the other beings.

4. Thirdly, this can be gathered from the species or modes of unity, for all are positive; it is therefore a sign that unity itself as such also adds something positive. The antecedent is evident first in quantitative unity, which is called one by continuation by Aristotle, Metaphysics V, c. 6; but continuity is not a negation, but something positive, since it consists in this, that the parts have a common term; that integrity, therefore, which results from continuation is the unity of continuous quantity, and it is something positive. Another is the unity of composition, for example from matter and form, in which way humanity is called one, of which we have already shown that it consists in a positive notion; whence also generation, which tends to this union, is a positive action; but conversely corruption, which dissolves it, formally consists in privation. Another unity is individual, specific and generic, and all these are positive, because both the genus is positively contracted to the species, and the species to the individual, and that conformity or agreement which is in the species or genus is positive.

5. Fourthly, we can argue from the effects or properties which are attributed to unity; one is that it founds the relation of identity or likeness, Metaphysics V, c. 15; but a real relation is not founded on a negation, but on something positive. Another is that one is the first measure of multitude; which cannot belong to a negation, since it is nothing. Whence Aristotle, Metaphysics X, c. 9, text 21, posits a relative opposition between one and many in the notion of measure and measured. Finally, one as such composes multitude; for multitude formally consists of unities formally; whence also in quantitative number the last unit is said to be its form; just as, therefore, number is formally something positive, so also is unity.

The true opinion

6. It must be said, first, that one adds nothing positive over being, neither of reason nor real, neither distinct from the nature of the thing nor by reason alone from being. This is the opinion of St. Thomas, In Metaph. IV, lect. 2, and I, q. 11, a. 1, where Cajetan comments; of the Scholastics, In I, dist. 24; where Capreolus, q. 1, a. 1; Durandus, qq. 1 and 2; Gabriel, q. 1, a. 3, dub. 3; Gregory, q. 1, a. 1; Henry, Quodlibet I, q. 1; Soncinas, Metaphysics IV, q. 4; Javellus, qq. 5 and 8; Jandun, q. 4; Fonseca, c. 2, q. 5. And it was also the opinion of the Commentator, Metaphysics IV, comm. 3, text 3, and Book X, comm. 8. And it is taken from Aristotle, Metaphysics V, c. 6, text 11, and Book X, c. 1, where he explains the notion of one through indivision, and indivision through the negation of division; and Metaphysics IV, c. 2, for this reason he says that one and being are one and the same nature, because, namely, it expresses no positive notion besides the notion of being.

7. And indeed concerning the being of reason after the manner of something positive (of which the discussion is in the first part of the conclusion) the matter is sufficiently certain and beyond controversy, because no being of reason as it were positive has hitherto been thought out which one formally expresses and adds to being; for either it is after the manner of a relation, and this not, because the name of one is altogether absolute, as we saw above, and as is evident from the word itself and from the common mode of conceiving; or it is after the manner of some absolute and positive predicate; this cannot be said, even if one gives oneself licence to feign. Someone might perhaps say that one adds a relation of identity to itself. But this is plainly false; for to be one and to be the same are very diverse predicates; and the first is in its own way a real predicate belonging to being without the feigning of the intellect; but the second is a predicate of reason belonging through the operation of the intellect; whence the first is the foundation of the second, in the way in which a relation of reason can have a foundation in the thing.

8. And so, this part being omitted, the other, about the real positive notion, which is chiefly intended, is wont to be proved most of all by this reason: that, if one adds to being a positive real notion, then it is necessary that being be included in it; therefore also one; therefore another positive notion will have to be added to it, through which it would be one; therefore one will so proceed to infinity, unless we stop at some real notion which is so per se being and one that to be thus one adds nothing over its entity; therefore by the same reason we must stop at the very notion of being. But to this argument Scotus answers that that notion of one is so positive that it is nevertheless not being. But this has been sufficiently disproved above. And moreover it cannot be denied, as regards the present point, that that real mode, or whatever it is which one adds to being, is one something in the way in which it is; for each being has only one mode of this kind, and not several, and has it distinct from the mode or unity of another being, but undivided in itself; it is therefore rightly asked whether that mode is one by itself and without any positive addition made to its entity, or with an addition; for, if with an addition, one will proceed further to infinity; but if without positive addition, through mere negation, why will the same not be said of any being whatever as such?

9. An evasion is refuted.—Some say that the mode of one itself, since it is that by which being is one, can also be one by itself, which cannot be said in this way of the notion of being, because it is not formally the notion of one, or unity as by which; for that which in some genus is by which, when it is simple and ultimate, can by itself be which; but this is not attributed to that which in no way formally participates that notion. The common example is in quantity, through which substance is quantified, and therefore it can be quantified by itself, which substance cannot. Which evasion has a certain appearance of subtlety, but in the present case there is no necessity of feigning that by which and which; for that notion of unity is not understood to be one on account of some positive notion which it has in itself and as it were exercises about itself, as quantity is quantified because it is extended and of itself apt to occupy place; but it is understood to be one through the mere negation of plurality or division; therefore in the same way it can be understood in the notion of being, nor is it necessary to feign something positive which would be for it the reason by which of being one.

10. The rejoinder is answered.—It can finally be said that this argument proceeds rightly against Scotus and others who posit that mode of one as distinct from the nature of the thing from being, yet does not urge so much if we say that that mode is indeed positive and real, yet distinct from being by reason alone; because then it will be said that that mode, although it is being, is nevertheless not distinct in the thing from being itself, and therefore is one by the same unity as being itself, and precisely and according to reason is not considered as one, but only as the notion of one, but really is one by itself, as being itself is. But against this answer it is objected that other inconveniences follow from it. First, that the notion of one is positive and an attribute of being, and quidditatively includes being itself, which is repugnant to a proper attribute. Second, that that mode is of the quiddity of being itself, as the divine attributes are of the quiddity of God, because, although they are distinguished by reason, in the thing they express positive notions which are not distinguished from the nature of the thing from God; but the consequent is false; both because otherwise one would not be an attribute of being, but its essence; and also because otherwise no created thing could be quidditatively and distinctly conceived unless it were formally conceived as one. Which inconveniences are indeed probable; perhaps, however, someone would not think it unfitting to concede them in the transcendentals, which are most simple.

11. Pursuing the discourse otherwise, then, I show that it concludes in the same way that this positive mode distinct by reason is not to be posited; for, that positive mode being prescinded by the intellect, in the remaining concept of being is understood whatever is necessary for unity; it is therefore a sign that nothing positive is prescinded, even through reason, from being, by which it would be one. In order that this may be understood, let us speak of some being in particular, as, for example, of God in so far as he is one; if, then, in him unity is a positive attribute distinct by reason from God, then God can be prescinded in the mind from his unity; but in God so conceived, without the addition of anything positive even according to reason, the negation of division or partition which he has in himself can be conceived, and also division, or a sufficient foundation of division, from all others; but by this very fact he is sufficiently conceived as one; therefore whatever positive thing is afterwards added, even according to reason, is superfluously feigned, nor can it be explained what it is or for what; and the same argument can be made in any other one being, and consequently in being in common. Secondly I declare this in composite beings by retorting the former arguments; for in a being of this kind, which comes about through composition, whatever positive physical thing can be considered pertains to the notion of being as it is such being, even if it is prescinded by reason from the concept of one; as in humanity the union of soul and body is of the essential notion of such a being as it is such being specificatively and in the thing itself; and similarly in a line the union of the parts at a point is of the notion of being as it is in such a species of continuous quantity; therefore every positive metaphysical notion too which is founded in such physical union pertains formally and according to reason to the notion of such a being, not in so far as it is conceived as one, but in so far as it is formally contracted or determined in the notion of such a being; therefore the notion of one can add nothing positive, even distinct by reason. Thirdly this is explained in simple beings, in which unity seems to be more perfect; indeed simplicity itself seems to be the greatest unity; but simplicity formally does not express a positive notion, even distinct by reason alone from the simple being and from the perfection which is conceived in it in the notion of being, or of such being; so much so that even in God, according to the more probable opinion of the theologians, simplicity as such adds no perfection to God, even according to reason, over the perfection of his supreme actuality, on which that negation which simplicity expresses is founded; therefore much less can unity as such express a positive notion. And this conclusion will be more evident from what follows and from the solutions of the arguments.

12. I say, secondly, that one adds over being some negation after the manner of a privation. So teach the authors cited, and it follows from the preceding assertion; for it is evident that one is in some way distinguished from being, both because it is its attribute, and because those names are not synonyms, but diverse formal and objective concepts correspond to them in the mind; therefore one expresses something besides being; but it does not express something altogether feigned through reason, as is self-evident, because to be one truly belongs to things themselves; nor does it express some relationship of reason, as has been shown; nothing, therefore, remains which it can add besides negation or privation.

What the negation is which one adds to being

13. Two things, however, remain to be explained here. The first is, what this negation is and how manifold. The second, how this negation is said to be after the manner of a privation. Concerning the first, all agree that one expresses the negation of division in being itself, which Aristotle signified when he said that one is being undivided in itself, as is evident from the places cited, and from Metaphysics X, c. 5. And it is evident by reason, because through division we understand one being to become many; therefore by no other reason is being better conceived to be one than by the negation of division; and in this all agree. The aforesaid words, however, are to be attentively considered; for it is one thing for being to express the negation of division in itself, another to express the negation of division from itself; for although each negation can be attributed to being, nevertheless it is the former which pertains to the notion of one; for the latter does not suffice, as Soncinas rightly noted, Metaphysics IV, q. 23, ad 1. And it is evident, both because that is not a proper negation which is added to being in the thing, but one which is considered through the mere reflection of reason; and most of all because not to be divided from itself belongs equally to being per se and to being per accidens or to multitude; for a heap of stones is as much not divided from itself as a man or an angel; yet, because it is not undivided in itself, it is not properly one being; the negation of division in itself, therefore, is what constitutes one, not the negation of division from itself.

14. Authors further doubt, however, whether some other negation is included in the notion of one. For many define one as that which is undivided in itself, and divided from every other; and therefore besides indivision in itself they say that one expresses the negation of union with another, which negation is explained by the name of division or distinction from another. So think Capreolus, Gabriel and Soncinas, in the places cited; because, just as it is of the notion of one that it be not divided in itself, so that it be not other than itself; for one of these two, namely to be other than itself or not to be other than itself, must necessarily be included in the notion of one, because, since they are contradictorily opposed, they are immediately repugnant; but to be other than itself is not of the notion of one, as is evident; therefore it will be of the notion of one that it be not other than itself. Rather, some add that the negation of division from another belongs to being prior according to reason to indivision in itself, because it belongs to being to be divided from non-being prior to being undivided in itself; therefore each negation is required for the notion of one. Whence also St. Thomas, I, q. 11, a. 2, ad 4, says that the concept of division from another is prior according to reason to the concept of unity. But others deny that division from another is of the notion of one, but only indivision in itself. So Fonseca, above, citing Giles, Metaphysics IV, q. 6; and Hervaeus, Quodlibet IV, qq. 2 and 3. His reason is that to be divided from another is not required in order that being be absolutely one, but only in order that it be one out of many; and therefore a thing is sufficiently conceived as one when it is understood as undivided, even if it is not conceived as divided from others. And it is confirmed, because a thing is absolutely one although there are no others from which it is distinguished.

15. The name of one can suffer equivocation.—But concerning this it is to be noticed that equivocation can be committed both in the name of one and of division from another; for sometimes in common and vulgar usage one is wont to signify that which is solitary and unique, in which way we say that there is one God, one sun; and in this way one expresses the negation of multitude, and does not so much express division from another as deny the company of another. But in this way to be one is not an attribute of being, as is self-evident; nor is that signification proper to one, nor rigorous, but only by the accommodation of usage is it sometimes extended to this; for rigorously it is true to say that here there is one man, although there are several; and therefore in the rigorous signification, in order to deny that there are several, the exclusive only one is added. Therefore the negation of multitude, or of several, in this sense does not enter the formal notion of transcendental one.

16. The real relation of division from another is outside the notion of one.—Again, to be divided from another can be conceived after the manner of a real relation, or to a real and existing term. And in this way it is certain that division from another is not of the notion of one; both because it is something posterior to it; for this is divided from that because it is such in itself and one something; and also because one of itself is prior to multitude and independent of it; but to be divided from another in this way requires multitude; indeed multitude thence arises, because there are several ones, of which one is not the other. Finally, for this reason we said above that something, in so far as it expresses a negation or relation of otherness of this kind from a real and existing term, is not an attribute of being; because per se it does not belong to every being, but per accidens from the coexistence of others; much less, therefore, can this be of the notion of one. Whence, before creatures existed, God was perfectly and completely one without this relation or negation. Rather, even if per impossibile no other things were possible outside God, he would be truly and perfectly one by the very fact that he would be undivided in himself in essence, even if he could not be divided from others, because others could not be. Nevertheless, because in fact, and in a certain way from the intrinsic notion of being considered according to its whole breadth, with any being whatever the existence of another is possible, therefore it follows upon every being that it can be distinct from another, which in truth belongs to each from the fact that it is one in itself. And in this way to be distinct from another in aptitude and fundamentally can be said to belong to every being in so far as it is one; yet this very thing does not formally enter the notion of one, but follows upon it, as it follows upon quantity that it is the foundation of equality or inequality.

17. How to be divided from another is necessarily conjoined with one.—Finally, to be divided from another can be conceived only after the manner of a negation. Which can also be compared either to an existing positive term, and in this way the reason concerning it is the same as concerning the relation; or to a positive term absolutely taken, whether existing or possible; and in this way to be divided from another belongs to every being in so far as it is one, because, just as it cannot belong to one being to be another, so it necessarily belongs to it not to be another; for these are contradictories, and therefore, if one of them is necessarily separated from one, namely to be other than itself, the other necessarily belongs to one, namely not to be other than itself, which is to be distinct from another. Which reason indeed does not prove that this negation primarily and most formally enters the notion of one, but that it belongs to it necessarily, whether per se in the first mode or consequently; and this latter seems truer, which the authors of the second opinion intend, and perhaps the authors of the first do not deny. They can therefore be reconciled; for what the latter deny formally and per se in the first mode, the former affirm consequently and per se in the second mode. And so Soncinas expressly explained it, Metaphysics IV, qq. 23 and 27, and this alone the reasons adduced prove.

18. Finally, if this negation or division of one being is compared not to a positive term but to a negative and contradictory one, then too it belongs to every being, by the very fact that it is one being, that it be divided from non-being, or that it be not non-being; yet this negation is only as it were through the reflection of the intellect; for as it is objectively understood to precede in being, it is rather an affirmation; for affirmation is not divided from negation through another negation. For this is impossible, because one would proceed to infinity; it is divided, therefore, by itself; so, then, being is divided from non-being not through another negation, but by itself, just as conversely non-being is divided from being not through another negation or affirmation, but by itself; and so most formally to be divided from non-being is nothing other than to be being. By this consideration, therefore, such a negation neither pertains to the notion of one nor is an attribute of being, since in truth it is none; but in so far as it can be thought out by the intellect, it is only an extrinsic denomination or relation of reason; and therefore it too does not intrinsically pertain to the notion of one, although Cajetan seems to think the opposite, I, q. 11, a. 4, at the end, of which we shall say more in the solutions of the arguments.

Whether the negation which one expresses is a privation

19. The second doubt was how one expresses this negation after the manner of a privation; and the reason for doubting is that privation expresses a negation in a subject apt by nature; but the indivision which one adds over being often expresses a negation of division in a being incapable of it; as in God, to be one denies the division of the divine essence, which cannot be divided; and it is similar in other things, especially simple or incorruptible ones, indeed in all beings, in so far as each is inseparable from itself; for no being can be divided from itself; but this indivision alone is of the notion of transcendental one. The answer is that the difficulty consists only in the explanation of the conclusion, namely, why this negation which one expresses is said to be after the manner of a privation. For because it does not deny a form of which the subject or being which is called one is capable, I therefore did not say that this negation is a privation; for this it would be necessary that it deny a form in a subject apt by nature, as the argument proves. But I said that it is after the manner of a privation, because in something it imitates privation and departs from mere negation. For, just as privation expresses a negation not in any way whatever, but as it were adhering to a real subject, so one expresses this negation as it were adding it to the real being which it connotes; and therefore non-being, or nothing, as such, is called neither one nor many, although the negation of division absolutely taken can be attributed to it, because non-being is undivided. But beings of reason, or feigned beings, are called one or many equivocally in so far as they too are equivocally beings, or rather are conceived as beings. One, therefore, expresses the negation of division in being, and as regards this it is said to be after the manner of a privation, whether such a being is capable of division or not. Fonseca, above, adds that the division which one denies is absolutely possible, granted that it is not possible to that being which is denominated one; as God is called one because he is undivided in essence, which division is possible in the creature, although impossible in God; and so that division is not impossible to being as being; and in this way it can be called a privation by reason of capacity at least in the common concept, in the way in which the mole is called blind, because as animal it is capable of sight, although not as such an animal. Which in the present case is said less properly on account of the analogy of being.

Solutions of the arguments

20. To the first argument of the contrary opinion the first and common answer is by conceding that division consists in negation, and consequently that indivision is the negation of a negation. So St. Thomas concedes, In I, dist. 24, q. 1, a. 3, ad 1. Whence in the solution ad 2 he concedes that, according to the thing, positive unity is more related to it than multitude is; because the negation of one thing from another, which multitude expresses, is in the thing itself; but the negation of the negation, which unity expresses, is merely through reason. Which doctrine Soncinas embraces, Metaphysics X, q. 4. To the argument, then, namely that the negation of a negation is an affirmation, the answer according to this opinion must be that formally and according to reason it is not so, because reason can reflect upon one negation and deny it, and through this negation explain some simple positive thing which it cannot declare as it is in itself. But according to the thing and equivalently that it is true; yet that positive thing which is circumscribed by those negations is nothing besides the entity of the thing itself which is called one. This answer is probable and can easily be defended; yet it seems to suppose that the negation which one expresses is either the negation of the division of this being from another being, or the negation of the division of this being from itself, which in truth are negations of reason; but the former does not pertain to the notion of one, as has been said, but follows upon it. But the latter negation is not proper to one, but common to multitude. Therefore the negation of division in itself is properly of the notion of one; but this seems to suppose no real negation in the thing itself which is denied according to reason through indivision.

21. Secondly, then, the answer is by conceding that one expresses indivision or the negation of division, and denying that this is the negation of a negation. For in the division which one denies two things can be considered: first, that the beings divided among themselves are as it were complete in themselves and terminated by their entities; second, that one is not the other. This latter expresses only a negation, as is self-evident; but the first expresses something positive, which is the foundation of that negation, which nevertheless in the thing is nothing besides the entities themselves, as can be explained in discrete quantity; for that lines are several expresses that each is terminated by its proper terms; whence follows the negation, namely, that they do not have a common term. The indivision, therefore, which one expresses denies division by reason of the positive thing which is found in divided things, not by reason of the negation which the division of one from another includes; just as conversely the negation which division expresses does not deny another negation, but the positive union or identity of one with another.

22. An objection is answered.—You will say: hence it follows that the negation which one expresses is the negation of multitude, which nevertheless we seem to have denied above. And it is evident that it is false, because one is prior to multitude; but a negation is posterior to the form which it denies. The answer is that one can be understood to deny multitude in two ways: in one way simply, or in the nature of things; and in this way we denied above that one expresses the negation of multitude, nor does the opposite follow from the said solution, as is self-evident. In another way, so that it denies multitude in the very thing which is called one, that is, that it is not several in itself; but in this sense it has not been denied by us above that one expresses the negation of multitude. Fonseca, however, denies this, in the said q. 5, sect. 5, and it is the opinion of St. Thomas, I, q. 30, a. 3, ad 3, and opusc. 42, c. 2, where he adduces the reason which Fonseca too uses, namely because one is prior to multitude. Which reason, if it were efficacious, could be made in the same way of division; for one too is by its nature prior to division, as I shall say below.

23. Others, therefore, concede that the indivision of one expresses the negation of multitude in being, under the notion by which it is one; which Giles taught, Metaphysics IV, q. 8, and St. Thomas favours, In I, dist. 24, q. 1, a. 3, saying that division, according to which something is distinguished from something, is in affirmation and negation, and therefore that multitude includes negation in its notion, according as those things are many of which one is not the other. And of division of this kind (he says), taken in this way in the notion of multitude, a negation is imported in the notion of one. And in the solution ad 4 he says: One is not the privation of that multitude which it constitutes, but of the multitude which is denied to be in that which is called one. And although St. Thomas there speaks of multitude as regards the negation included in it, as has been said, nevertheless perhaps it is better said that one denies multitude as in it there are several positively. Which is also favoured by the fact that the same St. Thomas, I, q. 11, a. 1, says that one is opposed to multitude after the manner of a privation, as the undivided to the divided, which Aristotle too says, Metaphysics X, text 9. And this opinion seems to me very probable; it is to be understood, however, of multitude as it is multitude, or by reason of plurality, not in so far as multitude itself can by another reason be considered as something one; of which below. Or certainly it can be said that one expresses the negation of division, not as it formally expresses a negation, but as it expresses the foundation of that negation, which is something positive, as I have declared; and because multitude absolutely includes a formal negation, therefore as regards this one does not altogether express the negation of multitude.

24. How one being is more one than another.—To the second, I concede first of all that the union by which the parts are joined to compose one is something positive; I concede also that in simple things the whole entity or integrity of the thing is positive. I deny, however, that it follows from this that one adds a positive notion over being, because all that positive element pertains to the entity of the thing, not to unity, as I declared above; but it is necessary to adjoin the negation of division, in order that such a being, whether simple or composite, be understood to be one. To the first confirmation the answer is that total negation or privation formally and according to itself does not admit of more and less, but can by reason of its foundation; and so one being is more one than another by reason of the foundation, in so far as it is more or less composite. But whether in the negation itself more and less can also be considered, so that that negation is not always simple or total, but sometimes only in a certain respect and in part, will be said below, sect. 4.

25. Whether and how one expresses perfection.—To the second confirmation it is similarly said, with St. Thomas, I, q. 6, a. 3, ad 1, and Cajetan there, that one by reason of the negation adds no perfection to being, but by reason of the foundation supposes some perfection. For if one is taken properly, as it expresses only to be undivided in itself, it supposes the entity of the thing and the union of the parts, if the thing is composite, which express perfection in the thing itself. If, however, one is taken as it excludes another and expresses to be unique or solitary, then it is clear that such a negation per se does not express perfection; indeed it does not always require it, nor come from it; for in God to be only one in essence comes from perfection; yet that there is only one person in him does not pertain to perfection, but rather the distinction of persons is there from supreme perfection.

26. To the third the answer is that by all those examples it is only proved that the negation which one expresses is not a pure negation, but founded in being; and if the being is composite, it includes some composition or positive union in which such a negation is founded; but if it is simple, it is founded in a simple entity; but how this belongs to each of the unities there enumerated, especially the generic and specific, will be treated below.

27. What certain attributes of one are, and how they belong to it, is explained.—To the fourth the answer is that all those things which are attributed to unity, in so far as they include something positive, belong to unity by reason of its foundation, not by reason of what it adds over being; and so the relation of identity, if it is understood of numerical or real identity, since it is a relation of reason, it is not unfitting that it be founded in a negation; but if it is understood of specific identity or of the likeness of one thing to another (supposing that such a relation is something real in the foundation, distinct from the nature of the thing from it), it is not founded in unity by reason of negative indivision, but by reason of that positive entity and formal notion which the foundation has; of which more fully below in its place. Similarly one is called the measure of multitude partly by reason of the positive, partly by reason of the negation; for multitude too includes something both positive and negative, as we shall see afterwards; for a measure must be both known and certain; in order that it be known, it is necessary that it have entity; but in order that it be certain, it is necessary that it consist in something indivisible; and as regards this we use unity, as it is something undivided, as a certain principle for measuring multitude. And in the same way one composes multitude by reason of positive entity, in so far as multitude itself is positive, as St. Thomas teaches, I, q. 11, a. 2, ad 2; but in so far as it includes a negation, it can in some way found the negation which is included in multitude, as we shall see below.

1. The reason for doubting is that from what was said in the preceding section it seems plainly to follow that one formally expresses only the negation, because it formally expresses that in which it is distinguished from being; but it is distinguished only in the negation which it adds; therefore it formally expresses that alone. Secondly, because each property or attribute formally expresses what it adds to its object; but one is an attribute of being; therefore it formally expresses only what it adds over being; but it adds only a negation; therefore. Thirdly, because, if besides the negation it expresses something, either that is being, or something else; this second cannot be thought; for if that is other than the negation, it must be positive; but it cannot be something positive of reason, as was shown above; it is necessary, therefore, that it be something positive and real, and consequently that it include being, according to what was said above against Scotus. But if the first is said, namely that what one formally expresses includes real being, all the inconveniences and arguments made above against the opinion asserting that one adds something positive over being follow, namely, that being is quidditatively included in its attribute, which is against the notion of subject and attribute. Likewise the process to infinity inferred above follows, because that which one formally signifies will also be one, etc. Finally it follows that the formal significate of one is altogether the same as its adequate significate, as it includes also the material. And finally it follows that the attribute of one formally includes the whole perfection of being, and consequently that the attribute is of equal perfection with its subject.

Various opinions

2. The former.—In this matter there are two opinions. The first affirms that one formally expresses only the negation explained above. Cajetan indicates this opinion, I, q. 11, a. 1, on the second argument of Scotus, when he says that one formally is no more outside nothing than other privative or negative things. Fonseca teaches it more fully and more clearly, in the said q. 5, sect. 5, and St. Thomas favours it, I, q. 6, a. 3, ad 1, in so far as he says that one does not import the notion of perfection, but only of indivision. The foundations of this opinion are posited at the beginning, by which it seems to be concluded that one in its formal significate does not include being, but only connotes it, and consequently formally expresses only indivision or negation.

3. The latter opinion.—The second opinion is that one formally expresses not negation alone, but the entity itself under the negation, which is the more common opinion of those writing on this place of Metaphysics IV: Soncinas, q. 3, a. 8; Javellus, qq. 5 and 8; Flandria, q. 3, a. 8; Jandun, q. 4; Capreolus too holds it, In I, dist. 24, q. 1, where concerning the first conclusion he adduces Avicenna, Metaphysics III, c. 3, saying: Unity is being which is not divided; so that being is of the essence of unity, and not its subject; for unity substantially is being itself which is not divided. And Soto indicates it, on the Logic, chapter on Property, q. 2, ad 2. St. Thomas favours it, In I, dist. 19, q. 4, a. 1, ad 2, saying that the very essence of created being, according as it is undivided in itself and distinct from others, is its unity; and dist. 24, q. 1, a. 3, where he says that one encloses in its understanding common being and adds the notion of privation; and De potentia, q. 9, a. 7, where he says that one signifies not indivision only, but being with it. But in these last two places St. Thomas openly speaks of the adequate significate of one, not of the formal, as Fonseca expounds; the first place, however, does not seem to admit this exposition.

4. This opinion is founded, first, because if one formally expressed only indivision, it would be a privative term; the consequent is false, because every privative term expresses some imperfection in the thing to which it is attributed, which cannot be said of one, otherwise it could not be attributed to God; therefore. But this reason is not of great moment; for it is not necessary that a privative term import imperfection, if the form which it denies does not pertain to perfection simply, as is evident in these terms, infinite, immaterial, which, although they are taken altogether privatively, express no imperfection; the same, therefore, can be the case with one, because the division which it denies does not express perfection simply. Indeed the same reason would proceed, if it were efficacious, even if one formally expressed being with indivision; for if privation purely taken expressed imperfection, even if something is adjoined to it, it will express the same imperfection adjoined to perfection.

5. This opinion is wont to be proved otherwise, because, on the testimony of Aristotle, Metaphysics IV, being and one signify the same nature; but if one formally expressed a pure negation, it could not signify the same nature as being, because being does not express a negation, but a positive nature. But this reason too does not convince; for if one, by signifying only a negation formally, were of another nature from being, on account of the distinction which exists between privation and the positive, by the same reason, although it formally expressed being with indivision, it would have to be said to be of another nature from being, at least in the way in which the whole composite is distinguished from the matter or subject, or as blind and Peter are distinguished. Aristotle, therefore, says that one and being express the same nature as regards the whole positive thing which each expresses; and it is also rightly expounded negatively, namely, that one does not express another nature (positive, of course) from being. Just as the same Aristotle, Physics I, c. 1, said that matter and privation are the same, namely negatively, because privation does not express a thing distinct from matter; so, then, it can easily be said in the present case.

Resolution of the question

6. I certainly think that the diversity between these opinions is rather about the manner of speaking than about the thing. For in the thing all agree that one, in its whole and adequate significate, expresses nothing other than undivided being, and that indivision adds nothing to being except the negation of division; and consequently it is necessary that all confess that in one there is nothing outside the notion of being as such except the negation alone; because the whole which is being, besides that which is added to it, is of its essential notion; but the negation alone is what is added to it; therefore that alone is outside its notion; whence it further comes about that one can be called an attribute of being only by reason of the negation which it superadds to being, because it is an attribute only in so far as it expresses something outside the notion of being. These things being posited in the thing, the remaining question about the formal significate¹ seems to be only about the imposition of the name. In which each opinion cited is probable, and is founded on a probable mode of conceiving the significate of this word one. For some conceive that, real being being supposed, one is constituted by the mere negation of division superadded to it, and therefore they say that one formally expresses only the aforesaid negation. But others conceive that unity is not as it were a certain privation adjoined to being, but is the very nature or entity of the thing, which entity or essence constitutes being; but as it is undivided entity, it constitutes one being.

7. The latter opinion is chosen.—An example illustrating the whole matter.—And this mode of conceiving seems to me more like the truth, and therefore I judge that the latter opinion is simply to be approved. First, on account of the reason now touched upon and indicated by St. Thomas, In I, in the place cited above, because one formally expresses real unity; but real unity is not a negation alone; therefore it is the entity itself under the negation. The minor is evident by induction; for God is called one from the unity of God, which consists in the undivided essence; and similarly Peter is called one in number because he has a nature one in number; whence his unity does not consist in a negation alone. And finally from the terms themselves it seems evident that real unity expresses more than a negation. Secondly, because one is not said univocally of being of reason and real being, as is self-evident; and yet, if you consider the negation precisely, it can equally be attributed to and denominate being of reason as well as real being; it is therefore a sign that one does not formally express the negation alone; otherwise the denomination of one could fall equally on being of reason and on real being, because the signification of a word is to be attended to chiefly from its formal significate. Just as the names of artefacts are judged not to signify figure alone in their formal significate, because they are not said equally nor univocally of things having the same figure in diverse materials, as saw is not said univocally of an iron and a wax one; so, then, neither will one signify negation alone formally, since it is not said equally of all things to which such a negation can equally belong; it therefore formally expresses the undivided entity itself. And hence a third argument can be taken, because one as it is transcendent does not formally express something supposing being, and as it were lying beside it and coming to it, as white formally expresses whiteness; for a thing is not so understood to be one as it is white; for it is one intimately through its own entity, but white through a form supervening on another entity; it is therefore a sign that one does not formally express the negation alone as it were superadded to the entity, but the intrinsic undivided entity itself. Finally, from what is to be said below it will be evident that almost necessarily one must think in this manner of the other transcendentals, good and true, which cannot formally express mere relations of reason, but the entity itself with some relation or denomination of this kind; therefore the same must be thought of one, for if the arguments which are made to the contrary about it proved anything, the same would proceed of the other transcendentals.

The arguments are answered

8. To the first the answer is that one is distinguished from being radically indeed (so to speak) by reason of the negation which it superadds to being; but formally it is not distinguished through the negation as through the form of one, but through undivided entity; and so being formally expresses entity as such, but one formally expresses the same entity as undivided.

9. To the second the answer is that that assumption is true in real properties most properly taken and adding to their subjects something distinct from them from the nature of the thing; for in these it is true that the names signifying such properties are wont formally to signify precisely what the property adds to the subject; but in these transcendental attributes, which do not add something real, it is not necessary to observe this; for, in order that they be not negations only, or altogether beings of reason, but signify in some way a real property, it is necessary that in some way they include the entity itself in their formal significate.

10. To the third the answer is that one in the concrete expresses being itself as undivided, but unity in the abstract expresses entity also in the abstract as undivided, and that unity of this kind is formally signified by the attribute of one; nor does any inconvenience follow from this; for that being taken in the concrete is predicated quidditatively of its attributes also taken in the concrete is no inconvenience; for so good is being, and true similarly, nor in these is it necessary to observe all the things which belong to real and most proper properties; for there the subject altogether prescinds from the property, and conversely, because they are distinguished from the nature of the thing; but here there is no such distinction, but only the addition of some negation or denomination; and therefore being is indeed not included in that which one adds, as was said above; but in one itself it is necessary that it be intimately included; nor does a process to infinity follow from this, because being and one, as regards the positive thing which it includes, are altogether the same, both in the thing and also in reason, except on account of the adjoined negation. But if we speak in the abstract of unity, it will not so properly be said to include being quidditatively as entity or essence; for in these the proportion must be kept, and as regards this, at least as regards the mode of signifying, the formal significate of one and the adequate one of the same are not the same. I say, however, as regards the mode of signifying, because in these most simple things the thing signified by the abstract and the concrete is the same, and so entity and being, unity and one, are the same, and differ only in reason and in the mode of conceiving and signifying. Wherefore there is no process to infinity, because just as being is being by its entity, but entity is entity by itself, and that by which being is being, but as such is not conceived as that which is, although in the thing it is most formally being itself; so in the same proportion one must speak of one and unity; for as regards the positive thing they signify the same, and differ only in that one signifies being or entity under indivision. Finally, in this way it is no inconvenience that one in the thing expresses the whole perfection which being expresses, although it does not express it under altogether the same concept or formal notion, because it does not express it precisely as it is perfection or entity, but as it is under indivision.

1. Various divisions of one.—Aristotle disputes on this matter, Metaphysics V, c. 6. It must, however, necessarily be set out beforehand in this place, in order that we may be able to explain which unity is an attribute of being. Aristotle, then, distinguishes various modes of one. And his first division is that one kind is one per accidens, another per se. And he deservedly places this division in the first place, because it also seems to be very analogous; for one per se is simply one, but per accidens only in a certain respect, and through a certain proportion to one per se. Aristotle, however, does not explain the notions of one per accidens and per se through their proper definitions, but only by various examples, by which he at the same time proposes various modes of unity per accidens and per se. For he says that the subject affected by an accident is one per accidens, as musical Peter. Likewise two accidents inhering in the same subject are, or constitute, one per accidens, as sweet white. This unity per accidens, however, we can explain in various ways in order to predications, either through incomplex terms, or through complex ones, or by predicating accident of accident, either in common or in the singular. And according to these Aristotle distinguishes various notions of this unity, which pertain rather to dialectical predications than to the metaphysical matter. Similarly Aristotle explains one per se by various examples, or by subdistinguishing it into various modes. For some things (he says) are one by continuation, as a line, water; some by binding together, as a house and other things which are made by art; others by reason of one form; others by reason of matter, either proximate or remote, as liquids (he says) are called one. Again (he says), one kind is one in number, another in species, another in genus, etc., which he pursues there. From all of which it is difficult to gather in what the notion of one per se and per accidens consists; for among the members which Aristotle enumerates in the latter place, many seem to be one only per accidens, as a house and artefacts. Likewise he says in the same place that several things are sometimes called one because they do, or undergo, or have, or are related to, some one thing. But all these seem to be one only per accidens, or by denomination rather than in reality. Again, among the unities which he posits there, some are real, as the numerical, others only of reason, as the generic and specific; it is therefore difficult to reduce this doctrine of Aristotle to some certain notion and method.

The division of being and of one into per se and per accidens is explained

2. In order, then, to declare this matter, since one follows upon being, in order that it may be understood what one per se and one per accidens are, it must at the same time be explained what being per se and per accidens are; for being too is so divided by the same Aristotle, in the same Book V, c. 7; which division is proper to real being; for beings of reason, as they are beings only equivocally, so they do not receive these denominations except equivocally. Real being, however, can be called per se or per accidens in two ways: in one way in the notion of being, in another way in the notion of effect. In this latter way that is called per se which comes about from the power and intention of the agent; but that is called per accidens which happens beyond the intention of the agent by chance and fortune; of which Aristotle says, Metaphysics VI, c. 2, that it is outside the consideration of science, namely in so far as it is exercised in the singular and per accidens, for as such it does not have necessity, but contingency. But the very common notion of cause or effect per accidens does fall under science; for so one disputes about chance and fortune and the contingency of effects; but nevertheless being per se and per accidens under this consideration pertains nothing to the present purpose.

3. What kind of one per se and what kind per accidens Aristotle indicates.—In the former way, then, being in the notion of being is called per se or per accidens in order to the unity which it has, or by reason of such unity; as, for example, because it consists of one nature of one predicament, or of natures of diverse predicaments; for so Aristotle, in the said Book V, texts 13 and 14, calls those things beings per accidens which consist of subject and accident, or when many accidents are conjoined in the same subject; but he says that that is being per se which is divided into the ten categories. And the same Aristotle, Metaphysics VII, text 43, and more clearly Book VIII, text 15, and De Anima II, text 7, indicates that that is being one per se which either is simple, or is composed of substantial potency and its proper act. Whence conversely that will be per accidens which is neither simple nor has the aforesaid composition, but consists of diverse things in another more imperfect mode. From which it may be understood that that is called being per se in the notion of being which is one per se; but that per accidens which is one only per accidens. For per se and per accidens are not here so called by reason of the mode of being per se or in another, in which way substance alone is being per se, while the others can be called per accidens, or rather accidental; but per se and per accidens are taken in order to unity; but what unity per se or per accidens in beings is has not been sufficiently declared from what has been said, nor is it explained in the same way by all.

4. Simple existence is not of the notion of one per se.—Some, then, say that that unity or union is per se from which one and the same being results, but that that is per accidens in which the beings which are united have several beings, as are substance and accident, or two accidents of diverse genera. But this explanation either supposes something false, or explains an obscure matter by another equally obscure; for either the discussion is of one simple being without composition which is in it, although it results from composition, in which way many say that from matter and form united one being results, and this sense supposes something false; for in order that being be one per se it is not necessary that it have a simple being of this kind; for below I shall show that beings composed of matter and form do not have a simple being, but a composite one. Or the discussion is of one composite being resulting from the union of several partial existences, and this indeed is true, but of that very being it remains to be inquired when from composition one per se results; for even an accident, for example whiteness, coming to a substance brings with it its own being, which with respect to the white composite can be called partial, and from it and from the being of the body or subject one being of the whole white thing can be said to be composed, and yet it is nevertheless said to be being per accidens.

5. How one per accidens comes about from two beings in act; but how one per se from one in potency and another in act.—In another way, then, it is frequently wont to be said that being per accidens is that which consists of several beings in act, but that that is per se which consists of being in potency and its act; for from several beings in potency nothing can consist, and therefore it is not necessary to adjoin that member. But this doctrine too, granted that it is true, needs exposition; for, badly understood, it can be the occasion of erring in many things. For it must be asked what is understood by being in act and in potency. For by being in act can be understood that which of itself has actual entity or existence; but by being in potency that which has no such actuality or existence. And in this way it is false that being per se cannot be composed of actual partial entities, or that it is required for being per se that it be composed of such act and the potency opposed to it; for this is the same as if it were said that being per se is composed of being and nothing, or of being in act and being in objective potency, which is a contradiction in terms, as will be evident from what is to be said below. Otherwise, then, by being in act can be understood being consisting of some formal act and the potency receptive of it. And in this way it does not happen that something is composed of two beings in act, so that each is composed in the aforesaid way, except either by aggregation, and then it is sufficiently clear that being per accidens arises, although its notion has not yet been sufficiently explained; or in some artificial mode; and then Aristotle seems to call such a being one per se, whence it consequently is also being per se and not per accidens. And in the physical and heterogeneous composite many think that there are partial composites of diverse notions and forms, from whose conjunction one per se coalesces. And next it remains to be explained, if to a being of this kind another is adjoined not similarly composed, nor after the manner of continuation or binding together, but simple after the manner of a form or act truly and physically united, why being one per se does not result from both. Or if it sometimes results and sometimes not, whence the reason is to be taken. Where various questions are indicated which depend on this, namely, why, when subsistence comes to a nature already integral, one per se results from both, but not when quantity or another similar form comes. Likewise, why the substantial form makes one per se with bare matter, but cannot make one per se with matter already informed by a substantial form, and similar questions.

The notion of being and one per se

6. In this matter, then, it seems it must be said that the notion of being per se consists in this, that it has precisely the things which are required per se and intrinsically for the essence, integrity or completion of such a being in its genus. Aristotle indicated this in the former place cited. And from the terms themselves it seems clear; for these most common and most simple things can scarcely be proved otherwise than by explaining the notions of the terms. Since, then, that is called being which has entity or essence, that will be properly and rigorously being per se which has one essence or entity. But that essence or entity will most properly be one which in its genus has whatever pertains to its intrinsic notion or consummation; therefore that being which is of this kind will under that notion be properly and per se being; but everything which falls short of this unity will be called being per accidens.

7. This, however, can be explained more fully if we divide being per se into simple and composite, which division can also be given of one per se, and Aristotle indicated it, Metaphysics X, c. 6, saying that one kind of one is divisible, another undivided. For, as St. Thomas noted, I, q. 6, a. 3, and q. 11, a. 1, of one per se one kind is undivided in act and potency, another only in act; the former is simple being, the latter composite. Of the simple, then, there is no difficulty; for every simple thing is being per se and one per se, because it is both undivided per se, and as such does not have the admixture of something extraneous so that it could be called being per accidens; and in this way any accident taken in the abstract is by that consideration being per se, and the soul in the notion of substance is being per se, although incomplete; but in so far as it consists of several powers, habits or acts, it already declines into being per accidens.

8. Of composite being, however, it is certain first of all that it can truly and properly be being per se and one per se, as all philosophers teach of substantial nature in so far as it consists of matter and form, and of the supposit in so far as it is in its own way composed of nature and subsistence. For since neither matter nor form are per se complete and integral beings in their genus, but have been instituted by their nature for composing it, that which is proximately composed of them is deservedly called, and is, an essence and nature one per se. And by the same reason, because that essence does not have intrinsic completion in its genus unless it is per se intrinsically and substantially terminated, therefore it too with its subsistence constitutes being one per se. This unity per se, then, consists in this, that it results from things constituting a complete being in some genus, a union intervening between them accommodated to constituting such a being, which in the composition of one nature is after the manner of substantial act and potency; but in the composition of one person it is after the manner of an integral nature and its term. And this reason can also be accommodated to beings as composed of genus and a difference per se contracting it within the proximate predicament; for genus and difference too are compared as potency and act ordered per se to constituting one complete and integral thing in its genus, although this composition is rather rational than real, and therefore can less impede the real and per se unity of being.

9. Besides these, however, there is another mode of composition in beings, which is called from integrating parts, which is first seen in quantity, but through it is understood also to be in material substances and accidents; and this too does not take away unity per se when it is through true and natural continuation. For so continuous quantity is properly and per se one in its genus; but the parts of which it consists are not said to be simply several in act, but in potency, as Aristotle often says, Metaphysics III, c. 6, and Metaphysics V, c. 13, where he says that number properly is only where the parts are not joined by a common term. And Averroes says the same, De Anima III, text 23. And the reason is that quantity by its nature postulates this extension and composition, which is wholly ordered to its completion in its genus, and therefore within it it has proper terms by which its parts can be joined and terminated. That whole composition and union, therefore, is per se and by its nature ordered to composing one being within the same genus. And although this belongs per se primarily to quantity taken according to itself, it nevertheless belongs also to material substance, which underlies quantity, as is seen first of all in homogeneous substance; for fire, water and the like are one per se even if they are taken in any magnitude whatever, provided they are continuous; otherwise a substance of this kind could never be one per se, because it can never not consist of these parts, even if it is taken in the least quantity, which is against all philosophers and against the common mode of thinking and speaking, and against the reason given above, because these beings by their nature postulate this kind of union and composition for their completion and integrity in their genus; therefore such composition does not take away unity per se in beings of this kind.

10. It is necessary, however (although this is to be treated more fully below), to notice briefly here what substance has from quantity in this kind of composition, and what substance itself has from its own substantial entity, although under quantity; for in the former way from substance and quantity one per se, as we are now speaking, is simply not made, because quantity is not of the completion of substance within the notion and breadth of its genus, and therefore quantitative integrity, as it is adjoined to substance and makes one with it, does not constitute being nor one per se. But material substance under quantity has its own substantial entity, in which it also has entitative parts composing and integrating the substantial entity itself, and having among themselves their substantial union; and in this way we say that substance so composed is one per se.

11. This, however, has some difficulty in heterogeneous substances, because their parts do not seem to be so intrinsically united and continued, but only bound together as it were by certain bonds. But nevertheless this substance too as so composed is one being per se. For who would deny that man is one being per se? And a posteriori this can be declared, for all parts of this kind serve one another, and separated per se they either cannot be preserved at all, or not for long; it is therefore a sign that they are all incomplete beings in their genus, and are ordered per se to composing some being; therefore that as so composed is being per se and one per se. Whence for this it is enough that those parts naturally have some conjunction and connection, whatever it may be; for it suffices that all can be informed by the same form, and agree to constitute with it one being having one being simply. Add that, although these heterogeneous members are not on every side immediately continuous with one another, they nevertheless always have continuation on some side, at least in some third thing, as in a nerve or other similar part, of which elsewhere.

12. From these things, then, an induction having as it were been made, it is sufficiently evident how in all substances being one per se consists in the notion explained by us. But almost the same induction can be applied to accidents; for of quantity it has already been said; but others, if they are altogether simple according to the thing, evidently have unity and indivision per se; but if they are composite, in order to make one per se they must in some way imitate quantity. For only a twofold composition can be understood. One is after the manner of extension, in which way there is one whiteness which is extended in the surface of one body; and this composition makes one per se after the manner of an integral whole. For the parts of that whiteness are so related that within their genus they are bound together and united in a mode proportioned to themselves and constitute one complete and integral being in their species; which composition and union those parts have under quantity or in quantity; yet they do not have it intrinsically and formally through quantity itself, but through their partial entities united among themselves by a proper bond and union of their genus. Which can be explained by this reason; for, if in a continuous surface of the same body, for example of a wall, half the part is white and half black, whiteness and blackness have indeed a certain continuity on the side of the subject, because the surface in which they inhere is also continuous, and nothing can be marked in it, however indivisible, which is not affected by whiteness or blackness; and nevertheless whiteness and blackness do not have among themselves the intrinsic union and conjunction which two partial whitenesses have among themselves; and therefore from them one is not made per se and properly, as it would be made from parts of whiteness; which same thing it is probable can happen in its own way in substances, if it happens that under the same continuous quantity there are substantial forms of diverse species under diverse parts of the quantity, as St. Thomas noted, In Metaph. V, text 7, lect. 7, letter D. Another composition in accidents can be after the manner of intension, supposing that the degrees of intension are in some way distinguished in the thing; of which elsewhere. And this composition, although, speaking per se, it does not come about in quantity or through quantity, is nevertheless to be understood and explained through proportion to it. Whence from such composition too one per se results, because all those degrees are as it were partial and incomplete beings within their genus, and by their nature are ordered to completing one thing within the same genus, and have among themselves a natural union and proper terms by which they may be joined or terminated. Therefore in accidents too the notion of being or of one per se consists in the aforesaid notion explained by us. But if perhaps in accidents another mode is found of making one out of many beings besides those mentioned, as in quantitative number, or, according to the opinion of some, in the habit of science, which arises from the collection of many species or habits, those are to be judged beings not per se but per accidens, in the proper and true notion of being, as Fonseca rightly taught, Metaphysics V, c. 7, q. 5, sect. 2, because they do not have among themselves any true and real union through which they would effect one per se, whatever may be the case whether under some predicamental notion they can be judged per se, of which below, in explaining the individual predicaments.

The notion of being and one per accidens

13. From the things which have been said of being and one per se, it may be gathered what must be said of being and one per accidens, which is distinguished from it; for first of all everything which consists of distinct things without physical and real union of them among themselves is rigorously being per accidens and not per se. It is proved both from what has been said, because in such a being the notion of being per se explained by us cannot be found; and also because that one cannot have one real essence; for one essence cannot be understood unless either because it is simple, or because it arises through the real union of many; but in the aforesaid case neither of these is found. Next, every being which is so one that it consists of distinct things, of which one is a complete being in some genus and through the adjunction of the other is perfected by a perfection of a diverse genus, such a being too is rigorously one per accidens, because the notion of being per se explained by us does not belong to it, nor can one true essence be found in such a being. Likewise because, by the very fact that one being is complete and integral in its genus, what is adjoined to it comes accidentally, and therefore it is said to compose one per accidens with it; and by this reason that which consists of things of diverse predicaments and diverse from the nature of the thing is truly said to be one per accidens. Rather, even in things of the same predicament this holds true, if they are of diverse genus or species, and one happens to the other in its notion and species already complete; and in this way from a potency and a habit, or an act, one per accidens comes about; and similarly a gilded silver vessel is being per accidens, and so of the others.

14. Secondly it is gathered from what has been said that in being one per accidens there is variety, and in it more or less. For one is being altogether by aggregation, in which many beings, integral and perfect per se, are heaped together without any union and without any order; and this seems to be most of all per accidens, because on every side it is opposed to being per se properly taken; and of this kind is a heap of wheat or of stones. But another is being per accidens consisting indeed of beings integral per se, not having physical union among themselves, but having some order among themselves, as is an army, a commonwealth, a house, and other similar artefacts, in which there can be as great a variety and as great a difference according to more and less as there can be greater or lesser union between the beings per se of which it consists; and in this way a tree into which a branch of another species has been grafted seems more one than a house, and a house more than an army; and so of the others. And in this order are to be placed mixed liquids, composed of simple ones imperfectly altered, as watered wine, oxymel, etc. Whence it also comes about that, although these are simply and absolutely beings per accidens, nevertheless respectively, that is, in comparison with that being which is one by mere aggregation, they are sometimes wont to be called beings per se. For, because intermediate things participate something of the extremes, in comparison with them they are wont to be called by diverse names; but beings of this kind agree in some way with beings per se, in so far as they are united in some form or relationship, and therefore they are sometimes so named. In which way Aristotle seems to have spoken in the cited place of Metaphysics V. Nevertheless, by this consideration and comparison, being composed of substance and an accident inhering in it seems much more able to be called being per se; for this is the third genus of beings per accidens, which seems to depart more from that first and lowest being by aggregation, and to approach more to one per se, because both the things of which it consists are not distinguished in supposit, as in the others, and they have among themselves a greater physical union, and one is truly in potency to the other, although an accidental potency, and the other by its nature is ordered to the other, and in union with it has its connatural perfection; in all of which such a being imitates that which is properly and per se one, although simply and absolutely it is one per accidens.

Of one simply and in a certain respect

15. Thirdly, from what has been said the other divisions of one are easily explained. For one kind can be called one simply, another in a certain respect. That is properly and rigorously called one simply which is one per se; but all the others can be called one in a certain respect; which seems manifest from the terms themselves; for being one per se is so called because it has unity simply and absolutely; but the others, because they depart from this unity, are called per accidens. This is evident also from the definition of one; for it is being undivided in itself; that, therefore, which is undivided simply will be one simply; but what is simply divided in itself, and has only some indivision in order to some end or to some form, will be one only in a certain respect; and so it happens in those things which are one only per accidens, as is evident from what has been said. Otherwise Gregory, In I, dist. 24, q. 1, and other nominalists there say that only simple being is one simply, because, in order to be one simply, it is necessary that there be nothing in it which is not itself; but this definition has been gratuitously devised by them, and according to it God alone would be one simply. Likewise it is repugnant to Aristotle, Metaphysics X, in the place cited, who distinguishes one into the indivisible and the merely undivided. For it conflicts with the common mode of conceiving and speaking; for being, although composite, is called being per se and simply; why, then, would it not also be called one simply? Likewise such a being is not many simply; therefore it will be one simply, because these two are opposed immediately and as it were contradictorily. Finally, by this reason the theologians teach that Christ, as composed of God and humanity, is one simply.

16. Here, however, two things seem to be observed: first, that it is one thing to say that some thing is one simply or in a certain respect, another that two things are one, in the way in which soul and body are said to be one humanity, or several men one. We are here speaking in the former way; for that is proper and absolute, that is, according to the absolute consideration of being and one according to which notion one is an attribute of being, and not according to the comparison or relation of one thing to another; indeed not even according to a comparison of reason of the same thing to itself, because, as I was saying above, this relation of reason of identity is not of the notion of one, which is absolute. But the latter manner of speaking, in order to be true, must be not so much formal as causal, as is evident in the said examples; for matter and form properly and formally are in truth not one, but compose one; and similarly several men are not so much a people as compose one people, and so of the others; and so that unity which is found in many, whatever it may be, supposes first according to reason some being constituted from them, which is proximately and immediately denominated one; and in this sense is to be understood what is wont to be said, that several things simply are one in a certain respect, as we shall touch on again in the following section.

17. Secondly it is to be observed that the discussion here is of the unity of the thing and not of the unity of reason; for the unity of reason (since it is not in things, but from the intellect) is properly not comprehended by the division posited; if, however, anyone wishes to reduce this unity to the said division, this will be unity most of all in a certain respect; and of this kind is the unity of genus, species, etc., in so far as it is effected through the comparison and denomination of the mind; which can also be greater or lesser in its order, according as it includes greater or lesser indivision according to reason, or according as it is founded in a greater or lesser agreement found in those things. But whether this foundation which precedes in things deserves the name of unity, we shall say afterwards.

18. And hence further the other terms which some use remain explained, as may be seen in Fonseca, in the said q. 5, sect. 6, namely that one is sometimes said of something absolutely, sometimes comparatively, as what is one with itself, or one with Peter in the notion of man or animal, etc. Likewise, that sometimes something is called one in itself and according to its proper notion, as Peter is called one in number; but sometimes something is called one in a superior or inferior notion, as animal in the notion of living thing, or in man. But these in truth are improper, for one is properly said only absolutely; but that comparative unity is not unity according to the thing, but either identity according to reason, or likeness founded in some unity, or certainly it is unity according to reason. And similarly no being is properly called one except according to its proper notion; for according to a superior or inferior notion something is not called one, except perhaps secondarily and by reason of another.

19. Finally it is necessary to note that some unity can be considered in things which belongs to being by reason of its entity, or in it precisely considered; but another unity can be understood belonging to one being through another being adjoined to it; as, for example, in matter (as we were saying above), let us understand entitative unity, belonging to it in its entity and by virtue of it, even if it is precisely considered and separated in the mind from quantity and from any other accident; but another unity is understood in matter by reason of quantity, from which it is called one quantitatively or numerically; and the same can be considered in whiteness and in other corporeal beings; for in immaterial ones only the former mode of unity is found. The unity, therefore, immediately belonging to entity by itself can be called unity per se, not in the sense in which we spoke above of being and one per se, but as per se is distinguished against through another; which mode of unity is found in every being in the way in which it is being, so that even being per accidens, in the way in which it is one per se and not through another, has that unity; and therefore this is the unity which belongs per se to being as being; and to remove equivocation it could be called intrinsic or entitative unity; for the other unity, which belongs through another, is accidental and as it were extrinsic, or denominative, of which more in the fifth section.

1. Hitherto we have only declared the notion of one and its various modes; but since this whole disputation tends to this, that we show that this attribute belongs to being, two things remain to be done. First, that we declare how this property is convertible with being and is its adequate attribute. Secondly, that we declare to which unity this belongs, which we shall do in the following section.

2. Concerning the first, the reason for doubting is that being is divided by one and many, as is evident from Aristotle, Metaphysics X, c. 1, and from St. Thomas, I, q. 11; indeed many contend that this is the first division of being, as Soncinas at length, Metaphysics X, q. 1; but a dividing member cannot be convertible with the thing divided; therefore neither one with being; therefore it is not its attribute. And it is confirmed; for one and many are opposed, on the testimony of Aristotle above; therefore they cannot belong to the same thing; therefore being which is many is not one; therefore one is not an adequate attribute of being.

3. In this doubt it must briefly be said that unity or one is an adequate attribute of being. So it is taken from Aristotle, Metaphysics IV, c. 2, text 3, saying that being and one follow each other mutually. Plato taught the same in the Parmenides, saying: Neither is being lacking to one, nor one to being, but these two rather are made equal throughout all things. The same St. Thomas, I, q. 11, aa. 1 and 2, and all philosophers. And it is evident by reason, first, because among the attributes of being one is placed in the first place, as we saw above; therefore it is necessary that it be convertible with being, because it is of the notion of an attribute properly so called that it be adequate to its subject; and therefore one is placed among the transcendentals, as being itself is. Secondly it is declared from the thing itself, because true and real unity supposes or includes entity, as was seen above; for what is nothing cannot be called one except equivocally and by extrinsic denomination; but upon every entity as it is entity indivision in itself follows or is necessarily conjoined; for if it is actually divided, as such it is not entity but entities; therefore the notion of one runs adequately with being. Thirdly, because every being is simple or composite; the simple is not only undivided but indivisible, in so far as it is simple; but the composite too, as it is such, is undivided; for if it is actually divided, it will not be composite. Therefore every being, both simple and composite, is one; but what is neither simple nor composite is not being; but will be either nothing, or several beings.

The division of being into one and many is explained

4. To the reason for doubting posited, then, St. Thomas answers, I, q. 11, a. 1, ad 2, that that which is undivided in one way can be divided in another, and that what under one notion is many can under another be one: And by this reason (he says) being is divided by one and many, as by one simply and many in a certain respect; for multitude itself too would not be contained under being unless it were contained in some way under one. And he adduces Dionysius, last chapter of On the Divine Names, saying that there is no multitude which does not participate in some way in unity; for things which are many in their parts are one in the whole; and things which are many in accidents are one in subject, etc. From which answer it is understood, first, that, formally and properly speaking, being is not divided into many as they are actually and formally many, because many of this kind, in so far as they are such, are in truth not being, but beings.

5. In two ways, then, multitude can be placed in the division of being: first, if it is understood not of actual multitude, that is, actually divided, which alone is properly multitude, as is evident from Metaphysics V, c. 13, text 18, but of multitude only in potency, in which way in the continuum there is said to be a multitude of integrating parts or of points, and in human nature a multitude of essential parts. And in this way St. Thomas seems to have understood the division, when he says that being is divided by one and many as by one simply and many in a certain respect; for that is one simply in which there are not many actually divided; and conversely those are called many in a certain respect which in the thing are not actually divided or disjoined, but only in potency. Whence in this sense these members, speaking per se, need not be distinguished in the thing, but in reason only; for the same being which is one simply is many in a certain respect or in potency, as is evident in the examples posited; unless we wish to understand those members with prescission or exclusion, in this way, that some being is so one that it is in no way many, neither in act nor in potency; but another is so one that it is also many in a certain respect or in potency or accidentally; in which sense that division will coincide with the division of being or of one into simple and composite. And according to this mode of interpreting it is easily evident that this division in no way stands in the way of the adequation of being and one; for that multitude does not exclude unity simply. Finally, in this sense it can be understood that in that division being is divided not as it is common to being per se and per accidens, but being per se itself, because among beings per se there are some which, although they are one in act, can nevertheless be many in potency.

6. In another way, however, that division can be expounded of multitude simply and properly, in which way Cajetan seems to have understood it when he says that those words of St. Thomas, in the said solution ad 2, being is divided by one and many, as by one simply and many in a certain respect, are to be so understood that simply and in a certain respect fall not upon one and many, but upon the verb is divided, that is, being is divided by one and many in such a way that one is being simply, but many in a certain respect. And in this way conversely it must be said that multitude is placed in the division of being in so far as it happens that things which are many simply are one in a certain respect. Whence the other member is understood of one simply and absolutely; and in this sense those members are always distinguished not by reason only but in the thing itself, because they include contradictory or privative opposition on the side of division; for those things are many simply which are actually divided in themselves; but that is one which is not actually divided in itself. And according to this sense too this division coincides with that by which being is divided into one simply and one in a certain respect; for many simply do not divide being except in so far as they are one in a certain respect. Whence it also comes about that the thing divided in this division so explained is not being per se, but that which is divided into being per se and per accidens; for every being per se is one simply; but many are not called one in a certain respect except in so far as they constitute some being per accidens, and so they cannot be placed in the division of being except at least under the notion of being per accidens; therefore the thing divided in that division cannot be being per se; for it would be repugnant to one member that it be convertible with the other; it must therefore be being abstracting from per se and per accidens. And so it is finally understood how the aforesaid division is not repugnant to the adequation of one and being; for it pertains to it that each thing be one as it is being, so that, if it is being per se, it is also one per se; but if it is being per accidens, it is also one per accidens; and as being can be signified abstractly, so also one; and therefore, as being in this sense is divided into one and many, so one itself too could be divided in the same way; for, as I said, it is the same as if it were divided into one simply and one in a certain respect.

1. From the things which have been said, some doubts which are wont to be treated by authors about this division can easily be defined. The first is whether this division is analogous or univocal.

2. The answer is that, if it is understood in the latter sense, it is analogous and almost equivocal, because the division of being into being per se and being per accidens, to which the aforesaid division is equivalent in that sense, as has been said, is analogous, by a certain analogy of proportionality, so that to being so taken one common concept does not correspond, because being per accidens as such is in truth not being but beings, and is only called being on account of a certain proportion or imitation of being per se. This opinion is proved first of all from Aristotle, Metaphysics IV, c. 2, at the end, where he openly teaches that analogy intervenes here. Next by reason, because things which are many simply are not one simply; for these two are altogether opposed; therefore neither are they being simply; for being and one, if they are taken in the same proportion, are convertible; therefore being is not divided univocally into one and many, but analogically. And St. Thomas indicated this, I, q. 11, a. 1, ad 2, according to the exposition of Cajetan adduced and declared above. Next, that this analogy is as great as we have said is declared in this way: because to be undivided is of the notion of one; but this indivision is not found in one per accidens of this kind except very analogically and almost equivocally, because in it are found many things actually divided, and the indivision is only according to a certain apprehension or relationship; therefore the notion of one does not belong to such a multitude except through a certain proportionality or imitation; therefore the notion of being belongs to it in the same way, because, as has been said, being and one correspond to each other with proportion. Likewise, because being is said from essence or from existence; but in that multitude there is not an essence nor an existence, but rather essences and existences.

3. You will say that this at most proceeds of those things which are so many simply that they are in no way one except by aggregation, as in a heap of stones, etc., because there in truth there is not unity but a certain nearness, which cannot be called unity except through a certain proportionality, as has been rightly declared. But in other beings per accidens, which have some union or coordination of parts, by reason of which they can in some way be called one per se, as we said above, the reason given does not seem to proceed, nor so great an analogy to intervene; for these seem to be comprehended under one concept of one transcendentally taken; for they have some real unity and indivision which is founded in the things themselves.

4. The answer is that this is indeed probable, especially when a physical and real union intervenes, as between substance and an accident intrinsically inhering in it; for in such a composite, just as there is a true and physical union, so there is some real unity, which, although it is not as great as that in the substantial composite, nevertheless has a real agreement with it, such as there is also between those unions; that, therefore, will suffice at least for the unity of the concept, granted that it be with some analogy, which depends on what is to be said below about the analogy of being. But of other artificial beings the matter is more doubtful, because there does not intervene there a real and physical union, and consequently neither a real indivision; therefore neither a real agreement in unity which would suffice for the unity of the concept in the notion of being or of one. Nevertheless the opposite can easily be defended, because that very composition with some conjunction or coordination is some union, which suffices for these beings to be conceived as in some way one per se; on account of which we said above that it is probable that under that notion they are directly contained under the object of metaphysics, and that there can be science of them as such; this, therefore, will also be enough for them to be able to be conceived under one transcendental concept of one.

5. And hence it follows a fortiori that, if that division is understood in the former sense explained above, so that the thing divided is being per se rigorously so called into one which is in no way many, and one which is many in potency, then much more is one divided according to a certain common concept of one per se or simply, because to be many in that way, namely in potency, does not exclude unity simply, as has been said; yet all analogy does not seem to be excluded from that concept, because God, who is contained in it, as he is not univocally being, so neither does he seem to be univocally one with the other creatures.

6. It could, however, probably be said that, although one, as regards the positive thing which it includes or connotes, is not said univocally of God and creatures, nevertheless as regards the included negation it is not repugnant that it be said univocally, because other negative predicates can be said univocally of God and creatures. As, for example, to be immaterial, as it precisely expresses the negation and lack of prime matter, belongs equally to the angels and to God, although the positive foundation of that lack is not univocal in them; so, then, it seems it can be said of the negation of division which one expresses. You will say that this at most proceeds of things indivisible as such, for example of the angel. But against this, first, because, if it is once conceded that transcendental one is said univocally of the angel and God, an argument is taken thence that it is said univocally also of man, for example, because, although man is not as perfectly one as the angel, he is nevertheless univocally one; therefore, if the angel is univocally one with God, man too will be univocally one with both. Secondly it is evident by an a priori reason, because one precisely expresses the negation of actual division; but this negation is integrally and perfectly found in being most properly and per se one, even if it is composite. But that in an indivisible substance something more is found besides that negation pertains indeed to a certain greater perfection of entity or of unity, yet does not suffice for analogy in the notion of one. Whence, since otherwise with respect to this negation there is no proper dependence or causality except by reason of the foundation, there seems to be no sufficient reason of analogy in it. Thirdly the same is confirmed, because otherwise prime matter, for example, would be more perfectly one than composite substance; and the same argument can be made of the soul, indeed of any simple accident whatever with respect to composite substance, and of the point with respect to quantity; for with respect to all it follows that one is analogous and is said first of the simple, although most imperfect, being.

7. But although these things are said probably, nevertheless it must simply be said that transcendental one is said analogically of God and creatures and of all those things of which being is said analogically, because (whatever may be the case with the negation) one does not formally express negation alone, as was seen above, but undivided entity or essence; and therefore where the essence is not univocal, neither can real unity be univocal. Likewise, because, as Aristotle said, Metaphysics IV, text 2, as regards the thing it is the same to say one and one being; therefore what is not simply being cannot be simply one; therefore what is analogically being will also be analogically one. This, however, holds most of all in God, in whom not only is the essence as such of another order, but also, as it founds the negation of one, it has a certain perfection of another notion and order. But in those beings in which, although the essence is more imperfect, nevertheless as it founds the negation of division it has a certain excess of simplicity or indivisibility, it can in some way be said that the notion of one is more perfect as regards the negation, but not simply, on account of the reason given. And hence again what was said above is confirmed, that one does not formally express the negation alone, but entity under negation.

1. In this matter Aristotle, Metaphysics IV, c. 2, indicates that one and many are opposed privatively. But in Book X, c. 1, he thinks that they are opposed neither relatively, because one is not said in relation to another; nor contradictorily, because neither is a mere negation, for neither can truly be said both of things which are not and of things which are; nor merely privatively, because neither consists in privation alone, but expresses something positive; nor finally merely contrarily, because they formally include some negation; whence he concludes that they are opposed in a certain way contrarily and in a certain way privatively. St. Thomas, however, I, q. 11, a. 2, thinks that this opposition approaches more to privative, because one (he says) is opposed to many as the undivided to the divided.

2. In order, however, that this may be explained more fully, it is to be considered that many can be compared to one in two ways: first, as they are many; secondly, as they are in some way one; in which way we said that multitude is a member dividing being in that partition by which it is divided into one and many. Wherefore, speaking formally of multitude as it is a member of that division, it differs from one simply so called as the imperfect from the perfect, and so they are as it were two disparate and distinct notions. Just as, if we consider number under the notion of one discrete quantity, or suppose that it has one formal notion as such, it will be distinguished from unity as a certain formal notion distinct from the formal notion of one, as two disparate natures or species are wont to be distinguished, or as the line is distinguished from the point. But considering multitude as it is multitude and a mere aggregation of several, we can then consider either only that which is positive in unity and multitude, and so they are related after the manner of whole and part, because multitude results in this way from unities; or we can consider the included negation, and so each includes some negation; for multitude, by expressing many positive beings, includes this negation, that one is not the other, which can be called the negation of identity; but one expresses the negation of division. And so they seem to be mutually opposed privatively according to diverse notions; for one includes the negation of division, which is of the notion of multitude; but multitude includes the negation of identity or real conjunction, which is of the notion of unity. Yet, because multitude includes unity and requires indivision in the individual unities of which multitude itself consists, but one conversely does not include multitude, nor the division which is of the notion of multitude, but rather removes it, therefore one is simply said to be opposed to multitude after the manner of privation, rather than conversely.

3. Whence, although St. Thomas, above, ad 2, says that unities compose multitude according to what they have of entity, not according to what they have of indivision, which he repeats in other places, as De potentia, q. 9, a. 7, ad 10 and 14, this nevertheless seems to be understood with proportion, namely of multitude in so far as it is something positive. But if all the things which multitude includes are considered, it seems it must be said otherwise; for, as the same St. Thomas says, I, q. 11, a. 2, ad 4, and in the said question of De potentia, a. 7, ad 15, in the understanding of multitude is included being divided from another, and that each of them is one in itself: for however much (he says) things are understood as divided, multitude will not be understood unless each of the divided things is understood to be one, and consequently undivided; it follows, therefore, that one composes multitude as regards all the things which are of its notion, not only by reason of the positive but also by reason of the negation which one expresses, because it is of the notion of multitude not only that one thing is not another, but also that each is undivided in itself, because otherwise they would not compose a certain and determinate multitude. Nor do I sufficiently understand what Cajetan means on the aforesaid solution ad 2 of St. Thomas, saying that multitude formally arises from unities formally, and consequently from negations, and nevertheless that the indivision of unity does not concur to compose multitude in so far as it exercises the privation of division, but in so far as it has the notion of being. For what is it for a privation to have the notion of being? For if this is said only by reason of the entity in which it is founded, it is repugnant to his former saying and to the reason given by us; but if the negation is said to have the notion of being in so far as it can be conceived after the manner of being, then the division is irrelevant, because it has this only by extrinsic denomination, and so the negation is rather only a being of reason than having the notion of real being, of which Cajetan speaks.

4. Finally, one and many can be compared in the notion of measure and measured, and in this way they can have a relative opposition, whether that be a real relation or one of reason, which seems more so, because this notion of measure seems to consist only in a certain extrinsic denomination, and to be founded more in our apprehension and use and mode of knowing than in some relation or relationship which is in the thing. Whence St. Thomas, in the said a. 2, attributes this opposition of measure and measured to quantitative unity with respect to number, which is in quantity, not to transcendental unity and multitude; which I do not see why it could have been said, except in order to human use or according to a certain denomination resulting thence; for, if the things themselves are considered according to themselves, transcendental one keeps the same proportion to its multitude as numerical or quantitative one to its number, because it is its principle and composes it, whence it can also be measured by it.

1. The Thomists speak in this matter in a diverse way of unity and multitude, of division and indivision. For they say that unity is by its nature prior to multitude, which is certain and self-evident; both because, speaking per se, one is independent of multitude in every genus; for one does not depend on many, but many on one, nor is one defined through many, but multitude is defined through unity; and also because one is the principle and composes multitude; whence also as regards the consequence of subsisting they are not convertible; for, if there is multitude, it is necessary that there be unity, but not conversely.

2. Of division and indivision, however, some say that division is by its nature prior to indivision and unity. So Soncinas teaches, Metaphysics IV, q. 23, ad 6, and Metaphysics X, q. 4; and Javellus there, q. 6; but Cajetan, I, q. 11, a. 2, around ad 4, uses a scarcely intelligible distinction; for he says that division is prior to unity simply according to itself, yet in intelligible being, and that it is posterior to unity simply, that is, according to being simply, which is to be in the nature of things. The former part he proves, because affirmation is prior to negation; but to be one is to be this, and not to be not-this; therefore division between those contradictory extremes naturally precedes unity; but the second he proves, because the negation of one being from another, which is a real negation, is posterior to unity; from which reasons the sense of the former distinction proposed by Cajetan is understood; for by negation in intelligible being he seems to understand the division of being from non-being, and of each being from such non-being, which others call a negation of reason only; but by negation according to the being of the thing he understands the division of one being from another, which is wont to be called a real negation. But, as is evident from what has been said above, the division which unity per se primarily denies is neither of these, but is the negation of the real division of the being itself in itself, and it is about this division that it is inquired whether it is prior or posterior to indivision.

3. And it seems to me indeed that division of this kind is in no way prior according to the thing to one or to the indivision included in it; for, if we compare these two generally and in their whole breadth, it is prior that some being be undivided in itself than that there be some division of one being from another or of some being in itself; but if we compare them in individual beings, each by its nature has indivision in itself prior to division. What division, then, or in what subject, is said to be or is according to itself prior to indivision or unity? Next, there is no reason which persuades the contrary, because, although indivision is opposed to division after the manner of privation, it is not therefore necessary that division be prior: first indeed, because, although in things which are properly and rigorously privatively opposed the habit is by its nature prior to the negation, because such a privation is only in a subject apt by nature, which by its nature regards the habit prior to the privation, nevertheless in privation broadly taken and improper, such as is the indivision of one, as has been explained, it is not necessary that the habit be prior to the negation; as, although immaterial privatively taken expresses a negation, it is simply prior that there be the immaterial in things than the material, because it does not express a privation properly so called and in a subject apt by nature which of itself would postulate first to be material rather than immaterial; and in man, for example, it is prior in the order of generation that he lack teeth than that he have them, which lack, although for the time of infancy it does not have the most proper notion of privation, nevertheless approaches it more than the negation of division which the indivision of one expresses; therefore much less is it necessary that in the present case division be by its nature prior to indivision. And therefore St. Thomas, I, q. 11, a. 2, ad 4, rightly taught that division is prior to unity not simply, but according to the notion of our apprehension.

4. Comparing these two, then, according to themselves and by their nature, as unity is prior to multitude, so indivision is prior to division; but as regards us division is said to be prior to indivision, because, since indivision is known as a negation, it is necessary that that of which it is the negation be apprehended first, because as regards us affirmation always precedes negation; this, however, will have to be understood of indivision taken formally for the negation, or for the foundation of the negation, according to the various modes of explaining the indivision of one which we treated above. And Aristotle speaks in the same way, Book X, text 6, of one or its indivision with respect to multitude; for he says that multitude is prior in reason on account of sense, in which last word he sufficiently declares that he speaks of priority as regards us; and so St. Thomas expounded it there, lect. 4. And he declares that this is to be understood of multitude by reason of division only; for, if multitude is taken according to the whole of what is of its notion, then even as regards us multitude is posterior, because it is nothing other (he says) than an aggregation of unities. Whence, although things which are divided are many, they nevertheless do not have the notion of many except after it is attributed to this and that that it is one.

1. Scotus, In I, dist. 8, q. 3, and in the Quodlibet, q. 5, a. 1, denies that this is the first division of being, but another by which being is divided into finite and infinite, because these two members formally contract being in so far as it is being; but the others contract being in so far as it is one; therefore that division is prior to this. The consequence is evident, because, just as the notion of being is prior to the notion of one, so also that division is prior which belongs to being as being than that which belongs to being as it is one; for that division belongs to being as it were per se in the first mode, this one per se in the second mode; just as, if in man there could be various modes of rationality and risibility, the division of man through the modes of rationality would be prior to that through the modes of risibility. The antecedent as regards the first part is declared, because essence is what constitutes being in so far as it is being; therefore the first diversity of essences as such is also the first division of being in so far as it is being; but one essence, as essence, differs from another in so far as the one is of so much essential perfection, the other of greater or lesser; and this is the first reason which being posited, and all others prescinded, the diversity of essences remains, and when it is taken away it does not remain; but this kind of diversity is found primarily and per se between the infinitely perfect essence and all the other finite ones; therefore the first division of being is that into finite and infinite. But the other part of the antecedent is evident from what has been said above, because those two members, namely one and many, in order to be able to divide being, must be equivalent to the division of being into one simply and one only in a certain respect, or into one per se and one per accidens; but this division formally taken is the division of being as it is one; therefore. But if anyone contends that being as being too can be divided through these two modes of unity, the same argument can return; for so this division will be as it were denominative (so to speak), for it will be a division through a property of being, whereas the former is essential, or through modes contracting being per se primarily and essentially.

2. But the Thomists contend that the first division of being is into one and many, or into being per se and per accidens. So Soncinas holds, Metaphysics X, q. 1, who attributes this to St. Thomas, I, q. 11, a. 2, ad 4, and In I, dist. 24, q. 1, a. 3, since he says that first there falls into the intellect being, second division, third one, fourth multitude. The foundation is that one is the first adequate attribute of being as being, belonging to it also as it abstracts from finite or infinite; therefore it belongs to being prior to finite or infinite. But first of all nothing can be gathered from that place of St. Thomas, because there he is not treating of the comparison of the division of being into one and many to other divisions of being, but of the mode and order in which one and many are conceived by us. That reason too is of no moment, because, in order that the comparison be made rightly, it is not to be made between one as it is an adequate attribute of being and the modes contracting being; for so Scotus would not deny that one belongs to being prior to finite and infinite or other similar modes, just as a property adequate to a genus and convertible with it is understood in reason to belong to it prior to the inferior contracting differences, because such a property belongs to it according to itself and precisely, but the contracting difference belongs by reason of the inferior. Rather, even if the opposed modes contracting being are taken disjunctively and attributed to being after the manner of one complex property, namely finite or infinite, etc., still one, as it is an adequate and incomplex property, will have to be judged prior in reason, either by the very fact that it is simpler, and according to itself more adequate and less dependent on the conception of another. All the more because, as I said above, these complex or disjunct predicates are in truth not properties of being in so far as it is being, because they essentially divide being itself. In order, then, that the comparison be made properly, it is necessary to speak of one according to the determinate modes of one, and in this way the reason given does not proceed, as is self-evident.

3. Otherwise, then, Javellus, treatise I De transcendentibus, c. 1, proposing various divisions of being, says that the first is into real being and being of reason; the second, of real being into one per se and per accidens; the third, into absolute and respective; the fourth (which is the third of real being) into one and many; the fifth, into the five transcendentals; the last, into finite and infinite; which order of divisions he confirms by no reasons. But what pertains to the present dispute, namely that, comparing those two divisions, namely into one and many, and finite and infinite, the former is prior to the latter, he proves by this apparent reason, because being is not divided into finite and infinite except in so far as it is good; but the other division, as has been said, is given of being in so far as it is one. Therefore this is prior to that, as the attribute of one is prior to the attribute of good. The major is evident, because finite and infinite divide being according to various grades of perfection; therefore they divide it as perfect; therefore as good; for perfect and good are the same. Whence also Scotus, because he thinks that there can be some real being which does not formally express perfection, premises another division, saying that being is first divided into quantified and non-quantified, namely by quantity of perfection, and afterwards divides quantified being into finite and infinite; therefore according to his opinion being is here divided as quantified or perfect. In which too Scotus seems to indicate that that division into absolute and relative is prior, because only relative being is called by him non-quantified, because relation as such does not express perfection. Whence it consequently comes about that only absolute being is divided into finite and infinite, which Javellus too teaches.

4. In this question it is necessary to suppose that the discussion is of real being, for being of reason, as was said above, does not have a common concept nor real agreement with real being, and therefore the division of being into real being and being of reason is not rightly numbered among the divisions of being, because it is rather a division of the name than of the thing; but here we are not treating of the various significations of the same word, but of the diverse modes in which the concept of the thing signified by the word can in reality be determined or contracted. Finally, here we are dealing only with the division of being which we said above is the proper object of metaphysics; but this is not being as it abstracts from real being and being of reason, but real being only.

5. Again, by the same reason it must be asserted that divisions of this kind are not to be understood with respect to being as it is divided into being per se and per accidens, taking being per accidens strictly for being altogether by aggregation; for, as was also shown above, such a division is not of some common concept, but of the word only according to an imperfect analogy of some proportionality. On account of which we said that being taken in that breadth is not the adequate object of this doctrine, but only real being per se, in the way in which it can have some unity of reason or concept founded in things, by reason of which it is capable both of real properties and divisions. And hence it comes about that, if that division of being into one and many is taken in the sense in which it coincides with the aforesaid division of being into per se and per accidens, then indeed it can be called prior to the division of being into finite and infinite, in the way in which the division or equivocation of the word is prior in every doctrine to be explained to the thing being divided in reality; in which sense that division into being of reason and of the thing too can be called first. Properly speaking, however, of real divisions contracting or dividing the adequate object of this science, that one cannot be counted in this order any more than the division of being into real and of reason, because in it too the word only is common, but not the concept, as has been shown.

6. It remains, then, that we compare these divisions in so far as in them real and per se being most commonly taken can be divided. These divisions, however, can be compared either in universality, for so one division can be called prior to another because it is more universal, and the other is in some way contained under it; or in the greater diversity and distance between the dividing members, for so that division can be called prior in which the dividing members are primarily and more distant among themselves; or finally they can be compared in the relationship of the dividing members to the thing divided itself, for so that division seems to have to be called prior in which the dividing members more per se and formally contract the thing divided according to its proper formal notion, as was declared in arguing for each opinion cited; nor does it appear by what other reason one division can be called prior to another.

7. From these things, then, three things seem to be able probably to be said in this dispute: the first is that, as regards universality, neither of these divisions is prior to the other; for each is adequate to being and embraces its whole breadth, nor is one in any way contained under the other or a subdivision of it; this is self-evident, because the thing divided of each is one and the same, as we suppose, and in each the dividing members include an immediate contradiction, by which they exhaust the thing divided. And this indeed is manifest in the division of being into one and many. But of the division into finite and infinite being, according to the opinion of Scotus, the matter is not so clear; for he, with many others, finds a medium between those two members of certain real beings which express no perfection; and therefore Scotus himself, as I was saying above, thought another division of being into quantified and non-quantified should be premised, so that only quantified being could adequately be divided into finite and infinite; whence it consequently comes about that this division so explained is less universal than the other into one and many; for that being which is called non-quantified, as it is being, so also it exists as one. I, however, suppose that the contrary doctrine is truer, and that there is no real being which from its proper and formal concept is not quantified, and consequently either finite or infinite, either simply or in its proper genus, of which we shall speak below, showing that every being expresses some perfection.

8. I say, secondly, that in the division of being just mentioned the dividing members are more distant among themselves and primarily differ than in the other division of being into one and many, and that in this way the aforesaid division is prior. For I suppose that infinite in that division is taken for infinite in entitative and essential perfection, especially because, as is evident elsewhere, only such an infinite is in the nature of things; for in created things there can be no infinite, absolutely speaking, which is not rather simply finite. But within God, whatever is in him is simply and essentially infinite, although according to our prescinded inadequate concepts something, especially relative, can be conceived as infinite only in some genus, infinity simply not being distinctly conceived in it, which is nothing to the present point. Hence, then, the assertion posited is evident, because the first division is given through the first diversity, which is between God and creatures; but the second not so, for under one member of it are contained God and several creatures which are simply and in all rigour one per se; but under the other only other creatures which are not beings per se in that way; but God and the creature are more distant among themselves than any notion of created being can be distant from another notion also created or at least common to God and creatures; for those are infinitely distant simply; but these not at all. This reason is explained in this way, because those two members of being, one and many, differ only according to the greater or lesser unity of being itself, and as far as depends on the force of that division those two members are no more distant among themselves than the unity of an army, for example, is distant from the unity of a man; for, although other beings can per se be more distant in unity, nevertheless by virtue of that division that greater diversity is not explained, but the aforesaid suffices; but finite and infinite being are much more distant among themselves than unity per se and per accidens as such; therefore in this sense that division is prior, as declaring the supreme and primary diversity or distance of being.

9. From which I infer that the same judgement is to be passed on the division of being into uncreated and created, and into being by essence and by participation, or into pure act and being in some way potential; for all these divisions coincide in the thing and under diverse negative or connotative concepts declare the same partition and diversity of being. And by the same reason I think that this division is prior to the division of being into substance and accident, even if they are equal in universality; because uncreated being is more distant, and primarily diverse, from created than accident is distant from substance as such or from created substance, which is the same. And by the same or greater reason that division is prior to the other into absolute and relative, because similarly the former two members are more distant and diverse; for the whole diversity between absolute and relative in creatures is preserved without infinite distance; indeed those two formal notions conceived are not so diverse among themselves that they cannot coincide in the same most simple thing, at least in God; whence also those two notions not only are not distant as created and uncreated being, but also of themselves neither postulates that it be created or uncreated, as the theologians teach in the matter of the Trinity.

10. Thirdly it must be said that, if those divisions are compared formally to the thing divided, then the division of being into infinite and finite is also prior with respect to being as such, although the other is prior with respect to one as one. This assertion the foundation adduced in favour of Scotus sufficiently proves, because the modes signified by finite and infinite are per se and formally determining the notion of being or of essence as such; for every real essence, by the very fact that it essentially includes reality, intrinsically and essentially postulates both some essential perfection and a mode or grade of such perfection. Whence also Cajetan, I p., q. 11, at the beginning, doubting why St. Thomas treated of the perfection and infinity of God before unity, answers that those two are contained within the breadth of the quidditative predicaments, but unity pertains to the attributes of being. Just as in God it is prior according to reason that he be perfect and infinite in essence than that he be one, because those two in our mode of understanding signify the most formal constitution of such an essence, so in created being such and so great an essential perfection of each is prior to its unity; therefore in common with respect to being the division of it through modes of essence primarily and supremely diverse, such as are signified by these words, finite and infinite, is more formal and prior than the division through modes of unity.

11. Nor does the reason of Javellus stand in the way of this; for it is denied that finite or infinite divide being in so far as it is good, speaking formally of good as it is an attribute of being, because, as we shall see below, to have some perfection as such is not an attribute of real being, but its essence; for by the name of essential perfection nothing else is signified than the very essence of the thing, which, in order that it be not feigned but real, must formally be something of perfection; for if it is an essence simply infinite, it is by itself supreme perfection; but if it is finite, it is some participation of that perfection. But what the notion of good, as it is an attribute of being, adds over the perfection of being, we shall say afterwards. But that that division into one and many, in the way in which it has been explained, is more formally a division of one as one than of being as being, is easily evident from what has been said, because those two members, in order to be able to divide being per se, must be so taken that they signify diverse modes of unity: whether by one there be signified that which is so one per se that it is in no way one per accidens, but by many that which is simply one per accidens, although by some reason it is one per se; or by one there be signified that which is so one that in it there is no multitude, even in potency, but by many every being which, although it is one per se, is in some way many, at least in potency; for by all these reasons only diverse modes of unity are described; but it is evident that the various modes of unity contract one more formally than being.

12. In these ways, then, the aforesaid divisions can be compared, nor does any other reason or cause now occur on account of which one division of being can be called prior to another. Whence also it is evident in passing that that order of divisions which Javellus posits rests or is founded on no reason; and especially most improper is that division by which he divides being into the six transcendentals (for of the others enough has already been said); for, since all the transcendentals are equal among themselves and convertible with being, that cannot properly be called a division of being, but is a certain enumeration both of being and of those things which are per se and adequately in being itself. 13. Finally it could be inquired here whether multitude or number as such expresses one real formality, and whether in this there is some difference between transcendental multitude and number which is posited as a species of quantity; but of this matter we shall speak more conveniently below in disputing about quantity.

1. This question can be treated in a twofold sense according to the twofold acceptation of numerical unity, namely either for quantitative unity or for singular unity; for so Aristotle said, Metaphysics III, text 14: Whether you say one in number or singular makes no difference; for in this way we expound the singular as that which is one in number. According to these two acceptations, then, two questions or opinions are to be treated.

Various opinions on quantitative unity

2. The first opinion was that of Avicenna, which St. Thomas reports, I, q. 11, a. 1, and In I, dist. 14, q. 1, a. 3, and In Metaph. IV, lect. 2, and the Commentator in the same place, comm. 3, who asserted that the unity which comes to beings from quantity is the very transcendental unity of things; whence he concluded that one adds quantity over being. Which opinion, taken so universally, is plainly false; both because it will be necessary to say either that there are no beings except quantified ones, or that unity is not an adequate attribute of being, but proper to material beings; and also because in material and quantified beings themselves there exists a proper unity and integrity, which each being has in itself, which is not formally from quantity, although it is not without quantity, as was touched upon in sect. 3, and will be said again in the following disputation and in the disputation on quantity.

3. But if this opinion only asserted that the unity of quantity is one of the transcendental unities, it would have some apparent probability. For, just as being is common to quantity and to the other predicaments, so transcendental one is common to all of them; whence, just as being is determined to the individual predicaments through proper modes of entity, and transcendental being, as included in the individual predicaments, is nothing other than such or such being, so transcendental one is determined to the individual predicaments through such modes of unity, and transcendental one as included in the individual predicaments will be nothing other than such or such one. Therefore transcendental unity in quantity is nothing other than such unity as quantity by its nature postulates. Therefore in this way it seems it can be said that quantitative unity is not distinguished from transcendental, not because it is convertible with it, but because it is a certain subjective part of it, in the way in which it can also be said that quantity is not distinguished from being. And in this way Durandus taught that opinion, In I, dist. 24, q. 2, who consequently says that in the individual predicaments special modes of unity and multitude can be distinguished, yet that there are no peculiar names imposed to signify these except in quantity, because the notion of divisibility or of the divisible continuum, from whose division number results, as is said in Physics III, c. 7, is found in a peculiar mode in quantity.

4. And this opinion proceeds by distinguishing quantity from the quantified thing; for those who think that quantity adds nothing to substance consequently say that transcendental one and that which is the principle of number are in no way distinguished among themselves, which Gregory tries to defend by many reasons, In I, dist. 24, qq. 1 and 2. Not that he thinks every one is quantified, but conversely, because he thinks every one is transcendental, and quantitative one is nothing other than transcendental one in substance or in material accidents. But of the distinction of quantity from the quantified thing we must speak elsewhere; now we suppose that quantity has an entity distinct from the others. Which being supposed, the opinion of Durandus can be confirmed by this reason; for being and transcendental one are convertible; therefore of whatever the one is said, the other too is predicated; but quantity is being; therefore it is transcendental one; but it is not transcendental one except by its quantitative unity; therefore that is contained under transcendental unity. Otherwise it would be necessary to feign two unities in one quantity, one transcendental, the other quantitative, which is superfluous and can scarcely be conceived by the mind.

5. But Averroes, above, and St. Thomas disprove this opinion of Avicenna, who consequently teach that quantitative unity differs from transcendental in this, that it adds to being something positive and real which transcendental unity does not add. From which some elicit that quantitative unity adds to quantity itself something positive, and in this way differs from the transcendental unity of quantity itself, and by reason of that positive thing is the principle of number, which is posited as a species of quantity, whereas transcendental multitude is not judged to make up a proper and real species of being. So Javellus holds, Metaphysics IV, q. 8, with Capreolus, In I, dist. 24, sole question, where he adduces various places of St. Thomas, and he is founded chiefly on this, that if quantitative unity were not something positive besides the negative indivision of quantity, neither would quantitative number be some certain real species, nor would there be any reason for constituting that number among the species of things rather than the number of any beings whatever. But if you ask what it is which unity adds over quantity, Capreolus seems to answer, in the explanation of the first conclusion, that in quantity two things are to be distinguished, namely the form of continuity, and the being which such continuous quantity gives to the subject; and he indicates that unity adds over quantity this latter being: Because the form (he says) of continuity is divisible into many, and therefore does not deserve to be called unity, of whose notion is indivisibility; but the being which that form gives to the subject is called unity, because it is in no way divisible, because, if that form or the subject is divided, the first being does not remain, nor is it divided, but each part of the divided thing has a new being and does not have that which it had before. And he cites Avicenna, Metaphysics III, c. 2, saying that unity is substantially that very thing which is not divided. Whence Capreolus indicates that this positive thing which quantitative unity adds over quantity is really distinct from it. But Giles, in the same distinction, q. 2, dub. 2, holding the same opinion, thinks of the positive addition that that addition is distinguished by reason only in this way, that quantity, in so far as it extends the parts of substance, is called continuous quantity, but in so far as it perfects substance, no account being taken of the parts, is called unity. Others, however, say that quantitative unity adds over quantity the notion of measure, from St. Thomas, I, q. 11, a. 2, and In Metaph. IV, lect. 3.

6. But this opinion is without doubt false, as Hervaeus, Thomas of Strasbourg, Durandus, Gregory and others noted in the said distinction. For that distinction which Capreolus feigns is fictitious and plainly unintelligible. Both because the being which quantity gives (according to the truer opinion) is not a thing distinct from actual and real quantity itself, as will be said generally below; and also because, granted that it were distinct, it would nevertheless not be more distinguished in quantity than the form of whiteness is distinguished in whiteness from the being which it gives to the subject, or in the form of stone the form itself from the being which it gives to matter; therefore either this distinction is not enough for the unity of quantity to be said to add something over quantity, or the same must be said of the unity of whiteness and of any other created form whatever; and moreover because, that being distinct from quantity being admitted, it is feigned without foundation to be more indivisible than quantity itself; for who would believe that, when wood is divided, in the individual divided parts the same quantity remains which was before, and that the same being of quantity which quantity itself conferred does not remain? For there is no greater reason for the corruption of one than of the other; indeed all too who think that being is really distinguished from the form from which it comes think at least that naturally and by ordinary power being is inseparable from it while it remains. But if perhaps Capreolus says that he is not speaking of the being of existence of quantity, but of a certain other distinct from quantity and its existence, this indeed needs no refutation, because it is a mere fiction devised without foundation. And moreover, in whatever way that being is explained, it cannot be more indivisible than quantity itself, because, just as the whole quantity gives being to the whole subject, so a part of quantity to a part of the subject, nor from the partial quantity which is in one part of the subject does any being come which is in the other parts of the subject, nor conversely; that being, therefore, must necessarily be coextended with quantity itself, nor can it be more indivisible than it. Especially since it is material and corporeal, and in a divisible subject. Nor is it true, what Capreolus says, that the form of continuity cannot be called unity because indivisibility is of the notion of unity; for above it has been proved by us that not indivisibility but only indivision is of the notion of unity, and therefore nothing prevents the form of unity, that is, in which unity is founded, from being divisible, provided it is undivided. This declaration of Capreolus, therefore, stands by no reason.

7. The other distinction of Giles too is none at all, except only in words; both because quantity does not perfect substance otherwise than by extending it into parts, and also because it is a contradiction to say that quantity has the notion of numerical unity in so far as it abstracts from parts; for it is of the intrinsic notion of this unity that it be in a quantified subject having parts, and it adds almost this alone over transcendental unity. The other exposition, finally, about the notion of measure is easily refuted; both because the notion of measure does not pertain per se primarily to unity, but follows upon it, as St. Thomas rightly teaches, In Metaph. IV, lect. 8, and Book X, lect. 2. And also because this notion of measure, if it is considered as regards aptitude, which is in the thing itself, is found in the same proportion in transcendental one with respect to multitude as in quantitative one with respect to the number of quantity; but if it is considered as regards the use of men, this matters little to the notion of unity as it exists in itself. Finally, against this whole opinion there stand both the testimonies of Aristotle and all the reasons by which it was proved above that the notion of one is placed in negation; for all of these proceed in the same proportion in numerical or quantitative unity, as is evident from Aristotle, Metaphysics V, text 11, and Book X, from the beginning, and from the reason given above, because, after anyone has feigned an entity or positive notion which this unity adds over quantity, if he understands it in the mind or in reality to be separated, and quantity alone to remain undivided, he will understand that one quantity remains; therefore whatever is added is added superfluously and without foundation.

The true notion of quantitative unity is declared

8. It is to be noticed, then, in order that both the thing itself and the opinion of St. Thomas in this part may be understood, what we were saying above, at the end of sect. 3, that in material substance there can be considered intrinsic and entitative unity, and accidental unity belonging to it denominatively from the affection of quantity; whence it comes about that quantity itself can be considered either as it is one in itself, or as by reason of it that which is affected by it is rendered one. This being supposed, it must first of all be said as regards this part that transcendental unity is not the quantitative unity which belongs to material substance denominatively and accidentally by means of quantity. This is evident from what has been said above, because neither in other things does transcendental unity consist in this, as is self-evident, nor in substance itself, or any other material form whatever, as is evident from what was said in sect. 3. For transcendental unity is most intrinsic to each being and belongs by virtue of its entity alone with a negation adjoined, as has been shown; whence, quantity being removed, intrinsic transcendental entitative unity is understood even in material substance. And it is confirmed, because substance, as it is one through quantity, is simply speaking one per accidens in the genus of being, since it consists of things of diverse predicaments; but substance, as it is transcendentally one, is not one per accidens, but per se; otherwise material substance could not have unity per se in its proper genus, which is very absurd. And the arguments which Gregory adduces in the aforesaid place also rightly prove this.

9. Next it must be said that in quantity itself the unity by which it itself is one is not other than the transcendental unity applied¹ to such a being, namely to quantity; this too the arguments of Durandus rightly prove, and those which we adduced in reporting his opinion. And from these it follows, first, that numerical or quantitative unity with respect to quantity adds nothing besides indivision, which is only a certain negation, as was said above. So hold the other authors cited, and Soncinas, Metaphysics X, q. 2; Soto, on the Categories, chapter on Quantity, q. 1. And the reasons made against Capreolus and others prove this. And it is evident also, because this unity is transcendental with respect to quantity; therefore it is of the same notion in it as it is in other things; just as, therefore, in other beings unity is the undivided entity of each, so in quantity its unity is quantity itself or the continuity of quantity as undivided. You will say: when continuous quantity is divided, its quantitative unity is lost and number results, as is said in Physics III, and yet transcendental unity is not lost, because, as we were saying above, the same entity remains in the individual divided parts which they had in the continuum; therefore they are diverse unities. The answer is by denying the minor, because, although the divided parts retain the same entity which they had as partial in the continuum, nevertheless simply the entity of the continuum was not placed in those parts alone, but also in their union and the term by which they were joined, or rather in that whole composite which resulted from all these, whose unity, both quantitative and transcendental, consisted in that whole as undivided; whence that unity is destroyed by division because the same indivision does not remain which was before, and because that whole is dissolved in the notion of a certain whole.

10. Secondly it is inferred from what has been said that quantitative or numerical unity, in so far as it belongs denominatively to substance, adds over substance a positive thing under a negation, namely quantity itself with indivision. So I think St. Thomas is to be understood; and Fonseca rightly noted this, Metaphysics V, c. 13, q. 3, sect. 3, from the same St. Thomas, In Metaph. IV, lect. 3. And it is easily evident, because, just as substance is quantified through quantity adjoined to it, so also it is one quantitatively on account of the one quantity which it has in itself; likewise hence it often comes about that substances which in their genus do not have transcendental unity are in some way called one quantitatively by reason of quantity, in which way a rod is called one which is partly green, partly dry.

11. Thirdly, finally, it is evident from what has been said how transcendental unity is related to quantitative unity; for in no sense are they convertibly the same, as the things adduced above evidently prove. If, however, we speak of quantitative unity according to itself or with respect to quantity, then they are related as inferior and superior; for it has been shown that quantitative unity is a certain transcendental unity, although not every transcendental unity is also quantitative. Whence transcendental one is found in all the predicaments; but the unity of quantity in the one predicament alone. But if we speak of quantitative unity as it belongs accidentally and denominatively to substance, or to other material accidents through quantity, then it differs from transcendental unity; for the latter is intrinsic and per se accompanying the entity of the thing; but the former is as it were extrinsic, in so far as it is adjoined through another entity. But because this numerical unity too, with respect to substance, is real, it is therefore necessary that it be in some way contained under the transcendental; and it is contained in the way in which substance as quantified is contained under being; just as, therefore, substance by the adjoining of quantity is accidentally quantified, and from both results a certain being composed per accidens, so it is also accidentally one, and that unity which results from both is also per accidens and proportioned to such a composite, and with respect to it is transcendental, although with respect to substance it is accidental. And from these things it is also evident that quantitative number and multitude keep among themselves the same proportion as numerical and transcendental one keep. But what is to be said of the notion of number, namely whether it constitutes a proper genus and species of being, and whether in this it differs from multitude, is to be said below in treating of quantity.

Transcendental unity is compared with singular unity

12. The second opinion to be examined in this place is that of some who say that transcendental unity is the individual unity of each singular being, which is also wont to be called numerical unity, in a diverse signification from that which was treated in the preceding opinion; for there numerical unity was taken for that which is the principle of quantitative number. For, because our knowledge begins from sense, and through sense we can number those things which have magnitude, therefore the multitude of these things has specially received the name of number, and therefore in this special mode the unity founded in quantity is called numerical unity. But here numerical unity is taken more broadly as it is distinguished against generic or specific, and is found in any singular being whatever, and it is called numerical in so far as from it multitude or transcendental number can be made up; but it is called individual or singular in so far as, as such, it is incommunicable to many inferiors, in which it differs from formal unity, both specific and generic. This opinion says, then, that this singular unity is the proper and real attribute of being, or transcendental unity. The foundation can be that transcendental unity, which is an attribute of real being, must be real unity; but in things there is no real unity besides numerical and singular unity; therefore that alone is the adequate attribute of being; therefore that alone is transcendental unity. And it is confirmed, for this unity is convertible with real being; for everything which is one in this way is real being. For although a being of reason can be called one in number, and so genera, species and individuals are distinguished by the dialecticians in beings of reason themselves, nevertheless that is as it were equivocally, by mere extrinsic denomination; but properly and rigorously speaking, whatever is simply one in number is real being; and conversely every real being is singular, and consequently one in number, because nothing is called real being except what is in things, or what is capable of real being; but in things there is nothing except the singular, nor is anything capable of real existence except an individual thing; therefore real being and one in number or singular are convertible; therefore the aforesaid singular unity is transcendental unity or an attribute of being.

13. But this opinion, if we attend to the common mode of speaking and conceiving, can seem difficult and singular. For first of all Aristotle, Metaphysics V, c. 6, text 11, among the unities of being posits not only singular unity, but also specific, generic and analogous, and universally he says: Whatever things do not have division, in so far as they do not have it, are so called one. And in Book IV, text 6, he gathers hence that it pertains to metaphysics to treat of genus and species, because these are in being, namely as comprehended among its attributes; but they are not comprehended except in so far as they are contained under unity. Moreover, the adequate attribute of some common object must belong not only to the inferiors contained under such an object, but also to the common object itself taken according to itself and formally; therefore to be one must belong not only to individual beings, but also to being as such; but as such it is not one in number, but only analogically and by formal notion; therefore. A similar argument is that of whatever being is said, transcendental one is said; but being is said not only of individuals, namely Peter and Paul, but also of common notions precisely taken, as of man, horse, etc.; for, although perhaps in these universality is through reason, as we shall say below, nevertheless the universal natures themselves are real, and are called true real beings; and so Aristotle, Peri Hermeneias I, c. 5, distinguishes that of things some are universal, others particular; man as such, therefore, is real being; therefore one by transcendental unity; and yet he is not one by singular and numerical unity; therefore transcendental unity extends more widely than individual or singular unity.

Resolution of the question

14. This difficulty depends much on the understanding of that difficult question about transcendental² and numerical unity, how they differ, and whether each is a true unity existing in things, and consequently whether universal unity too is in things. But since these must be treated singly for the exact explanation of this matter, it is now briefly said that the transcendental unity of which we are now treating is not to be limited to singular or universal, material or formal unity, but comprehends every unity which can be found in some real being or in the formal notion of real being. Transcendental unity, therefore, will be any notion whatever of real being per se, in so far as it is undivided adequately and according to itself. I say of being per se, in the way in which it was explained above by us to be the object of metaphysics; for, if it is taken more broadly, it has no unity, even formal, as has been said. I say also as undivided, because neither the notion of being alone nor the negation alone makes unity, but the undivided notion of being, as was shown above. Finally I say adequately and according to itself, because unity in each thing or real objective concept must be attended to according to its proper notion, and not according to some superior, inferior or extraneous one; for these are either inadequate or in a certain way per accidens; but the unity of each is adequate to it and belongs to it per se. Whence man is called one essentially because according to his proper adequate notion he is not divided in essential notion, although in individuals he is entitatively divided; but man will not be called simply one in that way because he is undivided in the notion of animal; for that indivision would not suffice for the aforesaid unity, because it does not belong to man adequately and per se primarily, but by reason of the superior. From these things, then, the notion of unity taken in common has been sufficiently explained. But in order that it may be explained more distinctly and radically, it is necessary that we speak in particular of individual, formal and universal unity, which are the proper metaphysical unities.