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.