II. To the Principal Arguments

238. To the first argument [n.213] I say that although the Philosopher’s understanding there is per se about matter (that is, about the entity that per se contracts the quiddity [nn.182, 206-207]), yet it is by application of it to what has matter, which is the other part of a composite, and to what does not have matter - I concede that the Philosopher’s intention was that everything not possessed of matter as some component nature is the same first as its ‘what it is’, because every such ‘what it is’ per se posits a ‘this’; and the reason for this is that he posited that everything such as not to have matter as part of itself is formally necessary. Now whatever can be in a nature formally necessary is actually in it; therefore anything whatever that can have that quiddity does have it, because there is no potency there distant from act; hence every possibility for supposits that he posited in such a nature he posited as being actual. Now if there were a possibility there for several individuals, there would be a possibility there for an infinity of individuals, and so the individuals would be actually infinite; therefore, since an infinity is impossible in any nature, so there is in this nature too (according to him) an impossibility for infinity. Therefore this nature is of itself a ‘this’, according to him.

239. But we disagree with him in the proposition that ‘everything such as not to have matter as part of itself is formally necessary’ [n.238], and so we disagree with him in the conclusion. For it is more rational for a theologian to disagree with a philosopher in the principle because of which the philosopher holds some conclusion, than to err with him in the conclusion and to disagree with him in the principle because of which he himself erred. For thus to agree with him is neither to philosophize nor to think theologically, because such a theologian does not have a reason that would be valid with the philosopher, because the philosopher would not be conceding the conclusion save because of that principle; nor even does such a theologian have a theological principle for his conclusion, because there is precisely a philosophical principle for it, which the theologian denies.a

a.a [Interpolation] The response [to the first argument, nn.238-239] stands on the fact that matter is taken in one way for the second (potential) part of a composite, in another way for the disposition that contracts a quiddity or for any entity that is outside the idea of the quiddity; and accordingly things that do not have matter can be understood in two ways. Likewise, a distinction must be made on the part of the predicate, for ‘whatever is the same as that which it belongs to’ can be understood in two ways: in one way about a real identity, and thus the ‘what it is’ is the same really as what it belongs to, whether it has matter or not (because as Aristotle argued in the beginning of the chapter ‘On Parts of Definition’ [n.213], “The singular does not seem to be other than its own substance;” and the argument is not sophistical but demonstrative); in another way it can be understood about the most precise identity, and thus the ‘what it is’ is the same as that which it belongs to when what has the quiddity is only quiddity and not something else (which indeed the Philosopher would place among things that do not have matter as the second part of a composite, because he posits that on this follows that there is in them no matter in the second way but that there is only quiddity there and not any condition contracting the quiddity, for the reason above posited, that they are formally necessary [n.238]). - Thereby to the form of the argument [n.213] I say that in things having matter the ‘what it is’ is not the same as what it belongs to in either the first or the second way. But then the minor is false, when it is said that angels are of this sort [n.213]; for in them there is in truth matter in the second way (though not first), because none is of himself a ‘this’, although Aristotle posited this because of the principle that the theologian has to deny.

240. On the same basis I say as to Avicenna [n.214] that his intention was that there is one angel in one species, but the proposition on which this conclusion rests -namely that ‘a superior angel causes an inferior angel’ (because he posits that there can only be one thing from one thing disposed in the same way)- is conceded by no Catholic theologian; therefore neither should his conclusion be conceded by any theologian.

241. As to the first of the reasons [n.215], it was said elsewhere [1 d.17 n.255] that formal difference can be taken for a difference in form (and what is called ‘formal difference’ seems properly to signify this), or ‘formal difference’ can be taken for a difference of forms, although the difference is not in the form as in the reason for the difference.

242. In the first way the major [n.215, sc. ‘every formal difference is a specific difference’] can be conceded, and thus the minor [sc. ‘angels differ by some formal difference’] is false. And the proof of the minor, namely that ‘an angel differs from an angel because he is a form, therefore angels have a formal difference’, involves the fallacy of the consequent; for the inference ‘the forms differ, therefore they differ formally (or they differ in form)’ does not follow, just as the inference ‘many men differ, therefore they differ in humanity’ does not follow; for it is one thing that ‘something is distinct’ and another that ‘it is the first reason for the distinguishing (or the distinction)’, because that the thing is the reason for the distinguishing entails that the thing is distinct, but that the thing is distinct does not entail that it is the reason for the distinguishing. And the logical reason is to this effect, that the negation included in the term ‘difference’ not only confounds the term of this relation [sc. the relation of difference] by confusing and distributing it, but also confounds the thing that specifies the difference (as that in which the difference is noted to be); the difference is indeed confounded (as to the negation included in the term ‘difference’), because if Socrates differs from Plato in whiteness then he is not the same as him, neither in this whiteness nor in that.Tr. The logical point in this paragraph seems to be as follows. The statement ‘A is different from B’ does not so much assert something of A as deny of it a relation with B (that A is not the same as B). So it distributes the term of the relation ‘different’, namely ‘B’ and everything about B in which something could differ from it; or, alternatively, it distributes the whole predicate ‘same as B’ (negative propositions logically distribute the predicate of the proposition). Accordingly it takes the predicate confusedly, that is, takes it to apply to everything that belongs to ‘B’, or to ‘same as B’, and leaves indeterminate what sort of sameness with B, if any, is being denied of A. Hence one cannot conclude from ‘A is different from B’ that A is not the same as B in humanity, say, or whiteness. One needs further premises for that purpose. Further, if the proposition does specify what the difference is in, as that A is not the same as B in humanity or whiteness, then the negation distributes and takes confusedly the specification as well. For the proposition ‘A is not the same as B in whiteness’, because it distributes and takes confusedly, or universally, the predicate ‘same as B in whiteness’, denies of A, if not further clarified, all likeness with B in all whiteness. But of course it could well be that A is not different from B in all whiteness but only in this or that shade of whiteness (A and B are both white, say, but A is a paler white). Thus the proposition ‘A differs from B in whiteness’ is, by itself, far too vague or confused to form the basis of any valid inference about what sort of difference in what sort of whiteness. And this error is committed by the argument ‘an angel differs from an angel because he is a form, therefore angels have a formal difference’. For in fact, as far as the premise is concerned, an angel could differ from an angel in form or because of form in a whole host of ways. So to conclude that the angel differs in this way (namely in ‘formal difference’) is to infer something not warranted by the premise, and so to commit the fallacy of the consequent. ⁶⁵ - But if the major

[n.215] is taken improperly, according to the second understanding [n.241], I deny the major.

243. As to the proof [sc. of the major, n.216] I say that the Philosopher in Metaphysics 8 is speaking of form as it indicates quiddity. This is apparent from his first comparison of forms with numbers; for he says [8.3.1043b32-36], “If substances are in some way numbers, they are so in this way - that definition is a sort of number, a divisible into indivisibles (for accounts are not infinite), and number is such.” That is: the resolution of definitions stops at an indivisible just as the resolution of numbers stops at an indivisible; and such a definition is of what he calls ‘substance’, that is ‘quiddity’, not form, which is a second part of quiddity.

244. I say that in this way [sc. as form indicates quiddity] nothing is added to form without varying the species, whether simply, that is, without making from one species another species (a contrary or disparate species), or in a certain respect, that is, without making another species from what is not such a species (for example, if a difference pertaining to quidditative being is added to a genus, then it makes a most specific species, and such a most specific species was not present before but only an intermediate species was present).

245. And I say that in this way nothing circumstantial to nature in inferior things adds anything to the form. Whether this something circumstantial is an individual property or is a more or less (or anything else that does not regard the nature as it exists in its quidditative being), it neither removes nor adds in this way anything to the substance. An example of this would be if a unity, as it is part of a triple, were a precise part as a numerical individual difference, and yet it could in itself be intensified or relaxed - this difference would belong per se to the unity but per accidens to it as it is part of a triple; so there would not be a different triple when the unity was intensified or relaxed.

246. So when you say that ‘any distinction of forms is like a distinction of number’ [n.216], this is false save as it is about what accords with the formal being that pertains to the quiddity per se; and such is not the case here.

247. As to the statement from Metaphysics 10 [n.217] I say that a fallacy of the consequent is involved in inferring, from the text, that ‘all forms make a difference in species’. For the Philosopher is really maintaining there that ‘a non-formal difference is not specific’, and from this it does not follow that ‘a non-specific difference is not formal’ (which they themselves want to have), just as this does not follow in the case of the affirmative propositions that are equivalent to these, because a universal affirmative does not convert with the terms disposed in the same way.The objectors want to argue from ‘no non-formal difference is specific’ to ‘every formal difference is specific’, and in order to do so they have to go through a series of logical obversions and conversions. So: ‘no non-formal difference is specific’ is obverted to ‘every non-formal difference is non-specific’, which is converted to ‘every non-specific difference is non-formal’, which is obverted to ‘no non-specific difference is formal’, which is converted to ‘no formal difference is non-specific’, which is obverted to ‘every formal difference is specific’. But in this series of obversions and conversions an invalid conversion is made, namely from ‘every non-formal difference is non-specific’ to ‘every non-specific difference is non-formal’. For a universal affirmative does not convert to a universal affirmative but to a particular affirmative, that is, in this case, to ‘some non-specific difference is non-formal’, and from this latter one can no longer validly get, as the objectors wish, the proposition ‘every formal difference is specific’. ⁶⁶

248. From the Philosopher then is got that ‘only a formal difference is specific’, not that ‘every difference in form is specific’, because although an exclusive proposition [sc. a proposition of the form ‘only A is B’] entails an affirmative proposition with the terms transposed [sc. ‘only A is B’ entails ‘every B is A’], it does not do so in the same way with terms not transposed [sc. ‘only A is B’ does not entail ‘every A is B’] - but there is a fallacy of the consequent in converting an indefinite proposition into a universal affirmative [sc. ‘only A is B’ is equivalent to ‘some A is B’ and ‘some A is B’ does not convert to ‘all A is B’]. Indeed from that place [from Aristotle, n.217] it seems rather that one can take the opposite of the proposition ‘every difference of forms is specific’; for the difference of a white man and a black horse is a difference of forms and in some way through forms, but it is not a specific difference (according to Aristotle there), because the forms are formal with respect to the natures in which they are [sc. white and black are formal with respect to this man and this horse], that is, they are consequent to the individuals, but they are not consequent per se or terminative per se of the quidditative being [sc. white and black are forms determining individuals, not species].

249. To the other argument [n.218] I say that if some individual - from the mere fact that it is without matter - had in itself the whole perfection of a species that of itself is of a nature to be in infinite individuals (as far as concerns itself), then it would seem to have infinite perfection from the mere lack of matter; but whatever can have an infinite perfection has it, and so there would be infinite perfection in any species, and consequently the perfection of a species would not be limited or determined by the determination or specification or limitation of the ultimate difference (which, by addition to the genus, constitutes the ultimate species), which is false and contrary to all the philosophers. So the assumed proposition is false that ‘the individual which can be without matter has, from this privative cause alone (that it is without matter), the whole perfection of the species’ [n.218], because if, along with this, one posits that nothing positive is done in respect of it (but there is just separation), nothing that was not there before is posited.

But if the proposition be set down as it has some probability, namely that ‘if a form were separated from matter, it would have the whole perfection of the species, because the species cannot be participated by matter’ [n.219], it is false and begs the question, unless it be understood in the sense that matter states the individual entity that contracts the form. By understanding in this way the equivocal meaning of the assumed proposition, then every form has the whole perfection of the species and is of itself a ‘this’; and then the minor - assumed thereunder, about an angel [sc. ‘an angel is a separate form not able to be participated by matter as by an individual entity contracting the form’] - is simply false, because although the essence that is the other part of a composite is not able to be participated by matter, yet it can be participated by several material things, that is, by several individuals having material entities, which entities are called ‘material’ - as has often been said - in respect of the contracted quiddity, to the extent quiddity is called form [nn.182, 201, 206-207, 238, 243].

250. To the next [n.220] I say that there is a fallacy of the consequent in the form of the arguing, ‘infinity is not intended, therefore plurality is not intended’; numerical plurality is not of itself infinite, but infinity can stand only if the plurality is not repugnant to it. So although no one per se intends infinity, yet someone can intend a numerical plurality that is not of itself infinite, and which, just as it admits of infinity, so it also admits of finitude.

251. And thus can their common saying be understood [sc. the order and beauty of the universe consists in species, nn.220-221], and truly:

Although order in the whole universe is principally found in the distinction of species, wherein there is the inequality pertaining to order, yet because, according to

Augustine City of God 19.13.n.1, “order is the fitting disposition of equal and unequal things, bestowing on each of them its own place,” the principal agent who intends the order of the universe (as the principal good internal to it) intends not only the inequality, which is one of the requisites for order (namely the inequality of species), but also the equality of individuals (namely in the same species), which is the other of the concurrent requisites for order. And individuals are intended simply by the First Cause insofar as he intends something ‘other than himself’, not as end, but as something other for the end; hence, for the sake of communicating his goodness, as for the sake of communicating his blessedness, he produced many individuals in the same species. But in the case of the most principal beings, God principally intended the individual.

252. And when the proposition ‘numerical difference is not intended’ [n.220] is taken in this way, it is false; and when it is proved in this way that ‘numerical difference can be infinite,’ the conclusion does not follow. The inference ‘numerical difference can be infinite, and the infinity is not intended, therefore the difference is not intended’ does not hold; for there can be some finite numerical difference, and there is; and it can be intended, and it is.

253. To the last [n.222] I say that although the Philosopher says that generation is perpetual ‘so as to preserve a divine existence’, and this in corruptible things where the species cannot remain for ever in one individual, yet he does not himself say that a multitude is precisely for the preservation of the species in corruptible individuals; hence such preservation is one cause of the multitude of individuals in the same species but it is not the precise cause; rather the one stated before is [sc. the goodness of God, n.251].

254. And as to what is adduced about the celestial bodies, that ‘in one species there is only one singular and one individual body’ [n.223], I reply: Aristotle’s reason was that such a singular body came from the whole matter of the species (and this not only actual matter but also potential matter, according to him), because there was, according to him, no possible matter in any such species that was not totally in the one individual of such species; for he posited that nothing new could be produced in immobile or eternal things as they are such, namely immobile and eternal [n.222]. And because theologians do not agree with him in this proposition ‘every eternal body is made of the whole matter, actual and potential, of the species’, therefore there should be no agreement with him in the conclusion.