LESSON VII

Whether from an Enunciation Having Many Conjoined Predicates It

Is Licit to Infer an Enunciation Which Contains the Same

Predicates Divisively

             21a 18 On the other hand, it is also true to say predicates of something singly; for example, it is true to say that some man is a man, or that some white man is white. However, this is not always the case.

             21a 21 When something opposed is present in the adjunct, from which a contradiction follows, it will not be true to predicate them singly, but false e.g., to say that a dead man is a man. When something opposed is not present in the adjunct, however, it is true to predicate them singly.

             21a 24 Or, rather, when something opposed is present in it, it is never true; but when something opposed is not present, it is not always true. For example, Homer is something, say, a poet. Is it therefore true to say also that Homer is, or not?

             21a 26 The "is" here is predicated accidentally of Homer, for the "is" is predicated of him with regard to the fact that he is a poet, not in itself.

             21a 29 Therefore, in whatever predications no contrariety is present when definitions are put in place of the names, and wherein predicates are predicated per se and not accidentally, it will also be true to predicate each one singly.

             21a 32 In the case of non-being, however, it is not true to say that because it is a matter of opinion it is something; for the opinion of it is not that it is, but that it is not.

             1. Aristotle now takes up the second question in relation to multiple enunciations. He first presents it, and then solves it where he says, When something opposed is present in the adjunct, from which a contradiction follows, it will not be true to predicate them singly, but false, etc. Finally, he excludes an error where he says, In the case of non-being, however, it is not true to say that because it is a matter of opinion, it is something, etc.

             The second question is this: Is it licit to infer from an enunciation having a conjoined predication, enunciations dividing that conjunction? This question is the contrary of the first question. The first asked whether a conjoined predicate could be inferred from divided predicates; the present one asks whether divided predicates follow from conjoined predicates.

             When he presents the question he says, On the other hand, it is also true to say predicates of something singly, i.e., what was previously said conjointly may be said divisively; for example, that some white man is a man, or that some white man is white. That is, from "Socrates is a white man," follows divisively, "Therefore Socrates is a man," "Therefore Socrates is white." However, this is not always the case, i.e., sometimes it is not possible to infer divisively from conjoined predicates, for this does not follow: "Socrates is a good lute player, therefore he is good." Hence, sometimes it is licit, sometimes not.

             Note that in inferring each part divisively he takes as an example "white man." This is significant, for by it he means to imply that his intention is to investigate when each part can be inferred divisively from a conjoined predicate, and not when only one of the two can be inferred.

             2. When he says, When something opposed is present in the adjunct, etc., he solves the question, first by responding to the negative part of the question, i.e., when it is not licit; secondly, to the affirmative part, i.e., when it is licit, where he says, Therefore, in whatever predications no contrariety is present when definitions are put in place of the names, and wherein predicates are predicated per se and not accidentally, etc.

             It should be noted, in relation to the negative part of the question, that a conjoined predicate may be formed in two ways: from opposites and from nonopposites. Therefore, he shows first that the parts in a conjoined predicate of opposites can never be inferred divisively. Secondly, he shows that this is not licit universally in a conjoined predicate of nonopposites, where he says, Or, rather, when something opposed is present in it, it is never true; but when something opposed is not present, it is not always true.

             Aristotle says, then, that when something that is an opposite is contained in the adjacent term, which results in a contradiction between the terms themselves, it is not true, namely, to infer divisively, but false. For example, when we say, "Caesar is a dead man," it does not follow, "Therefore he is a man," because the contradiction between "man" and "dead" which results from adding the "dead" to "man" is opposed to man, for if he is a man he is not dead, because he is not an inanimate body; and if he is dead he is not a man, because as dead he is an inanimate body.

             When something opposed is not present, i.e., there is no such opposition, it is true, i.e., it is true to infer divisively. The reason a divided inference does not follow when there is opposition in the added term is that in a conjoined enunciation the other term is destroyed by the opposition of the added term. But that which has been destroyed is not inferred apart from the destruction, which is what the divided inference would signify.

             3. Two questions arise at this point. The first concerns something assumed here: how can it ever be true to make such a statement as "Caesar is a dead man," since an enunciation cannot be true in which two contradictories are predicated at the same time of something (for this is a first principle). But "man" and "dead," as is said in the text, include contradictory opposition, for in man is included life, and in dead, nonlife.

             The second question concerns the consequent that Aristotle rejects, which appears to be good. The enunciation given as an example predicates terms that are opposed contradictorily. But from an enunciation predicating two contradictory terms, either both can be inferred (because it is equivalent to a copulative enunciation), or neither (because it destroys itself); therefore both parts seem to follow, since it is false that neither follows.

             4. These two questions can be answered simultaneously. It is one thing to speak of two terms in themselves, and another to speak of them as one stands under the determination of another. Taken in the first way, "man" and "dead" have a contradiction between them and it is impossible that they be found in the same thing at the same time. In the second way, however, "man" and "dead" are not opposed, since "man," changed by the destructive element introduced by "dead," no longer stands for what it signifies as such, but as determined by the term added, by which what is signified is removed. Aristotle, in order to imply both, says two things: that they have the opposition upon which contradiction follows if you regard what they signify in themselves; and, that one true enunciation is formed from them as in "Socrates is a dead man," if you regard their conjunction as destructive of one of them.

             Accordingly, the answer to the two questions is evident. In a case such as this two contradictories are not enunciated of the same thing at the same time, but one term as it stands under dissolution or transmutation from the other, to which by itself it would be contradictory.

             5. There is also a question about something else that Aristotle says, namely, something opposed is present . . . from which a contradiction follows. The phrase from which a contradiction follows seems to be superfluous, for contradiction follows upon all opposites, as is evident in discoursing about singulars; for a father is not a son, and white is not black, and one seeing is not blind, etc.

             Opposites, however, can be taken in two ways: formally, i.e., according to what they signify, and denominatively, or subjectively. For example, father and son can be taken for paternity and filiation, or they can be taken for the one who is denominated a father or a son. But, again, since every distinction is made by some opposition, as is said in X Metaphysicae, it could be supposed that opposites are wholly distinct.

             It must be pointed out, therefore, that although contradiction follows between all opposites or distinct things formally taken, nevertheless, contradiction does not follow upon all opposites denominatively taken. Father and son formally taken infer a mutual negation of one another, for paternity is not filiation and filiation is not paternity, but in respect to what is denominated they do not necessarily infer a contradiction. It does not follow, for example, that "Socrates is a father; therefore he is not a son," nor conversely. Aristotle, therefore, in order to establish that not all combined opposites prevent a divided inference (since those having a contradiction applying only formally do not prevent a divided inference, but those having a contradiction both formally and according to the thing denominated do prevent a divided inference) adds, from which a contradiction follows, namely, in the third thing denominated. And appropriately enough he uses the word follows, for the contradiction in the third thing denominated is in a certain way outside of the opposites themselves.

             6. When he says, Or, rather, when something opposed is present in it, it is never true, etc., he explains that the parts cannot universally be inferred divisively in the case of a conjoined predicate in which there is a nonopposite as the third thing denominated. He proposes this--Or, rather, when something opposed is contained in it, i.e., opposition between the terms conjoined--as if amending what he has just said, namely, it is always false, i.e., to infer divisively. What he is saying, then, is this: I have said that when there is inherent opposition it is not true but false to infer divisively; but when there is not such opposition it is true to infer divisively; or, even better, when there is opposition it is always false but when there is not such opposition it is not always true. That is, he modifies what he first said by the addition of "always" and "not always."

             Then he adds an example to show that division does not always follow from nonopposites: For example, Homer is something, say, a poet. Is it therefore true to say also that Homer "is," or not? From the conjoined predicate, is a poet, enunciated of Homer, one part, Therefore Homer is, does not follow; yet it is evident that these two conjoined parts, "is" and "poet," do not have the opposition upon which contradiction follows. Therefore, in the case of conjoined nonopposites a divided inference does not always hold.

             7. When he says, The "is" here is predicated accidentally of Homer, he proves what he has said. One part of this composite, namely, "is," is predicated of Homer in the antecedent conjunction accidentally, i.e., by reason of another, namely, with regard to the "poet" which is predicated of Homer; it is not predicated as such of Homer. Nevertheless, this is what is inferred when one concludes "Therefore Homer is."

             To validate his negative conclusion, namely, that it is not always true to infer divisively from conjoined nonopposites, it was sufficient to give one instance of the opposite of the universal affirmative. To do this Aristotle introduces that genus of enunciation in which one part of the conjunction is something pertaining to an act of the mind (for we are speaking only of Homer living in his poems in the minds of men). In such enunciations the parts conjoined are not opposed in the third thing denominated; nevertheless it is not licit to infer each part divisively, for the fallacy of going from the relative to the absolute will be committed. For example, it is not valid to say, "Caesar is praiseworthy, therefore he is," which is a parallel case, i.e., of an effect whose existence requires maintenance.

             Aristotle will explain in the following sections of the text how the reasoning in the above text is to be understood.

             8. When he says, Therefore, in whatever predications no contrariety is present when definitions are put in place of the names, etc., he replies to the affirmative part of the question, i.e., when it is licit to infer divisively from conjoined predicates. He maintains that two conditions--opposed to what has been said earlier in this portion of the text--must combine in one enunciation in order that such a consequence be effected: there must be no opposition between the parts conjoined, and they must be predicated per se.

             He says, then, inferring from what has been said: Therefore, in whatever predicaments, i.e., predicates joined in a certain order, no contrariety, in virtue of which contradiction is posited in the third thing denominated (for contraries mutually remove each other from the same thing), is present, or universally, no opposition is present, i.e., upon which a contradiction follows in the third thing denominated, when definitions are taken in place of the names . . . He says this because it may be the case that the opposition is not apparent from the names alone, as in "dead man," and again it may be, as in "living dead," but whether apparent or not it will be evident that we are putting together opposites if we posit the definitions of the names in place of the names. For example, in the case of "dead man," if we replace "man" and "dead," with their definitions, the contradiction will be evident, for what we are saying is "rational animate body, irrational inanimate body."

             In whatever conjoined predicates, then, there is no opposition, and wherein predicates are predicated per se and not accidentally, in these it will also be true to predicate them singly, i.e., say divisively what had been enunciated conjointly.

             9. In order to make this second condition clear, it should be noted that "per se" can be taken in two ways: positively, and thus it refers to "perseity" of the first, of the second, and of the fourth mode universally; or negatively, and thus it means the same as not through something else.

             It should also be noted that when Aristotle says of a conjoined predicate that it is predicated "per se," the "per se" can be referred to three things: to the parts of the conjunction among themselves, to the whole conjunction with respect to the subject, and to the parts of the conjoined predicate with respect to the subject. Now if "per se" is taken positively, although it will not be false, nevertheless in reference to any of these three the meaning will be found to be foreign to the mind of Aristotle. For, although these are valid: "He is a risible man, therefore he is man and he is risible" and "He is a rational animal, therefore he is animal and he is rational," nevertheless the opposite kind of predication infers consequences in a similar way. For example, there is no "perseity" in "He is a white musician, therefore he is white and he is a musician"; rather, there is an accidental conjunction, not only between the parts among themselves and between the whole and the subject, but even between the parts and the subject. It is evident, therefore, that Aristotle is not taking "per se" positively, for an addition that does not differentiate this kind of predication from the opposed kind of predication would be useless. Why add "per se and not accidentally," if both those that are per se in the way explained and those that are conjoined accidentally infer divisively?

             If "per se" is taken negatively, i.e., as not through another, and is referred to the parts of the conjoined predicate among themselves, the rule is found to be false. It is not licit, for example, to say, "He is a good lute player, therefore he is good and a lute player"; yet the art of lute-playing and its goodness are conjoined without anything as a medium. And the case is the same if it is referred to the whole conjoined predicate with respect to the subject, as is clear in the same example, for the whole, "good lute player," does not belong to man on account of another, and yet it does not infer the division, as has already been said. Therefore, "per se" is referred to the parts of the conjoined predicate with respect to the subject and the meaning is: when the predicates are conjointly predicated per se, i.e., not through another, i.e., each part is predicated of the subject, not on account of another but on account of itself and the subject, then a divided predication is inferred from the conjoined predication.

             10. This is the way in which Averroes and Boethius explain this and, explained in this way, a true rule is found, as can easily be manifested inductively; moreover, the reasoning is compelling. For, if the parts of some conjoined predicate so inhere in the subject that neither is in it on account of another, their separation produces nothing that could impede the truth of the divided predicates. And this meaning is consonant with the words of Aristotle, for by this he also distinguishes between enunciations in which the conjoined predicate infers a divided predicate, and those in which this consequence is not inherent. For besides the predicates having opposition in the additional determining element, there are those with a conjoined predicate wherein one part is a determination of the other in such a way that only through it does it regard the subject, as is evident in Aristotle's example, "Homer is a poet." The "is" does not regard Homer by reason of Homer himself, but precisely by reason of the poetry he left. Hence it is not licit to infer, "Therefore Homer is." The same is true with respect to negative enunciations of this type, for it is not licit to infer from "Socrates is not a wall," "Therefore Socrates is not." And the reason is the same: "to be" is not denied of Socrates, but of "wallness" in Socrates.

             11. Accordingly, it is evident how the reasoning in the text above is to be understood. "Per se" is taken negatively in the way explained here, and "accidentally" as "on account of another." The "accidentally" is used with the same signification in solving this and the preceding question. In both he understands "accidentally" to mean conjoined on account of another, but it is referred to diverse things. In the preceding question "accidentally" determines the way in which two predicates are conjoined among themselves; in the latter question it determines the way in which the part of the conjoined predicate is ordered to the subject. Hence, in the former, "white" and "musician" are numbered among the things that are accidental, but in the latter they are not.

             12. This exposition seems a bit dubious, however. For if it is not licit to infer divisively from a conjoined predicate because one part of the conjoined predicate does not regard the subject on account of itself but on account of another part (as Aristotle says of the enunciation, "Homer is a poet"), it will follow that there will never be a good consequence from the third determinant to the second, since in every enunciation with a third determinant, "is" regards the subject on account of the predicate and not on account of itself.

             13. To make this difficulty clear, we must first note a distinction. It is one thing to treat of the rule when inferring a second determinant from a third determinant, and when not; it is quite another thing when a divided inference is made from a conjoined predicate, and when not. The former is an additional point; the latter is the question we have been inquiring about. The former is compatible with variety of the terms, the latter not. For if one of the terms which is one part of a conjoined predicate will be varied according to signification, or supposition when taken separately, it is not inferred divisively from the conjoined predicate, but the other is.

             Secondly, note this proposition: when a second determinant is inferred from a third, identity of the terms is not kept. This is evident with respect to the term "is." Indeed, St. Thomas said above that "is" as the second determinant implies one thing and "is" as the third determinant another. The former implies the act of being simply, the latter implies the relationship of inherence, or identity of the predicate with the subject. Therefore, when the second determinant is inferred from the third, one term is varied and consequently an inference is not made of the divided from the conjoined.

             Accordingly, the response to the objection is clear, for although the second determinant can sometimes be inferred from the third, it is never licit for the second to be inferred from the third as divided from conjoined, because you cannot infer divisively when one part is destroyed by that very division. Therefore, let the consequence of the objection be denied and for proof let it be said that the conclusion--that such an inference is illicit under the limits of inferences which induce division from a conjoined predicate--is good, for this is what Aristotle is speaking of here.

             14. But the objection is raised against this that in the case of "Socrates is white, therefore he is," a divided inference can be made as from a conjoined predicate, in virtue of the argument that we can go from what is in the mode of part to its whole as long as the terms remain the same.

             The answer to this is as follows. It is true that white man is a part in the mode of man (because white diminishes nothing of the notion of man but posits man simply); is white, however, is not a part in the mode of is, because a part in the mode of its whole is a universal, the condition not diminishing the positing of it simply. But it is evident that white diminishes the notion of is, and does not posit it simply, for it contracts it to relative being. Whence when something becomes white, philosophers do not say that it is generated, but generated relatively.

             15. In accordance with this, the objection is raised that in saying "It is an animal, therefore it is," a divided inference is made in virtue of the same argument; for animal does not diminish the notion of is itself.

             The answer to this is that if the is asserts the truth of a proposition, the fallacy is committed of going from the relative to the absolute; if the is asserts the act of being, the inference is good, but it is of the second determinant, not of the third.

             16. There is another doubt, this time about the principle in the exposition; for this follows, "It is a colored quantity, therefore it is a quantity and it is colored"; but "colored" regards the subject through the medium of quantity; therefore the exposition given above does not seem to be correct.

             The answer to this and to similar objections is that "colored" is not so present in a subject by means of quantity that it is its determination, and by reason of such a determination denominates the subject; as "goodness," for instance, determines the art of lute-playing when we say "He is a good lute player." Rather, the subject itself is first denominated "colored" and quantity is called "colored" secondarily, although color is received through the medium of quantity. Hence, we made a point of saying earlier that one part of a conjoined predicate is predicated accidentally when it denominates the subject precisely because it denominates the other part. This is not the case here nor in similar instances.

             17. When he says, In the case of non-being, however, it is not true to say that it is something, etc., he excludes the error of those who were satisfied to conclude that what is not, is. This is the syllogism they use: "That which is, is 'opinionable'; that which is not, is 'opinionable'; therefore what is not, is." Aristotle destroys this process of reasoning by destroying the first proposition, which predicates divisively a part of what is conjoined in the subject, as if it said "It is 'opinionable,' therefore it is." Hence, assuming the subject of their conclusion, he says, In the case of that which is not, however; and he adds their middle term, because it is a matter of opinion; then he adds the major extreme, it is not true to say that it is something. He then assigns the cause: it is not because it is but rather because it is not, that there is such opinion.