LESSON XI

The Opposition of Universal and Particular Enunciations and the

Relation of an Opposed Affirmation and Negation to Truth and

Falsity

             17b 16 Affirmation is opposed to negation in the way I call contradictory when the one signifying universally is opposed to the same one not signifying universally, as in "Every man is white" and "Not every man is white"; "No man is white" and "Some man is white."

             17b 20 They are opposed contrarily when the universal affirmation is opposed to the universal negation; as in "Every man is just" and "No man is just."

             17b 22 Hence in the case of the latter it is impossible that both be at once true, but it is possible for the contradictories of these contraries to be at once true with respect to the same subject, as in "Not every man is white" and "Some man is white."

             17b 26 Whenever there are contradictions with respect to universals signifying universally, one must be true, the other false; this is also the case when there are contradictions with respect to singulars, as in "Socrates is white" and "Socrates is not white."

             17b 29 But when the contradictions are of universals not signifying universally, one is not always true and the other false; for it is at once true to say that man is white and man is not white, and man is beautiful and man is not beautiful.

             17b 33 For if he is ugly, he is not beautiful; and if he is becoming something, he is not yet it.

             17b 34 At first sight this might seem paradoxical, because "Man is not white" seems to signify the same thing as "No man is white"; but it neither signifies this, nor are they at once true necessarily.

             1. Now that he has determined the opposition of enunciations by comparing universal enunciations with indefinite enunciations, Aristotle determines the opposition of enunciations by comparing universals to particulars. It should be noted that there is a twofold opposition in these enunciations, one of universal to particular, and he touches upon this first; the other is the opposition of universal to universal, and this he takes up next, where he says, They are opposed contrarily when the universal affirmation is opposed to the universal negation, etc.

             2. The particular affirmative and particular negative do not have opposition properly speaking, because opposition is concerned with the same subject. But the subject of a particular enunciation is the universal taken particularly, not for a determinate singular but indeterminately for any singular. For this reason, when something is affirmed or denied of the universal particularly taken, the mode of enunciating is not such that the affirmation and negation are of the same thing; hence what is required for the opposition of affirmation and negation is lacking.

             3. First he says that the enunciation that signifies the universal, i.e., universally, is opposed contradictorily to the one that does not signify universally but particularly, if one of them is affirmative and the other negative (whether the universal is affirmative and the particular negative or conversely), as in "Every man is white," "Not every man is white." For, the "not every" is used in place of the particular negative sign; consequently, "Not every man is white" is equivalent to "Some man is not white." In a parallel way "no," which signifies the same thing as "not any" or "not some," is the universal negative sign; consequently, the two enunciations, "Some man is white," which is the particular affirmative, and "No man is white," which is the universal negative, are contradictories.

             4. The reason for this is that contradiction consists in the mere removal of the affirmation by a negation. Now the universal affirmative is removed by merely the negation of the particular and nothing else is required of necessity; but the particular affirmative can only be removed by the universal negative because, as has already been said, the particular negative is not properly opposed to the particular affirmative. Consequently, the particular negative is opposed contradictorily to the universal affirmative and the universal negative to the particular affirmative.

             5. When he says, They are opposed contrarily when the universal affirmation is opposed to the universal negation, etc., he touches on the opposition of universal enunciations. The universal affirmative and universal negative, he says, are contraries, as in "Every man is just," "No man is just"; for the universal negative not only removes the universal affirmative but also designates an extreme of distance between them inasmuch as it denies the whole that the affirmation posits; and this belongs to the notion of contrariety. The particular affirmative and particular negative, for this reason, are related as a mean between contraries.

             6. He shows how the opposed affirmation and negation are related to truth and falsity when he says, Hence in the case of the latter it is impossible that both be at once true, etc. He shows this first in regard to contraries; secondly, in regard to contradictories, where he says, Whenever there are contradictions with respect to universals signifying universally, etc.; thirdly, in regard to those that seem contradictory but are not, where he says, But when the contradictions are of universals not signifying universally, etc.

             First, he says that because the universal affirmative and universal negative are contraries, it is impossible for them to be simultaneously true, for contraries mutually remove each other. However, the particular enunciations that are contradictorily opposed to the universal contraries, can be verified at the same time in the same thing, for example, "Not every man is white" (which is opposed contradictorily to "Every man is white") and "Some man is white" (which is opposed contradictorily to "No man is white").

             A parallel to this is found in the contrariety of things, for white and black can never be in the same thing at the same time; but the remotion of white and black can be in the same thing at the same time, for a thing may be neither white nor black, as is evident in something yellow. In a similar way, contrary enunciations cannot be at once true, but their contradictories, by which they are removed, can be true simultaneously.

             7. Then he says, Whenever there are contradictions with respect to universals signifying universally, one must be true and the other false, etc. Here he shows how truth and falsity are related in contradictories. As was said above, in contradictories the negation does no more than remove the affirmation, and this in two ways: in one way when one of them is universal, the other particular; in another way when each is singular. In the case of the singular, the negation is necessarily referred to the same thing--which is not the case in particulars and indefinites--and cannot extend to more than removing the affirmation. Accordingly, the singular affirmative is always contradictory to the singular negative, the identity of subject and predicate being supposed.

             Aristotle says, therefore, that whether we take the contradiction of universals universally (i.e., one of the universals being taken universally) or the contradiction of singular enunciations, one of them must always be true and the other false. It is not possible for them to be at once true or at once false because to be true is nothing other than to say of what is, that it is, or of what is not that it is not; to be false, to say of what is not, that it is, or of what is, that it is not, as is evident in IV Metaphysicorum.

             8. When he says, But when the contradictions are of universals not signifying universally, etc., he shows how truth and falsity are related to enunciations that seem to be contradictory, but are not. First he proposes how they are related; then he proves it where he says, For if he is ugly, he is not beautiful, etc.; finally, he excludes a possible difficulty where he says, At first sight this might seem paradoxical, etc.

             With respect to the first point we should note that affirmation and negation in indefinite propositions seem to be opposed contradictorily because there is one subject in both of them and it is not determined by a particular sign. Hence, the affirmation and negation seem to be about the same thing. To exclude this, the Philosopher says that in the case of affirmative and negative enunciations of universals not taken universally, one need not always be true and the other false, but they can be at once true. For it is true to say both that "Man is white" and that "Man is not white," and that "Man is honorable" and "Man is not honorable."

             9. On this point, as Ammonius reports, some men, maintaining that the indefinite negative is always to be taken for the universal negative, have taken a position contradictory to Aristotle's. They argued their position in the following way. The indefinite, since it is indeterminate, partakes of the nature of matter; but matter considered in itself is regarded as what is less worthy. Now the universal affirmative is more worthy than the particular affirmative and therefore they said that the indefinite affirmative was to be taken for the particular affirmative. But, they said, the universal negative, which destroys the whole, is less worthy than the particular negative, which destroys the part (just as universal corruption is worse than particular corruption); therefore, they said that the indefinite negative was to be taken for the universal negative.

             They went on to say in support of their position that philosophers, and even Aristotle himself, used indefinite negatives as universals. Thus, in the book Physicorum Aristotle says that there is not movement apart from the thing; and in the book De anima, that there are not more than five senses.

             However, these reasons are not cogent. What they say about matter--that considered in itself it is taken for what is less worthy--is true according to the opinion of Plato, who did not distinguish privation from matter; however, it is not true according to Aristotle, who says in I Physicae, that the evil and ugly and other things of this kind pertaining to defect, are said of matter only accidentally. Therefore the indefinite need not stand always for the more ignoble.

             Even supposing it is necessary that the indefinite be taken for the less worthy, it ought not to be taken for the universal negative; for just as the universal affirmative is more powerful than the particular in the genus of affirmation, as containing the particular affirmative, so also the universal negative is more powerful in the genus of negations. Now in each genus one must consider what is more powerful in that genus, not what is more powerful simply.

             Further, if we took the position that the particular negative is more powerful than all other modes, the reasoning still would not follow, for the indefinite affirmative is not taken for the particular affirmative because it is less worthy, but because something can be affirmed of the universal by reason of itself, or by reason of the part contained under it; whence it suffices for the truth of the particular affirmative that the predicate belongs to one part (which is designated by the particular sign); for this reason the truth of the particular affirmative suffices for the truth of the indefinite affirmative. For a similar reason the truth of the particular negative suffices for the truth of the indefinite negative, because in like manner, something can be denied of a universal either by reason of itself, or by reason of its part.

             Apropos of the examples cited for their argument, it should be noted that philosophers sometimes use indefinite negatives for universals in the case of things that are per se removed from universals; and they use indefinite affirmatives for universals in the case of things that are per se predicated of universals.

             10. When he says, For if he is ugly, he is not beautiful, etc., he proves what he has proposed by something conceded by everyone, namely, that the indefinite affirmative is verified if the particular affirmative is true. We may take two indefinite affirmatives, one of which includes the negation of the other, as for example when they have opposed predicates. Now this opposition can happen in two ways. It can be according to perfect contrariety, as shameful (i.e., dishonorable) is opposed to worthy (i.e., honorable) and ugly (i.e., deformed in body) is opposed to beautiful. But the reasoning by which the affirmative enunciation, "Man is worthy," is true, i.e., by some worthy man existing, is the same as the reasoning by which "Man is shameful" is true, i.e., by a shameful man existing. Therefore these two enunciations are at once true, "Man is worthy" and "Man is shameful." But the enunciation, "Man is not worthy," follows upon "Man is shameful." Therefore the two enunciations, "Man is worthy," and "Man is not worthy," are at once true; and by the same reasoning these two, "Man is beautiful" and "Man is not beautiful."

             The other opposition is according to the complete and incomplete, as to be in movement is opposed to to have been moved, and becoming to to have become. Whence the nonbeing of that which is coming to be in permanent things, whose being is complete, follows upon the becoming but this is not so in successive things, whose being is incomplete. Thus, "Man is white" is true by the fact that a white man exists; by the same reasoning, because a man is becoming white, the enunciation "Man is becoming white" is true, upon which follows, "Man is not white." Therefore, the two enunciations, "Man is white" and "Man is not white" are at once true.

             11. Then when he says, At first sight this might seem paradoxical, etc., he excludes what might present a difficulty in relation to what has been said. At first sight, he says, what has been stated seems to be inconsistent; for "Man is not white" seems to signify the same thing as "No man is white." But he rejects this when he says that they neither signify the same thing, nor are they at once true necessarily, as is evident from what has been said.