LESSON XII

There Is Only One Negation Opposed to One Affirmation

             17b 37 It is evident also that there is one negation of one affirmation;

             17b 39 for the negation must deny the same thing that the affirmation affirms, and of the same subject, either something singular, or something universal, and either universally or not universally.

             18a 2 For example, the negation of "Socrates is white" is "Socrates is not white." (If something else is said of the same subject or the same thing of a different subject, it will not be opposed to it but different from it.) The negation opposed to "Every man is white" is "Not every man is white"; to "Some man is white," "No man is white"; to "Man is white," "Man is not white."

             18a 7 We have said that there is one negation opposed contradictorily to one affirmation, and what these are; and that the others are contraries, and what these are; and that in every contradiction one is not always true and the other false, and what the reason is for this, and when it is the case that one is true and the other false.

             18a 12 Affirmation or negation is one when one thing is signified of one thing, whether the subject is universal and is taken universally or not; as in "Every man is white" and "Not every man is white"; "Man is white" and "Man is not white"; "No man is white" and "Some man is white"; provided the "white" signifies one thing.

             18a 18 But if one name is imposed for two things, from which there is not one thing, the affirmation is not one. For example, if someone were to impose the name "cloak" on horse and man, the enunciation "Cloak is white" would not be one affirmation, nor would "Cloak is not white" be one negation.

             18a 21 For this is no different from saying "Horse and man is white," and this no different from saying, "Horse is white" and "Man is white." If, then, these signify many things and are many, it is evident that the first enunciation ["Cloak is white"] signifies many things--or nothing, for there is not such a thing as a horse-man.

             18a 26 Consequently, in such enunciations it is not necessary that one contradictory be true and the other false.

             1. Having distinguished the diverse modes of opposition in enunciations, the Philosopher now proposes to show that there is one negation opposed to one affirmation. First he shows that there is one negation opposed to one affirmation; then he manifests what one affirmation and negation are, where he says, Affirmation or negation is one when one thing is signified of one thing, etc. With respect to what he intends to do he first proposes the point; then he manifests it where he says, for the negation must deny the same thing that the affirmation affirms, etc. Finally, he gives a summary of what has been said, where he says, We have said that there is one negation opposed contradictorily to one affirmation, etc.

             2. He says, then, that it is evident that there is only one negation of one affirmation. It is necessary to make this point here because he has posited many kinds of opposition and it might appear that two negations are opposed to one affirmation. Thus it might seem that the negative enunciations, "No man is white" and "Some man is not white" are both opposed to the affirmative enunciation, "Every man is white." But if one carefully examines what has been said it will be evident that the only negative opposed to "Every man is white" is "Some man is not white," which merely removes it, as is clear from its equivalent, "Not every man is white." It is true that the negation of the universal affirmative is included in the understanding of the universal negative inasmuch as the universal negative includes the particular negative, but the universal negative adds something over and beyond this inasmuch as it not only brings about the removal of universality but removes every part of it. Thus it is evident that there is only one negation of a universal affirmation, and the same thing is evident in the others.

             3. When he says, for the negation must deny the same thing that the affirmation affirms, etc., he manifests what he has said: first, from reason; secondly, by example.

             The reasoning is taken from what has already been said, namely, that negation is opposed to affirmation when the enunciations are of the same thing of the same subject. Here he says that the negation must deny the same predicate the affirmation affirms, and of the same subject, whether that subject be something singular or something universal, either taken universally or not taken universally. But this can only be done in one way, i.e., when the negation denies what the affirmation posits, and nothing else. Therefore there is only one negation opposed to one affirmation.

             4. In manifesting this by example, where he says, For example, the negation of "Socrates is white," etc., he first takes examples of singulars. Thus, "Socrates is not white" is the proper negation opposed to "Socrates is white." If there were another predicate or another subject, it would not be the opposed negation, but wholly different. For example, "Socrates is not musical" is not opposed to "Socrates is white," nor is "Plato is white" opposed to "Socrates is not white."

             Then he manifests the same thing in an affirmation with a universal universally taken as the subject. Thus, "Not every man is white," which is equivalent to the particular negative, is the proper negation opposed to the affirmation, "Every man is white."

             Thirdly, he gives an example in which the subject of the affirmation is a universal taken particularly. The proper negation opposed to the affirmation "Some man is white" is "No man is white," for to say "no" is to say "not any," i.e., "not some."

             Finally, he gives as an example enunciations in which the subject of the affirmation is the universal taken indefinitely; "Man is not white" is the proper negation opposed to the affirmation "Man is white."

             5. The last example used to manifest his point seems to be contrary to what he has already said, namely, that the indefinite negative and the indefinite affirmative can be simultaneously verified; but a negation and its opposite affirmation cannot be simultaneously verified, since it is not possible to affirm and deny of the same subject.

             But what Aristotle is saying here must be understood of the negation when it is referred to the same thing the affirmation contained, and this is possible in two ways: in one way, when something is affirmed to belong to man by reason of what he is (which is per se to be predicated of the same thing), and this very thing the negation denies; secondly, when something is affirmed of the universal by reason of its singular, and the same thing is denied of it.

             6. He concludes by summarizing what has been said: We have said that there is one negation opposed contradictorily to one affirmation, etc. He considers it evident from what has been said that one negation is opposed to one affirmation; and that of opposite affirmations and negations, one kind are contraries, the other contradictories; and that what each kind is has been stated. He does not speak of subcontraries because it is not accurate to say that they are opposites, as was said above. He also says here that it has been shown that not every contradiction is true or false, "contradiction" being taken here broadly for any kind of opposition of affirmation and negation; for in enunciations that are truly contradictory one is always true and the other false. The reason why this may not be verified in some kinds of opposites has already been stated, namely, because some are not contradictories but contraries, and these can be false at the same time. It is also possible for affirmation and negation not to be properly opposed and consequently to be true at the same time. It has been stated, however, when one is always true and the other false, namely, in those that are truly contradictories.

             7. The Philosopher explains what one affirmation or negation is where he says, Affirmation or negation is one when one thing is signified of one thing, etc. He did in fact state this earlier when he said that an enunciation is one when it signifies one thing, but because the enunciation in which something is predicated of a universal, either universally or not universally, contains under it many things, he is going to show here that unity of enunciation is not impeded by this.

             First he shows that unity of enunciation is not impeded by the multitude contained under the universal, whose notion is one. Then he shows that unity of enunciation is impeded by the multitude contained under the unity of a name only, where he says, But if one name is imposed for two things, etc.

             He says, then, that an affirmation or negation is one when one thing is signified of one thing, whether the one thing that is subjected be a universal taken universally, or not, i.e., it may be a universal taken particularly or indefinitely, or even a singular. He gives examples of the different kinds: such as, the universal affirmative "Every man is white" and the particular negative, which is its negation, "Not every man is white," each of which is one. There are other examples which are evident. At the end he states a condition that is required for any of them to be one, i.e., provided the "white," which is the predicate, signifies one thing; for a multiple predicate with a subject signifying one thing would also impede the unity of an enunciation. The universal proposition is therefore one, even though it comprehends a multitude of singulars under it, for the predicate is not attributed to many singulars according as each is divided from the other, but according as they are united in one common thing.

             8. When he says, But if one name is imposed for two things, he shows that unity of name alone does not suffice for unity of an enunciation. He first makes the point; secondly, he gives an example, where he says, if someone were to impose the name "cloak" on horse and man, etc.; thirdly, he proves it where he says, For this is no different from saying "Horse and man is white," etc.; finally, he infers a corollary from what has been said, where he says, Consequently, in such enunciations, it is not necessary, etc.

             If one name is imposed for two things, he says, from which one thing is not formed, there is not one affirmation. The from which one thing is not formed can be understood in two ways. It can be understood as excluding the many that are contained under one universal, as man and horse under animal, for the name "animal" signifies both, not as they are many and different from each other but as they are united in the nature of the genus. It can also be understood--and this would be more accurate--as excluding the many parts from which something one is formed, whether the parts of the notion as known, as the genus and the difference, which are parts of the definition, or the integral parts of some composite, as the stones and wood from which a house is made. If, then, there is such a predicate which is attributed to a thing, the many that are signified must concur in one thing according to some of the modes mentioned in order that there be one enunciation; unity of vocal sound alone would not suffice. However, if there is such a predicate which is referred to vocal sound, unity of vocal sound would suffice, as in "'Dog' is a name."

             9. He gives an example of what he means where he says, For example, if someone were to impose the name "cloak," etc. That is, if someone were to impose the name "cloak" to signify man and horse and then said, "Cloak is white," there would not be one affirmation, nor would there be one negation.

             He proves this where he says, For this is no different from saying, etc. His argument is as follows. If "cloak" signifies man and horse there is no difference between saying "Cloak is white" and saying, "Man is white, and, Horse is white." But "Man is white, and, horse is white" signify many and are many enunciations. Therefore, the enunciation, "Cloak is white," signifies many things. This is the case if "cloak" signifies man and horse as diverse things; but if it signifies man and horse as one thing, it signifies nothing, for there is not any thing composed of man and horse.

             When Aristotle says that there is no difference between saying "Cloak is white" and, "Man is white, and, horse is white," it is not to be understood with respect to truth and falsity. For the copulative enunciation "Man is white and horse is white" cannot be true unless each part is true; but the enunciation "Cloak is white," under the condition given, can be true even when one is false; otherwise it would not be necessary to distinguish multiple propositions to solve sophistic arguments. Rather, it is to be understood with respect to unity and multiplicity, for just as in "Man is white and horse is white" there is not some one thing to which the predicate is attributed, so also in "Cloak is white."

             10. When he says, Consequently, it is not necessary in such enunciations, etc., he concludes from what has been said that in affirmations and negations that use an equivocal subject, one need not always be true and the other false since the negation may deny something other than the affirmation affirms.