Lecture 9 — The opposition of affirmation and negation absolutely

17a26. Since it is possible to enunciate that what belongs to a subject does not belong to it and what does not, does, and that what does belong to it, does, and what does not, does not, and to enunciate these in regard to those times outside of the present as well as of the present, it would be possible to deny whatever someone affirms and to affirm what he denies. It is evident, therefore, that there is a negation opposed to every affirmation and an affirmation opposed to every negation.

17a33. We will call this opposed affirmation and negation “contradiction.”

17a34. I mean by “opposed” the enunciation of the same thing of the same subject—not equivocally, however, nor in any of the other ways that we have distinguished in reference to the specious difficulties of the sophists.

Since it is possible to enunciate. Having made the division of the enunciation, Aristotle now deals with the opposition of the parts of the enunciation, that is, the opposition of affirmation and negation.

He has already said that the enunciation is speech in which there is truth or falsity. Therefore, he first shows how enunciations are opposed to each other;

second, he raises a doubt about some things previously determined and resolves it, at: in enunciations about that which is or has taken place (18a28; [164]).

He not only shows how one enunciation is opposed to another, but that only one is opposed to one, at: it is evident also that there is one negation of one affirmation (17b38; [154]).

In showing how one enunciation is opposed to another, he first treats of the opposition of affirmation and negation absolutely;

second, he shows in what way opposition of this kind is diversified on the part of the subject, at: since some of the things we are concerned with are universal (17a38; [125]).

About the first he does two things.

First, he shows that there is a negation opposed to every affirmation and vice versa;

second, at: we will call this opposed affirmation and negation “contradiction” (17a33; [115]), he explains the opposition of affirmation and negation absolutely.

In relation to the first point—that there is a negation opposed to every affirmation, and vice versa—the Philosopher assumes a twofold diversity of enunciation.

The first arises from the very form or mode of enunciating. According to this diversity, enunciation is either affirmative (in which it is enunciated that something is), or negative (in which it is signified that something is not).

The second is the diversity that arises by comparison to reality. Truth and falsity of thought and of the enunciation depend upon this comparison, for when it is enunciated that something is or is not, if there is agreement with reality, there is true speech. Otherwise, there is false speech.

The enunciation can therefore be varied in four ways according to a combination of these two divisions.

In the first way, what is in reality is enunciated to be as it is in reality—for example, when Socrates runs, we say, “Socrates is running.”

In the second way, it is enunciated that something is not that which it is not in reality. This is characteristic of true negation, as when we say, “An Ethiopian is not white.”

In the third way, it is enunciated that something is what in reality it is not, as when it is said, “The raven is white.”

In the fourth way, it is enunciated that something is not what it is in reality, for example, if it is said that “snow is not white,” which is a false negation.

In order to proceed from the weaker to the stronger, the Philosopher puts the false before the true, and among these he states the negative before the affirmative.

He begins, then, with the false negative; it is possible to enunciate, that what is, namely, in reality, is not (17a26).

Second, he posits the false affirmative: and that what is not, namely, in reality, is.

Third, he posits the true affirmative, which is opposed to the false negative he gave first: and that what is, namely, in reality, is.

Fourth, he posits the true negative, which is opposed to the false affirmative: and that what is not, namely, in reality, is not.

In saying what is and what is not, Aristotle is not referring only to the existence or nonexistence of a subject. What he is saying is that the reality signified by the predicate is in or is not in the reality signified by the subject. For what is signified in saying, “The raven is white,” is that what is not, is, although the raven itself is an existing thing.

These four differences of enunciations are found in propositions in which there is a verb of present time, and they are also found in enunciations in which there are verbs of past or future time. He said earlier that every enunciative speech must contain a verb or a mode of the verb. Here he makes this point in relation to the four differences of enunciations: similarly it is possible to enunciate these, that is, that the enunciation be varied in diverse ways, in regard to those times outside of the present, that is, with respect to the past or future, which are in a certain way extrinsic in respect to the present, since the present is between the past and the future.

Since there are these four differences of enunciation in past and future time as well as in present time, it is possible to deny everything that is affirmed and to affirm everything that is denied. This is evident from the premises, for it is only possible to affirm either that which is in reality according to past, present, or future time, or that which is not. It is also possible to deny all of this. It is clear, then, that everything that is affirmed can be denied, and vice versa.

Now, since affirmation and negation are in itself opposed, that is, in an opposition of contradiction, it follows that any affirmation would have a negation opposed to it, and conversely. The contrary of this could happen only if an affirmation could affirm something that the negation could not deny.

When he says: we will call this opposed affirmation and negation “contradiction” (17a33), he explains what absolute opposition of affirmation and negation is.

He does this first through the name;

second, through the definition where he says: I mean by “opposed” (17a34; [116]).

He says that “contradiction” is the name imposed for the kind of opposition in which a negation is opposed to an affirmation (and conversely). By saying: we will call this “contradiction”, we are given to understand—as Ammonius points out—that he has himself imposed the name “contradiction” for the opposition of affirmation and negation.

Then he defines contradiction when he says: I mean by “opposed” (17a34).

Since contradiction is the opposition of affirmation and negation, as he has said, whatever is required for the opposition of affirmation and negation is required for contradiction. Now, opposites must be about the same thing, and since the enunciation is made up of a subject and predicate, the first requirement for contradiction is affirmation and negation of the same predicate. For if we say, “Plato runs, and Plato does not discuss,” there is no contradiction.

The second is that the affirmation and negation be of the same subject, for if we say, “Socrates runs, and Plato does not run,” there is no contradiction.

The third requirement is identity of subject and predicate not only according to name but according to the thing and the name at once. Clearly, if the same name is not used, there is not one and the same enunciation; similarly, there must be identity of the thing, for as was said above, the enunciation is one when it signifies one thing said of one thing. This is why he adds: not equivocally, however, for identity of name with diversity of the thing—which is equivocation—is not sufficient for contradiction.

There are also certain other things that must be observed with respect to contradiction so that all diversity is destroyed except the diversity of affirmation and negation, for if the negation does not deny in every way the same thing that the affirmation affirms, there will not be opposition.

Inquiry can be made about this diversity in respect to four things.

First, are there diverse parts of the subject? For if we say that an Ethiopian is white as to teeth and not white as to foot, there is no contradiction.

Second, is there a diverse mode on the part of the predicate? For there is no contradiction if we say, “Socrates runs slowly,” and “Socrates is not moving swiftly,” or “An egg is an animal in potency,” and “An egg is not an animal in act.”

Third, is there diversity on the part of measure, such as of place or time? For there is no contradiction if we say, “It is raining in Gaul,” and “It is not raining in Italy,” or “It rained yesterday,” and “It did not rain today.”

Fourth, is there diversity from a relationship to something extrinsic? For example, when we say, “Ten men are many in respect to a house, but not in respect to a market.”

Aristotle designates all of these when he adds: nor in any of the other ways that we have distinguished; in other words, it is usual to determine in disputations against the specious difficulties of the sophists, that is, against the fallacious and quarrelsome objections of the sophists, which he mentions more fully in Sophistical Refutations 1.5, 166b28–167a36.