_Contrary Negation_ 2. Thus, Contrary Negation in its essence is affirmation with a negative intention, and we may take as a type of it in this wider sense the affirmation of a positive character with the intention of denying another positive character. _E.g._ when you deny “This is a right-angled triangle” by asserting “This is an equilateral triangle,” you have typical contrary negation. It is not really safe to speak of contraries except with reference to _judgments_, intended to deny each {129} other; but it is common to speak of species of the same genus as contraries or opposites, because the same thing cannot be both. [1] [1] Bain, p. 55 ff. We must therefore distinguish _contrary_ from _different_. Of course the same thing or content has many different qualities, and even combines qualities that we are apt to call contrary or opposite. But as Plato was fond of pointing out, a thing cannot have different or opposing qualities in the same relation, that is to say, belonging to the same subject under the same condition. The same thing may be blue in one part of it and green in another, and the same part of it may be blue by daylight and green by candlelight. But the same surface cannot be blue and green at once by the same light to the same eye looking in the same direction. _Different_ qualities become _contrary_ when they claim to stand in the same relation to the same subject. Right-angled triangles and equilateral triangles do not deny each other if we leave them in peace side by side. They are then merely different species of the same genus, or different combinations of the same angular space. But if you say, “This triangle is right-angled,” and I say “It is equilateral,” then they deny each other, and become true contraries. Then the _meaning_ of denial is always of the nature of _contrary_ denial. As we always speak and think within a general subject or universe of discourse, it follows that every denial substitutes some affirmation for the judgment which it denies. The only judgments in which this is not the case are those called by an unmeaning tradition Infinite Judgments, _i.e._ judgments in which the negative predicate {130} includes every determination which has applicability to the Subject. This is because the attribute denied has no applicability to the Subject, and therefore all that has applicability is undiscriminatingly affirmed, in other words, the judgment has no meaning. “Virtue is not-square.” This suggests no definite positive quality applicable to virtue, and therefore is idle. You may safely analyse a significant negative judgment, “A is not B” as = “A is not B but C,” or as = “A is X, which excludes B.” For X may be undetermined, “a colour not red.” But then if the meaning is always affirmative or positive, why do we ever use the negative form? _Why use Negation?_