476. There, then, we have an example of a genuine triad and of a triadic conception. But what is the general description of a genuine triad? I am satisfied that no triad which does not involve generality, that is, the assertion of which does not imply something concerning every possible object of some description can be a genuine triad. The mere addition of one to two makes a triad; and therein is contained an idea entirely indecomposable into the ideas of one and two. For addition implies two subjects added, and something else as the result of the addition. Hence, it is wrong to define two as the sum of one and one; for according to such a definition, two would involve the idea of three. The idea characteristic of two is other. The corresponding idea characteristic of three is third. Medium is nearly as broad, and so is uniter.
477. The genuine triad contains no idea essentially different from those of object, other, third. But it involves the idea of a third not resoluble into a formless aggregation. In other words, it involves the idea of something more than all that can result from the successive addition of one to one. This »all that can« involves the idea of every possible something, and therefore of generality. The genuine triad, then, must involve generality.
478. The world of fact contains only what is, and not everything that is possible of any description. Hence, the world of fact cannot contain a genuine triad. But though it cannot contain a genuine triad, it may be governed by genuine triads.
So much for the division of triads into the monadic, dyadic, and triadic of [or?] genuine triads.
479. Dyadic triads are obviously of two kinds, first, those which have two monadic subjects, as a high perfume and a burning taste are united in many essential oils, and secondly, those which have all their subjects individuals.
480. Genuine triads are of three kinds. For while a triad if genuine cannot be in the world of quality nor in that of fact, yet it may be a mere law, or regularity, of quality or of fact. But a thoroughly genuine triad is separated entirely from those worlds and exists in the universe of representations. Indeed, representation necessarily involves a genuine triad. For it involves a sign, or representamen, of some kind, outward or inward, mediating between an object and an interpreting thought. Now this is neither a matter of fact, since thought is general, nor is it a matter of law, since thought is living.
481. So much for the first order of subdivisions of the three classes of triads. Passing to the lower subdivisions, I find among those of the degenerate triads nothing of particular philosophical interest; though something may have been overlooked. But among the lower subdivisions of the genuine triads there is an abundance.
482. We first consider the first two of the three chief divisions of genuine triads, which are the laws of quality and the laws of fact. The laws of quality are all of one type. Namely, they all simply determine systems of qualities, of which Sir Isaac Newton's law of color-mixture with Dr. Thomas Young's supplement thereto, is the most perfect known example.
483. The laws of fact divide themselves at the outset into those which must be true if there be any true answer to every question that has a meaning, or, as we say, into laws logically necessary and laws logically contingent. To this division another is intimately connected. Namely, of laws logically contingent the most universal are of such a kind that they must be true provided every form which by logical necessity must be thought of a given subject is also a form of its real being. Calling this kind of necessity, metaphysical necessity, we may divide laws logically contingent into laws metaphysically necessary and laws metaphysically contingent.
484. The general law of quality, as distinct from the classificatory system of quality (of which we can have but a fragmentary knowledge), has three clauses, relating respectively to single qualities, to pairs of qualities, and to triads of qualities. The first clause is that every quality is perfect and in itself such as it is. The second more complex law is that two qualities have one or other of two sorts of relations to one another; namely, they may be, first, independent of one another, somewhat resembling and somewhat differing from one another, or secondly, one of them may be merely a further determination of the other, this latter being essentially the first of the pair in the order of evolution, or synthesis, while it is the second of the pair in the order of involution or analysis. The third clause relates to the respects, or third qualities, in which two compared qualities agree or differ. The first of these respects is the quality of the quality, or, as we may say, its hue, in which respect the tastes of sugar and salt differ, or the pitch of sounds, or the respect in which red, blue, and green differ. The second respect is the absolute intensity of the quality, loudness in sounds, luminosity in color, strength in tastes and smells, etc. The third respect is purity, or the relative intensity of the strongest elements. It is great in high colors and in musical sounds. In some cases strength and weakness have peculiar hues. Bright colors tend toward yellow, dim colors toward violet. Very faint sounds tend toward a certain pitch. Purity and impurity may have their peculiar hues.
485. The general law of logic has likewise its three clauses. The monadic clause is that fact is in its existence perfectly definite. Inquiry properly carried on will reach some definite and fixed result or approximate indefinitely toward that limit. Every subject is existentially determinate with respect to each predicate. The dyadic clause is that there are two and but two possible determinations of each subject with reference to each predicate, the affirmative and the negative. Not only is the dyadic character manifest by the double determination, but also by the double prescription; first that the possibilities are two at least, and second that they are two at most. The determination is not both affirmative and negative, but it is either one or the other. A third limiting form of determination belongs to any subject [with regard] to [some other] one whose mode of existence is of a lower order, [the limiting case involving] a relative zero, related to the subjects of the affirmation and the negation as an inconsistent hypothesis is to a consistent one. The triadic clause of the law of logic recognizes three elements in truth, the idea, or predicate, the fact or subject, the thought which originally put them together and recognizes they are together; from whence many things result, especially a threefold inferential process which either first follows the order of involution from living thought or ruling law, and existential case under the condition of the law to the predication of the idea of the law in that case; or second, proceeds from the living law and the inherence of the idea of that law in an existential case, to the subsumption of that case and to the condition of the law; or third, proceeds from the subsumption of an existential case under the condition of a living law, and the inherence of the idea of that law in that case to the living law itself.1) Thus the law of logic governs the relations of different predicates of one subject.