§5. Triads

511. Laws which connect phenomena by a synthesis more or less intellectual, or inward, are divided somewhat broadly into laws of the inward relations, or resemblances, of bodies, and laws of mind.

512. The laws of resemblances and differences of bodies are classificatory, or chemical. We know little about them; but we may assert with some confidence that there are differences between substances — i.e., differences in the smallest parts of bodies, and a classification based on that, and there are differences in the structure of bodies, and a classification based on that. Then of these latter we may distinguish differences in the structure of the smallest pieces of bodies, depending on the shape and size of atomicules, and differences in the manner in which bodies are built up out of their smallest pieces. Here we have a distinction between that kind of structure which gives rise to forms without power of truth [true?] growth or inorganic structures, and the chemistry of protoplasms which develope [or] living organisms.

513. Finally laws of mind divide themselves into laws of the universal action of mind and laws of kinds of psychical manifestation.

514. Thus the general scheme of the division of laws is as follows:

{Logical law

{ {Metaphysical law

{

{ { {Law of time

{ {Law of space

{

{ {Nomological laws of physics

{ { {Classificatory laws of physics

{

{ {Nomological laws of psychics

{Classificatory laws of psychics

515. We now come to thoroughly genuine triads, the third class of the third class of triads; and at this stage of the inquiry it is well that we should take our bearings and note just where we are, in order that we may lay out our course for the next advances in the discussion. The monad has no features but its suchness, which appears in logic — let us remember that logic must be our guide throughout — as the signification of the verb. This already receives embodiment in the lowest of the chief forms of logic, the term. The dyad introduced a radically different sort of element, the subject, which first shows itself in the proposition. The dyadic proposition has two subjects, each a sort of mimic monad, but the two [are] of different kinds, one being active, the other passive. The triad brings a third sort of element, the expression of thought, or reasoning, consisting of a colligation of two propositions, not mere dyadic propositions, however, but general beliefs; and these two propositions are connected by a common term and tend to produce a third belief. They not only tend to make the belief, but they also tend to render it true. This reason first emerges in the syllogism, which has three such colligations of premisses. Take the stock example,

All men die;

Enoch is a man;

Therefore, Enoch dies.

These propositions are not dyadic. The first is not so, because it is a rule, not a mere individual fact; the second is not so, because its second term is not a mere monadic quality, still less an individual unit, it is a class-term. The third is not so, because it is thought as a result. Each pair of these three propositions is a reason tending to render the third true. The first and third do so by means of their common monadic character. The first gives dying as a specimen character of all men; now the third declares as a consequence that Enoch dies. This gives Enoch one character of men, and so far as Enoch's dying is a consequence goes toward making him a man. The second and third propositions tend to make the first true by means of their common dyadic subject. The second proposition declares Enoch to be a specimen of a man. The third declares as a consequence that Enoch dies. This makes one man die; and so far as Enoch's dying is a consequence tends to render it true that all men die. Finally, the first two propositions bring about the truth of the third. In this particular case they do so absolutely. They generally tend to do so in a way which ought not to be more convincing, but is more in the way in which the objective truth is conceived to result than the other two. They do so by means of their community with respect to the middle term man, a term which as combining the characters of subject and predicate has a triadic element. For combination is triadism, and triadism is combination. Just as the logical verb with its signification reappears in metaphysics as a quality, an ens having a nature as its mode of being, and as a logical individual subject reappears in metaphysics as a thing, an ens having existence as its mode of being, so the logical reason, or premiss, reappears in metaphysics as a reason, an ens having a reality, consisting in a ruling both of the outward and of the inward world, as its mode of being. The being of the quality lies wholly in itself, the being of the thing lies in opposition to other things, the being of the reason lies in its bringing qualities and things together.

516. In the degenerate dyad there is a metaphysical correspondent to a proposition; but it is a proposition whose two subjects are mere qualities. In the first degenerate triad there is a metaphysical correspondent to a syllogism; but it is a syllogism whose three reasons lie in mere qualities. Thus, orange color is intermediate between red and yellow. The syllogism is this:

Orange has in its own nature a certain indescribable but felt relation to red;

Yellow has a similar relation to orange; as a result,

Yellow has a similar relation to red.

Now, if yellow has a relation to orange and as a result yellow has the same relation to red, this can only be because orange has that same relation to red.

517. In the second degenerate triad there is likewise a metaphysical correspondent to a syllogism; but it is a syllogism whose premisses lie in mere coexistences of dyadic facts. For example:

A is the mother of B;

B is the wife of C;

it results that A is the mother-in-law of C.

In the genuine triad, however, there is a real law, and a real case under the law; so that the reasons are not merely reasons in form, but they really govern the truth.

518. But though there be a real operation of law, yet one of the three reasons may be wanting in triadic reality:

All colors are compounds of so much red, green, and blue;

Yellow is a color;

as a result, Yellow is compounded of proportions of red, green, and blue.

The middle term here is little more than a disjunction of qualities, differing from that only in the separate colors not being explicitly thought. Accordingly, that colors are compounded and that yellow is as a result so compounded only in form goes to make yellow a color; for in the very essence of color it is already given that yellow is a color. This triad is, therefore, only two-thirds genuine, one of its three reasons not being really operative.

519. A somewhat similar case arises when the middle term is a mere generalized dyadic existence.

All bodies are attracted toward one another proportionally to their masses and inversely as the square of the distance, multiplied by a fixed modulus;

The earth and moon have such and such masses and are at such a distance;

as a result, The earth and moon attract one another by so much.

But the last two propositions can hardly be said really to go toward making the truth of the first, since that law is nothing but the expression of the way bodies do move as facts. As far as it concerns the earth and moon it is so in the fact itself, and the earth and moon having such masses and distance as they have does not affect the brute fact, but only makes a certain proposition express that fact.

520. But there is a third kind of genuine triad in regard to which neither of the qualifications of their thorough genuineness applies for the reason that the result is of such a nature that it could not subsist were it not for the middle term which sustains it. A gives B to C. Say he does this by a formal legal act. Then, in this act A deprives himself of B; he also enters into an engagement with C and by virtue of these two sides of the act of gift, and of their unity, C acquires possession of B. But this is a remote result. The immediate result is that he acquires possession of B by the gift of A and without the action of A he could not acquire that possession.