§2. Notes on the Preceding
564. I must acknowledge some previous errors committed by me in expounding my division of signs into icons, indices and symbols. At the time I first published this division in 1867 I had been studying the logic of relatives for so short a time that it was not until three years later that I was ready to go to print with my first memoir on that subject. I had hardly commenced the cultivation of that land which De Morgan had cleared. I already, however, saw what had escaped that eminent master, that besides non-relative characters, and besides relations between pairs of objects, there was a third category of characters, and but this third. This third class really consists of plural relations, all of which may be regarded as compounds of triadic relations, that is, of relations between triads of objects. A very broad and important class of triadic characters [consists of] representations. A representation is that character of a thing by virtue of which, for the production of a certain mental effect, it may stand in place of another thing. The thing having this character I term a representamen, the mental effect, or thought, its interpretant, the thing for which it stands, its object.
565. In 1867, although I had proof (duly published)1) that there was only a third category of characters besides nonrelative characters and dual relations, yet I had not discovered that plural relations (which it had not occurred to me were sometimes not reducible to conjunctions of dual relations) constitute that third class. I saw that there must be a conception of which I could make out some features, but being unfamiliar with it in its generality, I quite naturally mistook it for that conception of representation which I obtained by generalizing for this very purpose the idea of a sign. I did not generalize enough, a form of error into which greater minds than mine might fall. I supposed the third class of characters was quite covered by the representative characters. Accordingly, I declared all characters to be divisible into qualities (nonrelative characters), relations, and representations, instead of into non-relative characters, dual relations, and plural relations.
566. I observed in 18671) that dual relations are of two kinds according as they are or are not constituted by the relate and correlate possessing non-relative characters. This is correct. Two blue objects are ipso facto in relation to one another. It is important to remark that this is not true of characters so far as they are dissimilar. Thus, an orange and justice are not brought into relation to one another by the disparateness of their characters. Drag them into comparison, and then they stand in the relation of dissimilarity, a relation of a quite complex nature. But as the orange and justice exist, their qualities do not constitute a relation of dissimilarity. It must not be overlooked that dissimilarity is not simple otherness. Otherness belongs to hecceities. It is the inseparable spouse of identity: wherever there is identity there is necessarily otherness; and in whatever field there is true otherness there is necessarily identity. Since identity belongs exclusively to that which is hic et nunc, so likewise must otherness. It is, therefore, in a sense a dynamical relation, though only a relation of reason. It exists only so far as the objects concerned are, or are liable to be, forcibly brought together before the attention. Dissimilarity is a relation between characters consisting in otherness of all the subjects of those characters. Consequently, being an otherness, it is a dynamo-logical relation, existing only so far as the characters are, or are liable to be, brought into comparison by something besides those characters in themselves.
567. Similarity, on the other hand, is of quite a different nature. The forms of the words similarity and dissimilarity suggest that one is the negative of the other, which is absurd, since everything is both similar and dissimilar to everything else. Two characters, being of the nature of ideas, are, in a measure, the same. Their mere existence constitutes a unity of the two, or, in other words, pairs them. Things are similar and dissimilar so far as their characters are so. We see, then, that the first category of relations embraces only similarities; while the second, embracing all other relations, may be termed dynamical relations. At the same time, we see from the above remarks that the dynamical relations at once divide themselves into logical, hemilogical and non-logical relations. By logical relations, I mean those in respect to which all pairs [of] objects in the universe are alike; by hemilogical relations those in respect to which there is in reference to each object in the universe only one object (perhaps itself) or some definite multitude of objects which are different from others; while the alogical relations include all other cases. The logical and hemilogical relations belong to the old class of relations of reason, while relations in re are alogical. But there are a few not unimportant relations of reason which are likewise alogical. In my paper of 1867, I committed the error of identifying those relations constituted by non-relative characters with relations of equiparance, that is, with necessarily mutual relations, and the dynamical relations with relations of disquiparance, or possibly non-mutual relations. Subsequently, falling out of one error into another, I identified the two classes respectively with relations of reason and relations in re.