Every reference to a correlate, then, conjoins to the substance the conception of a reference to an interpretant; and this is, therefore, the next conception in order in passing from being to substance.
Reference to an interpretant cannot be prescinded from reference to a correlate; but the latter can be prescinded from the former.
§10. Reference to an interpretant is rendered possible and justified by that which renders possible and justifies comparison. But that is clearly the diversity of impressions. If we had but one impression, it would not require to be reduced to unity, and would therefore not need to be thought of as referred to an interpretant, and the conception of reference to an interpretant would not arise. But since there is a manifold of impressions, we have a feeling of complication or confusion, which leads us to differentiate this impression from that, and then, having been differentiated, they require to be brought to unity. Now they are not brought to unity until we conceive them together as being ours, that is, until we refer them to a conception as their interpretant. Thus, the reference to an interpretant arises upon the holding together of diverse impressions, and therefore it does not join a conception to the substance, as the other two references do, but unites directly the manifold of the substance itself. It is, therefore, the last conception in order in passing from being to substance.
§11. The five conceptions thus obtained, for reasons which will be sufficiently obvious, may be termed categories. That is,
BEING,
Quality (Reference to a Ground),
Relation (Reference to a Correlate),
Representation (Reference to an Interpretant),
SUBSTANCE.
The three intermediate conceptions may be termed accidents.
§12. This passage from the many to the one is numerical. The conception of a third is that of an object which is so related to two others, that one of these must be related to the other in the same way in which the third is related to that other. Now this coincides with the conception of an interpretant. An other is plainly equivalent to a correlate. The conception of second differs from that of other, in implying the possibility of a third. In the same way, the conception of self implies the possibility of an other. The Ground is the self abstracted from the concreteness which implies the possibility of an other.
§13. Since no one of the categories can be prescinded from those above it, the list of supposable objects which they afford is,
What is.
Quale—that which refers to a ground,
Relate—that which refers to ground and correlate,
Representamen—that which refers to ground, correlate, and interpretant.
It.
§14. A quality may have a special determination which prevents its being prescinded from reference to a correlate. Hence there are two kinds of relation.
1st. That of relates whose reference to a ground is a prescindible or internal quality.
2d. That of relates whose reference to a ground is an unprescindible or relative quality.
In the former case, the relation is a mere concurrence of the correlates in one character, and the relate and correlate are not distinguished. In the latter case the correlate is set over against the relate, and there is in some sense an opposition.
Relates of the first kind are brought into relation simply by their agreement. But mere disagreement (unrecognized) does not constitute relation, and therefore relates of the second kind are only brought into relation by correspondence in fact.
A reference to a ground may also be such that it cannot be prescinded from a reference to an interpretant. In this case it may be termed an imputed quality, If the reference of a relate to its ground can be prescinded from reference to an interpretant, its relation to its correlate is a mere concurrence or community in the possession of a quality, and therefore the reference to a correlate can be prescinded from reference to an interpretant. It follows that there are three kinds of representations.
1st. Those whose relation to their objects is a mere community in some quality, and these representations may be termed Likenesses.
2d. Those whose relation to their objects consists in a correspondence in fact, and these may be termed Indices or Signs.
3d. Those the ground of whose relation to their objects is an imputed character, which are the same as general signs, and these may be termed Symbols.
§15. I shall now show how the three conceptions of reference to a ground, reference to an object, and reference to an interpretant are the fundamental ones of at least one universal science, that of logic. Logic is said to treat of second intentions as applied to first. It would lead me too far away from the matter in hand to discuss the truth of this statement; I shall simply adopt it as one which seems to me to afford a good definition of the subject-genus of this science. Now, second intentions are the objects of the understanding considered as representations, and the first intentions to which they apply are the objects of those representations. The objects of the understanding, considered as representations, are symbols, that is, signs which are at least potentially general. But the rules of logic hold good of any symbols, of those which are written or spoken as well as of those which are thought. They have no immediate application to likenesses or indices, because no arguments can be constructed of these alone, but do apply to all symbols. All symbols, indeed, are in one sense relative to the understanding, but only in the sense in which also all things are relative to the understanding. On this account, therefore, the relation to the understanding need not be expressed in the definition of the sphere of logic, since it determines no limitation of that sphere. But a distinction can be made between concepts which are supposed to have no existence except so far as they are actually present to the understanding, and external symbols which still retain their character of symbols so long as they are only capable of being understood. And as the rules of logic apply to these latter as much as to the former (and though only through the former, yet this character, since it belongs to all things, is no limitation), it follows that logic has for its subject-genus all symbols and not merely concepts.2 We come, therefore, to this, that logic treats of the reference of symbols in general to their objects. In this view it is one of a trivium of conceivable sciences. The first would treat of the formal conditions of symbols having meaning, that is of the reference of symbols in general to their grounds or imputed characters, and this might be called formal grammar; the second, logic, would treat of the formal conditions of the truth of symbols; and the third would treat of the formal conditions of the force of symbols, or their power of appealing to a mind, that is, of their reference in general to interpretants, and this might be called formal rhetoric.
There would be a general division of symbols, common to all these sciences; namely, into,
1°: Symbols which directly determine only their grounds or imputed qualities, and are thus but sums of marks or terms;
2°: