… if the ground determines the subject in itself, there will be no relation of the representation to its object in itself but only in the subject. No quality of the object will be implied by the representation, therefore, since that would be a ground of agreement in the object. The representation will therefore be unsusceptible of truth. An imperfect example of such a representation is a proper name the ground of which is a convention between the persons who use it. Such a representation may be called an index.
… the relation of a repraesentamen to its object (correlate) may be a real relation and, then, either an agreement or a difference, or it may be an ideal r[elati]on or one from which the reference to a correspondent (subject of representation) cannot be prescinded by position. [—] In the second case, there is a real difference of the repraesentamen from its object, that is to say not a mere difference in quality but also a bringing of them together in nature; in this case the representative character of the one will consist in constant accompaniment by the other, so that it indicates the existence of the latter without noting any characters of it. Such a representation may be termed an index.
An index represents its object by a real correspondence with it - as a tally does quarts of milk, and a vane the wind. [—] An index is a representation whose relation to its object is prescidible and is a Disquiparence, so that its peculiar Quality is not prescindible but is relative.
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.
… if the triple relation between the sign, its object, and the mind, is degenerate, then of the three pairs
two at least are in dual relations which constitute the triple relation. One of the connected pairs must consist of the sign and its object, for if the sign were not related to its object except by the mind thinking of them separately, it would not fulfill the function of a sign at all. Supposing, then, the relation of the sign to its object does not lie in a mental association, there must be a direct dual relation of the sign to its object independent of the mind using the sign. In the second of the three cases just spoken of, this dual relation is not degenerate, and the sign signifies its object solely by virtue of being really connected with it. Of this nature are all natural signs and physical symptoms. I call such a sign an index, a pointing finger being the type of the class.
The index asserts nothing; it only says “There!” It takes hold of our eyes, as it were, and forcibly directs them to a particular object, and there it stops. Demonstrative and relative pronouns are nearly pure indices, because they denote things without describing them; so are the letters on a geometrical diagram, and the subscript numbers which in algebra distinguish one value from another without saying what those values are.
One very important triad is this: it has been found that there are three kinds of signs which are all indispensable in all reasoning; the first is the diagrammatic sign or icon, which exhibits a similarity or analogy to the subject of discourse; the second is the index, which like a pronoun demonstrative or relative, forces the attention to the particular object intended without describing it; the third is the general name or description which signifies its object by means of an association of ideas or habitual connection between the name and the character signified.
There may be a mere relation of reason between the sign and the thing signified; in that case the sign is an icon. Or there may be a direct physical connection; in that case, the sign is an index. Or there may be a relation which consists in the fact that the mind associates the sign with its object; in that case the sign is a name.
… a symbol, in itself, is a mere dream; it does not show what it is talking about. It needs to be connected with its object. For that purpose, an index is indispensable. No other kind of sign will answer the purpose. That a word cannot in strictness of speech be an index is evident from this, that a word is general - it occurs often, and every time it occurs, it is the same word, and if it has any meaning as a word, it has the same meaning every time it occurs; while an index is essentially an affair of here and now, its office being to bring the thought to a particular experience, or series of experiences connected by dynamical relations. A meaning is the associations of a word with images, its dream exciting power. An index has nothing to do with meanings; it has to bring the hearer to share the experience of the speaker by showing what he is talking about.
The index is physically connected with its object; they make an organic pair, but the interpreting mind has nothing to do with this connection, except remarking it, after it is established.
A sign which denotes a thing by forcing it upon the attention is called an index. An index does not describe the qualities of its object. An object, in so far as it is denoted by an index, having thisness, and distinguishing itself from other things by its continuous identity and forcefulness, but not by any distinguishing characters, may be called a hecceity.
Index (in exact logic). A sign, or representation, which refers to its object not so much because of any similarity or analogy with it, nor because it is associated with general characters which that object happens to possess, as because it is in dynamical (including spatial) connection both with the individual object, on the one hand, and with the senses or memory of the person for whom it serves as a sign, on the other hand.
Indices may be distinguished from other signs, or representations, by three characteristic marks: first, that they have no significant resemblance to their objects; second, that they refer to individuals, single units, single collections of units, or single continua; third, that they direct the attention to their objects by blind compulsion. But it would be difficult if not impossible, to instance an absolutely pure index, or to find any sign absolutely devoid of the indexical quality. Psychologically, the action of indices depends upon association by contiguity, and not upon association by resemblance or upon intellectual operations.
An index is a sign which would, at once, lose the character which makes it a sign if its object were removed, but would not lose that character if there were no interpretant. Such, for instance, is a piece of mould with a bullet-hole in it as sign of a shot; for without the shot there would have been no hole; but there is a hole there, whether anybody has the sense to attribute it to a shot or not.
A Sign degenerate in the lesser degree, is an Obsistent Sign, or Index, which is a Sign whose significance of its Object is due to its having a genuine Relation to that Object, irrespective of the Interpretant. Such, for example, is the exclamation “Hi!” as indicative of present danger, or a rap at the door as indicative of a visitor.
An Index or Seme is a Representamen whose Representative character consists in its being an individual second. If the Secondness is an existential relation, the Index is genuine. If the Secondness is a reference, the Index is degenerate. A genuine Index and its Object must be existent individuals (whether things or facts), and its immediate Interpretant must be of the same character. But since every individual must have characters, it follows that a genuine Index may contain a Firstness, and so an Icon as a constituent part of it. Any individual is a degenerate Index of its own characters. Examples of Indices are the hand of a clock, and the veering of a weathercock.
… what is an index, or true symptom? It is something which, without any rational necessitation, is forced by blind fact to correspond to its object.
An Index is a sign which refers to the Object that it denotes by virtue of being really affected by that Object. It cannot, therefore, be a Qualisign, because qualities are whatever they are independently of anything else. In so far as the Index is affected by the Object, it necessarily has some Quality in common with the Object, and it is in respect to these that it refers to the Object. It does, therefore, involve a sort of Icon, although an Icon of a peculiar kind; and it is not the mere resemblance of its Object, even in these respects which makes it a sign, but it is the actual modification of it by the Object.
An index is a representamen which fulfills the function of a representamen by virtue of a character which it could not have if its object did not exist, but which it will continue to have just the same whether it be interpreted as a representamen or not. For instance, an old-fashioned hygrometer is an index. For it is so contrived as to have a physical reaction with dryness and moisture in the air, so that the little man will come out if it is wet, and this would happen just the same if the use of the instrument should be entirely forgotten, so that it ceased actually to convey any information.
A pure icon can convey no positive or factual information; for it affords no assurance that there is any such thing in nature. But it is of the utmost value for enabling its interpreter to study what would be the character of such an object in case any such did exist. Geometry sufficiently illustrates that. Of a completely opposite nature is the kind of representamen termed an index. This is a real thing or fact which is a sign of its object by virtue of being connected with it as a matter of fact and by also forcibly intruding upon the mind, quite regardless of its being interpreted as a sign. It may simply serve to identify its object and assure us of its existence and presence. But very often the nature of the factual connexion of the index with its object is such as to excite in consciousness an image of some features of the object, and in that way affords evidence from which positive assurance as to truth of fact may be drawn. A photograph, for example, not only excites an image, has an appearance, but, owing to its optical connexion with the object, is evidence that that appearance corresponds to a reality.
I define an Index as a sign determined by its dynamic object by virtue of being in a real relation to it. Such is a Proper Name (a legisign); such is the occurrence of a symptom of a disease (the symptom itself is a legisign, a general type of a definite character. The occurrence in a particular case is a sinsign).
An index is a sign fit to be used as such because it is in real reaction with the object denoted.
… an analysis of the essence of a sign, (stretching that word to its widest limits, as anything which, being determined by an object, determines an interpretation to determination, through it, by the same object), leads to a proof that every sign is determined by its object, either first, by partaking in the characters of the object, when I call the sign an Icon; secondly, by being really and in its individual existence connected with the individual object, when I call the sign an Index; thirdly, by more or less approximate certainty that it will be interpreted as denoting the object, in consequence of a habit (which term I use as including a natural disposition), when I call the sign a Symbol.
… I had observed that the most frequently useful division of signs is by trichotomy into firstly Likenesses, or, as I prefer to say, Icons, which serve to represent their objects only in so far as they resemble them in themselves; secondly, Indices, which represent their objects independently of any resemblance to them, only by virtue of real connections with them, and thirdly Symbols, which represent their objects, independently alike of any resemblance or any real connection, because dispositions or factitious habits of their interpreters insure their being so understood.
Peirce, C. S. (1895 [c.]). On the Logic of Quantity, and especially of Infinity (MS [R] 16)
Peirce, C. S. (1895 [c.]). On the Logic of Quantity (MS [R] 17)
Peirce, C. S. (1903 [c.]). On the Foundations of Mathematics (MS [R] 7)
Peirce, C. S. (1903 [c.]). On the Foundations of Mathematics (MS [R] 8)