Aburks=icon,%20index,%20and%20symbol%20[semiótica].pdf

Icon, Index, and Symbol Arthur W. Burks Philosophy and Phenomenological Research, Vol. 9, No. 4. (Jun., 1949), pp. 673-689. Stable URL: http://links.jstor.org/sici?sici=0031-8205%28194906%299%3A4%3C673%3AIIAS%3E2.0.CO%3B2-3 Philosophy and Phenomenological Research is currently published by International Phenomenological Society.

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ICON, INDEX, AND SYMBOL This paper is divided into two sections. The first makes a critical examination of Peirce's classification of signs into icon, index, and symbol. The second offers an analysis of the nature of indexical signs which goes considerably beyond what Peirce has said on the subject.

I. Peirce's Classification of Signs into Icon, Index, and Symbol Charles 5. Peirce's division of signs into icon, index, and symbol is the simplest of his many classifications of signs, and is, moreover, the most important of them all, for it contains the essence of even the most complicated of them without sharing their repetitive and unwieldy character. Historically, the more complicated classifications developed as expansions of the simpler one, in recognition of distinctions that can and should be made. Peirce made these distinctions, however, in a way which is too bound up with his system of categories to be of use outside his philosophy, and without adding anything novel to his original trichotomy.' In this section, then, we shall attempt to provide a critical exposition of Pierce's earliest and most basic classification. Let us begin with a preliminary explanation of the three kinds of signs, the symbol, the index, and the icon, to be taken in that order. We can best do this in terms of the following examples: (1) the word 'red', as used in the English sentence, 'The book is red'; (2) an act of pointing, used to call attention to some particular object, e.g., a tree; (3) a scale drawing, used to communicate to a machinist the structure of a piece of machinery. All of these are signs in the general sense in which this term is used by Peirce: each satisfies his definition of a sign2as something which represents or signifies an object to some interpretant (1.346, 2.228, 4.531).3 In the above examples the objects are: the color red, the tree, and the structure of the machine, respectively; the interpretants are, in each case, the minds understanding the sign. But there are 1 For a brief discussion of the entire hierarchy of Peirce's classifications, see "Peirce's Sixty-Six Signs," by Paul Weiss and Arthur Burks, The Journal of Philosophy, Vol. X L I I (1945)' pp. 383-388. 2 The use of Peirce's definitions of 'sign', 'icon', 'index', and 'symbol' here and throughout the rest of this section is not intended to imply that the author regards them as satisfactory for the theory of signs. I n particular, we find Peirce's definition of an index inadequate for a number of reasons (see footnotes 8, 14, and 18) and so replace i t in the second section with a new analysis of indices. 3 These and the following numerical references are to the Collected Papers of Charles Sanders Peirce, edited by Charles Hartshorne and Paul Weiss.

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some important differences in the way in which these signs signify or represent their objects, and it is on the basis of these differences that the classification is made. A sign represents its object to its interpretant symbolically, indexically, or iconically according to whether it does so (1) by being associated with its object by a conventional rule used by the interpretant (as in the case of 'red'); (2) by being in existential relation with its object (as in the case of the act of pointing); or (3) by exhibiting its object (as in the case of the diagram). Let us examine further the application of these criteria to our three examples. Consider first the word 'red'. The word 'red' is a symbol because it stands for the quality red to an interpretant4 who interprets it in virtue of the conventional linguistic rule of English establishing the meaning of this word. Thus any word is a symbol, including words that are indexical (e.g., 'this') and words that are iconic (e.g., an onomatopoetic word). Consider next the act of pointing. Its object is whatever is pointed to, that is, whatever is in a certain physical relation to the sign. Here the tree is selected or indicated by virtue of its being in the direction of the pointed finger, only a few yards away from it, etc. Hence the act of pointing is an index, i.e., a sign which determines its object on the basis of an existential connection. The symbol 'this' is also an index, because (apart from the conventional element by virtue of which it is a symbol) it may function very much the same as the act of pointing; i.e., instead of pointing to a tree one may use the phrase 'this tree'. The object of a specific occurrence or token of 'this' is determined or selected by virtue of its being in some existential relation to the occurrence of the sign itself. Consider, finally, the diagram. The diagram is an icon because it represents the structure of the machine by exemplifying or exhibiting the same structure in some respects. The draftsman communicates to the machinist the fact that one wheel of the machine has twice the diameter of another by drawing the first wheel with twice the diameter of the second, and so on. I n the same way, an onomatopoetic word when used orally is an icon (as well as a symbol) because the sound of the word suggests or exhibits the sense. I n his unpublished writings Peirce gives us an example of a written analogue of onomatopoetic words, a kind of iconic handwriting that he calls art chirography. He wrote out Poe's "The Raven" in such a hand as to convey the poetic ideas by means of the handwriting as well as the words. This concludes our preliminary explanation of icons, indices, and symIn the interest of brevity this reference to an interpretant will not usually be made explicit hereafter.

bols. We are now ready to take up in greater detail the two which have more novel aspects, the icon and the index; what Peirce has to say about the symbol we can best treat in connection with these. 4 , study of Peirce's theory of sighs is difficult not only because of the unusually fragmentary character of his writings on this subject but also because of the presence of certain inconsistencies and confusions. In many instances these discrepancies are only apparent, resulting from the fact that Peirce tried to work out his views in different ways, and with a varying terminology, a t different times. In other instances the inconsistencies and confusions are real, resulting from his tendency to lump things together and overlook important differences in his eagerness to discover the basis for a comprehensive philosophic system. I n treating the icon and the index, then, we will first examine certain of Peirce's basic statements on each, clarify them, and decide which are consistent with his definitions of 'sign', 'icon', 'index', and 'symbol'. Following that we will take up his views concerning the importance of each kind of sign.

Our definition of an icon states that it is a sign which exhibits or exemplijies its object (cf. 2.282, 3.556, 4.448, 4.531). Peirce, however, often says that an icon is similar to its object (1.558,2.247,2.255,2.276,2.314). Now the first criterion implies that the object of an icon is a general quality (universal) dr relation, whereas the second implies that it is a particular thing or group of things. We have spoken of the diagram as an icon of the structure of the machine; the second criterion makes the diagram an icon of the machine itself. Of course the diagram is similar to the machine only in certain abstract respects; namely, its two-dimensional structure corresponds to the three-dimensional structure of the machine. But in the same way, according to the first criterion, the diagram is an icon of only certain ones of the qualities or relations it exhibits, not of all. Though either way of looking a t the matter is permissible, to avoid confusion Peirce should have distinguished them and adopted one or the other. (The present writer prefers the former and has framed the definition of 'icon' accordingly.) Peirce sometimes implies that a symbol is an icon merely if it possesses or exhibits the quality or relation it signifies (2.247, 2.255, 2.314). On this criterion any token of 'black' printed in black ink is iconic even though the reader (interpretant) is unaware of the fact that it is displaying the quality it represents, i.e., that it is autological. Such a criterion, however, contradicts the original definition of an icon as a sign which exhibits its object to an interpretant; for the definition implies that a sign is not iconic unless the

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interpretant recognizes that it is such. In other words, the interpretant must, in the semiotic reference, make conscious use of the fact that the sign exhibits its object. This is the case in the example of the scale drawing, for the machinist knows that the diagram is iconic (this information is not communicated to him by iconic sigis-see below) and hence makes use of the fact that it is drawn to scale. Similarly, when one reads the sentence 'This line is set in pica' set in pica type, he learns what pica type is by consciously making use of the fact that it is exhibited by the sentence. Again, to understand the author's preceeding sentence one must be aware of the convention of exhibiting an instance (token) of a sentence between quotation marks in order to make a sign (name) for that sentence. Thus in order for a sign to be an icon the interpretant must know that it exhibits its object. In addition, the interpretant must know the exact respect or respects in which it does SO.^ The diagram is an icon of the structure of the machine, but not an icon of the material of which the machine is made. The interpretant knows that this is the case because of the convention associated with diagrams; hence the diagram is not only an icon but is also a symbol (a sign which is associated with its object by a conventional rule employed by the interpretant). More explicit use of symbols is made on the diagram itself in stating the scale of the drawing to the machine, etc. Peirce himself failed to recognize that since any sign embodies or exhibits a number of qualities and relations, some symbolic means is required to communicate both the fact that a sign is an icon and the respect in which it is iconic, and so also failed to see that (here can be no pure icons. This failure led him to include among icons things which are not really signs, e.g., a color, or in fact any quality (2.254, 2.276). Let us turn now to Peirce's views concerning the importance of iconic signs. Such signs are, of course, convenient for representing certain things: a scale drawing of a structure is much simpler than the equivalent description. Peirce, however, attached considerably greater importance to them than this, in connection with his broader thesis that all three kinds of signs are required for a satisfactory general-purpose l a n g ~ a g e . ~By such a 6 More strictly, the interpretant must know the respect@) in which an icon claims t o represent its object, for there is always the possibility of error, e.g., one part of the drawing may not be drawn to the proper scale. 6 Peirce never explicitly expresses this general thesis; but that this is his position is obvious from his remarks concerning speculative grammar, that branch of. the theory of signs which classifies signs (1.559, 2.229, 2.341, 3.430), and also from the fact that the icon-index-symbol trichotomy is a special case of his three categories of First, Second, and Third, which are supposed to constitute a classification of the essential, general features of the universe. The present writer makes no attempt a t a full formulation of this general thesis, since we are not here concerned with what constitutes a satisfactory, all-purpose language, but only with what kinds of languages require icons and indices.

language he means a system of signs capable of efficiently describing both the generic and the specific features of the universe and of formulating the procedures and results of the empirical sciences, mathematics, etc. Icons, he held, are required for mathematical or deductive reasoning; for such reasoning is based on the observation of mental images, which exhibit the relations being reasoned about and hence are icons (3.363, 3.556, 3.560, 3.619, 5.148, 5.162). Peirce's theory of mathematical reasoning is thus an intuitionistic one, and is, in fact, an interesting variant of Kant's views.7 We may conclude then that Peirce's assertion that icons are required for mathematical reasoning (and hence for a satisfactory general-purpose language) rests upon his intuitionistic theory of mathematics, and so need not be accepted by one who does not hold to such a theory. Peirce held that the function of an index is to refer to or call attention to some feature or object in the immediate environment of the interpretant. If, for example, a man remarks, "Why, it is raining!" i t is only by some such circumstances as that he is now standing here looking out a t a window as he speaks, which would serve as an Index . that he is speaking of this place a t this time, whereby we can be assured that he cannot be speaking of the weather on the satellite of Procyon, fifty centuries ago. (4.544)

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The indexical element of this remark is implied in the speaker's use of the present tense, as well as in his bodily orientation, both of which give the meaning here and now; the sentence 'It is raining' uttered under these circumstances is equivalent in meaning to the sentence 'It is raining here and now'. Such time and place references as 'here', 'now', 'there', 'then', 'yesterday', 'tomorrow', etc., are all indexical symbols. The pronouns '1', 'YOU','he', 'this', 'that7, etc., and such expressions as 'this city', 'that bridge', are also indexical symbols. The following quotation explains why pronouns are indices in a typically Peircean manner: Modern grammars define a pronoun as a word used in place of a noun. That is an ancient doctrine which, exploded early in the thirteenth century, disappeared fiom the grammars for several hundred years. But the substitute employed was not very clear; and when a barbarous rage against medieval . There is no reason for saying thought broke out, it was swept away. that I, thou, that, this, stand in place of nouns; they indicate Bhings in the directest possible way. . A pronoun is an index. A noun, on the other hand, does not indicate the object it denotes; and when a noun is used to

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7 For a detailed discussion of Peirce's theory of mathematical reasoning, see the author's "The Logical Foundations of the Philosophy of Charles Sanders Peirce," Chs. I1 and 111, PhD Dissertation, University of Michigan, 1941. Because he regarded icons as so fundamental in deductive reasoning, Peirce thought they could be made the basis of an improved logical symbolism or language. His system of existential graphs was an attempt to work out such a language (4.368).

show what one is talking about, the experience of the hearer is relied upon to make up for the incapacity of the noun for doing what the pronoun does a t A proonce. Thus, a noun is an imperfect substitute for a pronoun. noun ought to be defined as a word which may indicate anything to which the first and second persons have suitable real connections, by calling the attention of the second person to it. (2.287n)

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In these assertions about indices, as well as in his definition of an index, Peirce is pointing out a little recognized function of indices (the case where an index indicates its object directly), though in his enthusiasm he overlooks the commonly recognized function of these signs (the case where an index indicates its object by referring to another sign that names the object). Examples of the first case occur in the sentence 'I am going into this house', uttered by a person as he turns into a driveway; here 'I' refers directly to the speaker ('I' means the person uttering ' I 1 )and 'this house' indicates a physical object directly pointed to. An example of the second case occurs when 'he' is used in a book to refer to the person named in the previous sentence; here 'he' does not indicate an object directly, but indirectly, via a sign in the preceding sentence. To put the difference in Peirce's terms, in the first case the index is existentially related to its object (its object is the thing pointed out in the immediate environment); while in the second case the index is existentially related to a sign of its object (its object is the thing named by the proper name or descriptive phrase found in the preceding sentence). On the basis of this distinction we can make the following criticisms of Peirce's treatment of the index. First, to cover both cases his definition of an index would have to be revised to read: an index is a sign which signifies its object through an existential connection to this object or to a sign of this ~ b j e c t . ~ Second, it ought to be recognized that the common definition of a pronoun does fit the second case fairly well. I n speech and writing, indexical symbols are used to refer back (or forward) to ideas, persons, places, times, etc., which have been denoted or named by previous signs. I n this case indices do serve as substitutes for previously used linguistic expressions. Third, it should also be recognized that a noun or descriptive phrase is a poor substitute for a pronoun only when the object to be indicated is present (so that a description is unnecessary) or when the object has already beeh named or described (so that the pronoun can do the job more directly and more conveniently). In reversing the role of the noun and the pronoun in the common definition, Peirce was trying to heighten the contrast between his own position and the usual one. Aside from these signs which are clearly indexical by Pierce's definition, 8 Though this definition would amend one inadequacy of Peirce's definition of an index, i t is still unsatisfactory; see footnotes 14 and 18.

there are a number of entities which he classifies as indices but which either are not signs a t all or are signs but not indices. I n each instance he is led to do this because of some basic confusion. To begin with, Peirce confuses the cause-effect relation with the semiotic relation. Thus he says that "a low barometer with a moist air is an index of rain. . . . A weathercock is an index of the direction of the wind. .." (2.286). I t is true that the word 'sign' is often used to cover such cases (e. g., in 'Clouds are a sign of rain7), but a weathercock is not a sign in the sense of Peirce's definition-the interpretant does not use the weathercock to represent or denote the direction of the wind. What the interpretant does is to infer the direction of the wind from the weathercock's position, on the basis of his knowledge that this position is the effect of the wind. Secondly, Peirce confuses the concept of index with that of grammatical subject. Some grammatical subjects include indexical signs (e. g., 'this book7in 'This book is red'), but others are composed exclusively of symbols (e. g., 'the number four' in 'The number four is even'). In both cases the subject denotes or names an object (a book and the number four, respectively), but only in the first case does it do so on the basis of an existential connection. Thus in saying that every subject is an index (1.372, 2.262, 2.296, 2.357, 3.419, 4.58) Peirce is confusing the naming or denoting function of a subject with the particular way this function is accomplished in cases where the subject is an index. Thirdly, Peirce confuses the existential relation involved in an indexical sign with that involved in the ostensive or operational definition of a symbol. A symbol is ostensively defined to an interpretant by putting the interpretant in existential connection with (i. e., pointing to) instances and counter-instances of the concept signified by that symbol. Thus 'red' may be defined ostensively by pointing out various red and non-red things. This means that an index (the act of pointing) is required for the ostensive definition of a symbol, but it does not make the symbol so defined an index. Peirce does not recognize this distinction, and as a consequence wrongly classifies certain signs as indices. For example, he classifies 'meter' as indexical on the ground that a meter is defined by reference to a standard denoted by indices (2.305, 4.544). Again, he holds that 'existence' and 'imaginary' are indexical. His argument amounts to saying that these are names of basic categories and hence must be defined ostensively: existence is not a predicate, he argues, and so the distinction between the "real world of existence" and the "ideal world of mathematics" must be shown by means of indices (2.295, 2.305, 2.337, 3.363, 4.544). Let us now consider Peirce's views on the importance of indices. He

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held, as in the case of icons, that indices are required for a satisfactory general-purpose language; but most of his arguments for this thesis break down when the confusions we have just discussed are eliminated. For example, he argues that indices are required in every language since every language must include signs that function as grammatical subjects (2.295, 2.369, 3.363). Again, he states that indices are required for mathematics, both because mathematical propositions have subjects (3.392, 3.399,6.471) and because indices,are needed to establish ostensively the fact that mathematical propositions refer to an "ideal, abstract world" and not to the "real world of existence" (2.305, 2.337, 3.363). Peirce does say that a date or position cannot be described (and so indices are required) and that to use a map we must know independently the location of two of its points in nature (3.419). He does not, however, explain why descriptions and diagrams (symbols and icons) cannot do the work of indices. We will attempt to supply this explanation in our analysis of the utility of the index in the next section.

11. An Analysis of Indexical-Meaning I n carrying out our analysis of the nature of indexical signs it will be convenient to introduce some new terms, such as 'indexical-meaning', and to use some old ones, such as 'information', in quite specific senses. When each such term is presented for the first time it will be italicized, and thereafter it will be used only in the sense defined. I t will develop that the fundamental kind of indexical sign is the indexical symbol (rather than the pure index), and in presenting the concept of indexical-meaning we will need to analyze the distinction between indexical and non-indexical symbols. A clear formulation of this distinction requires the use of Peirce's type-token distinction (4.537). Consider a non-indexical symbol, e. g., 'red'. here are many occurrences of this word, each consisting of a written or printed pattern of a certain shape or a characteristic pattern of sound. Whenever such a pattern occurs in an appropriate contextg it is taken by the interpretant to signify the color red. Each occurrence of a pattern of 'red' which is reacted to by an interpretant in this way is called a token of 'red'. A token of a non-indexical symbol is thus an event of a certain character (i. e., having

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9 The context must be taken into account when a written or spoken token of the word by itself has two or more alternative meanings all but one of which are eliminated by the context. Thus, in the sentences, 'He ran fast', 'He was stuck fast', and 'He has started to fast', 'fast' has three different meanings, even though the sight and sound patterns are the same in each case. Similarly, 'meet' and 'meat' 'and 'mete' when spoken sound the same, yet they have different meanings, We shall use 'ambiguous' in a special sense to apply to such words.

a sound or sight pattern characteristic of the word), and so has a location in space and time. The class of all tokens of a given wordlo is called a type. There are two different tokens when a speaker uses 'red7 in two different sentences, and two more when 'red' occurs once in a printed sentence but is read twice; and all of these tokens belong to the same type. A type will, of course, be without spatiotemporal location. The type-token distinction may be applied in the same way to indexical symbols. Each occurrence of the word 'now' is a token, and the class of all tokens of 'now' is a type. Note, now, that the spatiotemporal location of a token of a non-indexical symbol is irrelevant to its meaning:" 'red' means the same thing when used a t different times and places, each token signifying the same color. Moreover, the meaning of a token of a non-indexical symbol is always the same as the meaning of the type to which it belongs. The case is different with an indexical symbol, however, for the spatiotemporal location of a given token of such a symbol is relevant to the meaning of that token: 'now' means Cwo different things when it is uttered on two different days.12 Since the meaning of the type to which any symbol belongs (whether indexical or non-indexical) is always the same, it follows that the meaning of a token of an indexical symbol is different from the meaning of the type to which it belongs. Yet even in the case of the indexical symbol, the meaning of the token clearly has something in common with the meaning of its type. For the meaning of a token of any kind of symbol is specified a t least in part by a general linguistic rule applicable to all tokens of the type. We shall refer to the common element in the meaning of a token and the meaning of its type as the symbolic-meaning of the token or type. It is obvious that the complete meaning of a type (either indexical or nonindexical) is its symbolic-meaning. Furthermore, the complete meaning - --

l o Or rather, of a given word in one of its meanings. There are three different types in the three sentences involving 'fast' cited in the last footnote. 11 We are assuming here and hereafter t h a t ambiguity has been eliminated. This restriction is necessary, for if a nonlindexical symbol is ambiguous its meaning is specified by its neighboring signs and hence in some sense depends on its spatiotemporal location. Cf. footnote 12. 12 This phenomenon might be regarded as a kind of ambiguity, i.e., we could say that the spatiotemporal context specifies the meaning of the ambiguous word 'now'. However, we prefer not to use the word 'ambiguity' for this kind of phenomenon, but t o reserve it for those situations where the meaning of a sign is specified by its neighboring signs, a s in the examples of footnote 9. This being our usage of 'ambiguity', we can say t h a t the ambiguity of a symbol is theoretically eliminable; whereas if the other usage were adopted, we could not say t h a t ambiguity is eliminable (for, as we shall show, indexical symbols are indispensable).

of a token of a non-indexical symbol is also its symbolic-meaning. But the symbolic-meaning of a token of an indexical symbol is only part of its full meaning: we shall refer to its full meaning as its indexical-meaning. For example, every token of the type 'now' has the same symbolic-meaning: 'now' means the time at which 'now' is uttered. But in order to know the indexical-meaning of a token of the type 'now', one must know not only its symbolic-meaning but its temporal location as well. To summarize the distinction between indexical and non-indexical symbols: Any two tokens of a given type of symbol have the same symbolicmeaning, but two tokens of a given type of indexical symbol may have (and generally do have) different indexical-meanings. A consideration of the theoretical and practical function of indexical signs will help to clarify the nature of indexical-meaning. In this connection, it is desirable to treat separately the two kinds of indices distinguished in the preceding section of the paper: those which indicate their objects directly, and those which indicate their objects by referring to signs which name these objects. The latter kind of index serves as a substitute for the name or descriptive phrase it refers to-it functions as a variable abbreviation; and its utility derives from the fact that it is shorter than the name for which it is an abbreviation. Clearly, this kind of index can be dispensed with in a language, for it is theoretically possible to repeat names and descriptive phrases as often as n e e d be. The modus operandi of the second kind of index is evident and needs no further analysis. We will therefore confine our attention to the first kind of index (which indicates its object directly) in the remainder of the section. Suppose an interpretant sees a book on a table and wishes to assert that it is red. He can do so quite simply by pointing to the book and uttering the following token sentence: (A) 'This book is red'. This sentence contains indices and hence could not be expressed in a language composed exclusively of non-indexical symbols. The question we want to examine first in connection with (A) is: Could we express in a language limited to non-indexical symbols some sentence which would, theoretically, serve as a substitute for (A)? This will be possible if the object indicated by 'this book' can be named or identified without the use of indices. An analysis of the theoretical circumstances under which indices can be dispensed with in denoting particular existent objects has been made by C. H. Langford in connection with the identity of indiscernibles.I3 We will present his analysis in the terminology of 'index' and 'symbol'. l3

"Otherness and Dissimilarity," Mind, Vol. XXXIX N.S. (1930), pp. 454-461.

Consider a universe which consists of two parts, one located so as to be a mirror-image of the other, each part having the same internal construction as the other. Consider further a particular object, e. g., a cubical yellow box with a door on it, and its mirror-image counterpart. The intrinsic qualities of these would be identical-both would be cubical, hollow, of exactly the same shade of yellow, of exactly the same size, etc. Moreover, certain of their relational properties would also be identical-if one box were near a green chair its counterpart would be near a green chair, etc. On the other hand, these objects would differ in relational properties of the following sort. If an observer pointed to one green chair it would be true of one yellow box that it was near this green chair, and it would be false of the other yellow box. Furthermore, to an observer the door of one box would be a left-hand door, while the door of the other would be a right-hand door. Now the act of pointing is indexical; and right and left are also indexical (2.290)) for as Rant showed of the right- and lefthand gloves of a perfect pair, they cannot be distinguished descriptively, i. e., by means of non-indexical symbols. Hence it is clear that the relational properties on which these two objects agree can be named by nonindexical symbols, and that the ones on which they disagree can be specified only by indices. Let us call these properties symbolic-properties and indexical-properties, respectively. Leibniz's principle of the identity of indiscernibles is ordinarily stated as follows: there do not exist in the universe two things which have exactly the same specific properties. So stated the principle is vague, for it is not made clear whether or not indexical-properties are to be included. Let us assume that they are not, in which case the principle of the identity of indiscernibles becomes: there do not exist in the universe two things which have exactly the same specific symbolic-properties. When stated in this way the principle is clearly false of the dual universe which we have been describing. There are two cubical yellow boxes which have exactly the same symbolic-properties and differ only as to indexical-properties. It follows, then, that indices are required for denoting particular objects in a universe in which the identity of indiscernibles is false: since one yellow box has the same symbolic-properties as its mirror-image counterpart, it can be denoted or named only by means of an index. (Of course, since their symbolic-properties are identical there is not much of interest to say of one box that cannot also be said of the other.) On the other hand, if the identity of indiscernibles as stated above is true and there is no such dual universe, any object will have a t least one symbolic-property not shared by any other object. I t can therefore be named or identified by means of this property, and hence without the use of indices. Our question, then, as to whether it is theoretically possible to formulate a

substitute sentence for (A) solely in terms of non-indexical symbols depends upon the truth-status of the principle of the identity of indiscernibles. It is theoretically possible only if the identity of indiscernibles is true. Let us assume for the moment that it is theoretically possible to identify an object in the universe without the use of indices, and consider whether it is practical to do so. An interpretant, in order to know that he is naming an object by means of a symbolic-property unique to it, must have some way of knowing that this property is, in fact, unique to the object he is designating. This tyould require a knowledge of the entire universe, which is, of course, a practical impossibility. I t may seem that the interpretant could overcome his difficulty by setting up a coordinate system and naming his object not by its unique property, but by its spatiotemporal location x, y, 2, and t in this reference system. But setting up a coordinate system without the use of indices is subject to the same difficulty, for the interpretant must now know how to characterize uniquely his origin and axes solely in terms of symbolic-properties. From a practical point of view, then, we cannot dispense with indices: we can formulate no practical substitute sentence for (A) without the use of indices. But it is of interest to consider a sentence (B) which does make use of a reference system involving indices, and which is in some sense a substitute for (A). Let the interpretant adopt some commonly-accepted, indexical coordinate system (e. g., standard units of measure, standard reference points such as the equator and a prime meridian, and the standard calendar), find the location of the book in this system, and then assert the token sentence: (B) 'The book at x, y, 2, and t is red7. Two questions arise concerning the relation of (B) to (A). First, what is the practical convenience of replacing (A) with (B)? We answer by noting that it is usually more convenient to have a fixed reference system when the interpretant wishes to refer to an object outside his immediate environment, or when he wishes to refer to a number of objects conjointly. On the other hand, (A) is more useful than (B) when the interpretant wishes to refer to an object within his immediate environment. I n using an index as in (A), he can carry his reference point with him and denote a nearby object without a knowledge of the relation of this object to the rest of the universe. Since a person frequently does not know his own location in a reference system (he may be lost geographically, or he may have forgotten the date), he can utilize sentences like (A) in many cases where he cannot utilize sentences like (B). Second, in precisely what sense is (B) a substitute for (A)? Clearly, these two tokens differ in meaning: (A) contains the symbolic expression 'this book' and (B) the symbolic expression 'the book a t x, y, z, and t', and these differ in symbolic-meaning. Furthermore, different procedures

are required for verifying (A) and (B). If a person is present when (A) is uttered he can verify it by direct observation, whereas he would have to determine his location to verify (B). Yet though these sentences do differ in meaning, in one sense of 'information7they both convey the same information, for they both refer to the same object and predicate the same property of it. We can say, then, that (B) is a substitute for (A) in the sense that it conveys the same information; but it is not an exact substitute for (A) in the sense that it differs in indexical- and symbolic-meaning. This situation, where two sentences of different meaning convey the same information, is not unique to sentences involving indices, of course, for it occurs whenever two proper names for the same object are substituted in the same propositional function. But in the case of indices the circumstances under which sentences of different meaning are used to convey the same information are of interest. Suppose a man located in Ann Arbor, Michigan, says on May 12, 1947, 'It is raining here now7. He cannot convey the same information on the following day by asserting a token with the same symbolic-meaning (i. e., another token of 'It is raining here now7),for such a token will have a different indexical-meaning. Rather, he asserts a token of a sentence with a different symbolic-meaning: 'It rained here yesterday'. In fact, after May 12, 1947, no sentence can ever b,e uttered (though of course one can be referred to) which has the same meaning as the first token sentence above; for any token of the type 'It is raining here now' occurring after May 12, 1947, will differ in indexical-meaning from the token uttered on that date. This fact constitutes no limitation on one's ability to communicate -information, of course, for as we have just pointed out the same information is communicated at a later date by a sentence with a different meaning. I t may be objected that, in speaking of indexical-meaning, we have been using 'meaning' in an odd sense. The essential fact about an indexical sign is, however, that its indexical-meaning is a genuine mode of meaning; and although Peirce confused this point with a number of others (as we saw in the previous section of the paper) he displayed real insight in recognizing it. The meaning of a sentence is whatever must be understood in order to be able to verify that sentence, and to decide the truth-status of any token of 'It is raining here now' one must know not only its symbolic-meaning but also its indexical-meaning. For if one knows only the former, he does not know what specific information 'is relevant to the truth-status of that token. Employing the criterion for meaning given above, we can make a detailed analysis of the nature of indexical-meaning. That is, using the criterion that the meaning of a sign, or group of signs, is what must be

understood or known by the interpretant in order to be able to find or recognize the object of that sign, we can make our analysis by listing the different pieces of information that an interpretant must know about a token of an indexical symbol-in order to locate the object it indicates. (1) The spatial, temporal, or spatiotemporal location of the token must be known to determine the object it indicates: e. g., to find the time a token of 'now' indicates one must know when the token was uttered; to find the book a token of 'this book' indicates one must know where and when that token was used; etc. (2) The object indicated must be specified. A token is in existential relation to every other existent thing, and hence it must be understood which one of these is being referred to. The description of the object may be conveyed by a noun accompanying a 'this' or 'that' (as in 'this book', 'this color', 'this city', 'this star', etc.) or it may be incorporated in the sign itself (as in 'now', which indicates a time, 'here), which indicates a place, etc.). In either case the object is signified on the basis of a rule of linguistic usage, and hence this information is part of the symbolicmeaning of the token. (3) Finally, the interpretant needs to know a set of directions relating the token to the object it indicates. For there are usually many objects of the sort described by (2) existentially related to the token.14, Thus there may be many books in the neighborhood of a token of 'this book', and the one indicated is found by observing the direction of a pointed hand or the bodily orientation of the speaker. There are two cases to be considered here: (3a) The set of directions may be associated with the sign symbolically, i. e., on the basis of a linguistic rule. Thus a token of 'I' means the person uttering that tohen; in other words, it is part of the symbolic-meaning of 'I' that one finds the object indicated by a token of this type by proceeding from the token to the speaker. Similarly, the object indicated by 'now' is the temporal location of the token, the object indicated by 'today' is the day on which the token is uttered, and the object indicated by 'this city' is the city in which the token occurs. (3b) The set of directions may be shown by an act of pointing, a bodily orientation, etc. Examples are 'this book', 'that tree', accompanied by appropriate gestures. We can now summarize what must be known by an interpretant in order. to find the object indicated by a token of an indexical type, i. e., what factors constitute its indexical-meaning: (1) The spatiotemporal location of the token. 14 This analysis reveals the inadequacy of the expression 'in existential relation to' in Peirce's definition of the index. Since a token is in existential relation to every other existent thing, the possibilities must be limited by factors (2) and (3).

(2) A description of the object indicated. (3) A set of directions relating the token to its object (a) conveyed symbolically, or (b) conveyed by a physical act of pointing. Factors (2) and (3a) are characteristic of the type and hence constitute the symbolic-meaning of the type and its tokens. (1) and (3b) depend upon the token and hence, when added to the symbolic-meaning of the token, give its indexical-meaning. The object indicated by the token is the object described by (2) reached by proceeding from (1) according to the directions of (3). Though factor (2) is present in some indices ('now', 'this book'), it is not present in all ('this', 'that', an act of pointing). But unless (2) is present, explicitly or implicitly, the sign cannot indicate a definite object.15 A token of 'this', or an act of pointing, is existentially related to and points to many objects, and so when unaccompanied by a descriptive element cannot indicate any particular one of them.16 For example, if one is pointing to a book the reference may be to any of various objects: this book, this copy of a book, this red cover, this leather binding, this color (red), etc. Of course, the descriptive element may not be made explicit but may be contributed by the context. Thus if two people are discussing books and one points to a book and says 'This is interesting', what he says is short for 'This book is interesting'. The fact that an indexical sign has a well-defined or complete indexical-meaning only when (2) is present, explicitly or implicitly, leads to several conclusions worth noting. First, a pure index (an act of pointing) cannot have a complete indexical-meaning, and therefore the fundamental kind of indexical sign is the indexical symbol, as was stated a t the beginning of this section.'' (Of course, some indexical symbols, e. g., 'this' and 'that', are like a pure index in that they do not have a complete indexical-meaning.) Second, the general form of indexical reference is not 'This is a B' but 'This A is a B'. Finally, a sign may have a well-defined indexical-meaning and yet fail to 15 This fact was noted by C. H . Langford in a mimeographed paper entitled "Some Points About the Use of Language," 1940, p. 4. The author is indebted to Professor Langford for permission to make reference to this paper. 16 I t is for this reason that ostensive definition cannot be accomplished by presenting a single instance of the concept to be defined. See the author's "Empiricism and Vagueness," The Journal of Philosophy, Vol. X L I I I (1946), p. 478. 17 Note that we reached the same conclusion in the case of the icon: a symbol is required along with an icon to signify a definite object. The symbol is therefore more fundamental than the icon or the index. Furthermore, the index is more fundamental than the icon, for, as we saw, indices cannot be dispensed with, whereas, unless we accept the kind of theory of mathematical reasoning that Peirce accepted, icons are dispensable. Hence Peirce was wrong in regarding icon, index, and symbol as equally fundamental and independent kinds of signs.

indicate an object.18 For it is possible to make a mistake and describe, under (2), an object when in fact there is no such object. Thus a person may say 'The chair in the next room is made of oak' when in fact there is no chair in the next room. There is even the possibility of perceptual error in regard to objects in the perceptual field of the interpretant. It might be proposed that we should not use an indexical sign unless we are sure it indicates. But how certain must we be before using an index? If we insist upon Cartesian surety we are limited to using indexical signs which indicate private sense-data of the present moment: e. g., 'This circular sense-datum is red', 'Now (referring to subjective time) it seems to be raining', etc. This means that certainty is attained a t the price of making communication private. I t is clearly necessary in a public language to allow signs with well-defined indexical-meanings to fail to indicate.lg The possibility that an index may fail to indicate raises the problem of how to analyze the contradictory of 'This A is B', that is, the problem of finding a sentence which is equivalent to 'It is not the case that this A is B' but which is more nearly in standard form (i. e., which has the negation brought inside, just as 'It is not the case that all A is B' translates into the standard form 'Some A is not B'). I t might appear that 'This. A is non-B' is such a sentence. However, 'This A is non-B' and 'It is not the case that this A is B' are not equivalent, for if 'this A' does not indicate, the first is false while the second is true. I n other words, 'This A is B' and 'This A is non-B' are not contradictories but contraries, for both will be false if 'this A' does not indicate.20 Thus there are two conI t is a possibility not allowed 18 This point is also made by Langford; Ibid, p. 5. for in Peirce's definition of an index. 1 9 The conclusion might be drawn from the fact that a well-formed indexical expression may not indicate that all such expressions are meaningless except in context; Russell seems to follow this line of argument in his theory that definite descriptions are incomplete symbols. That this conclusion does not follow has been pointed out by Alonzo Church, who showed that a definite description need not be construed as an incomplete symbol since it can have a sense (Frege's 'Sinn') even if i t lacks a denotation (Frege's 'Bedeutung'); see The Journal of Symbolic Logic, Vol. V (1940), pp. 162-163 and VII (1942)' p. 47. We have been arguing the same point but with regard to a restricted class of definite descriptions, namely, those involving indices, such as 'the chair in the next room'. 20 Langford, op. cit., p. 10. See also in this connection the controversy between Langford [Mind N.S. Vol. XXXVI (1927), pp. 342-346, Vol. XXXVII (1928), pp. 73-81, and, Vol. XXXVIII (1929), pp. 219-2251 and J. A. Chadwick [Ibid., Vol. XXXVI (1927), pp. 347-353 and Vol. XXXVII (1928), pp. 471-4841 on the contradictories of certain singular propositions; and a recent continuation of this discussion by E. J. Nelson [Ibid., Vol. LV (1946), pp. 319-3271, A. Pap [Ibid.,Vol. LVI (1947), pp. 72-76], and W. V. Quine [The Journal of Symbolic Logic, Vol. X I 1 (1947), pp. 52-551.

ditions under which 'This A is B' is false: (1) 'this A' does not indicate, and (2) 'this A' does indicate but the A indicated is not a B, i. e., 'This A is non-B' is true. By disjoining these two conditions we get the sentence that we are looking for, but it must be recognized that since these conditions include a statement of the relation of a sign to its object, it is not possible to formulate the sentence in the language containing 'this A'; rather, it is necessary to formulate it in the metalanguage of that language. The desired contradictory of "This A is B)' is therefore "Either 'this A' does not indicate or this A is non-B." I t is interesting to note that as a consequence "This A is B" is equivalent to "'This A' indicates and it is not the case that this A is non-B." Similarly, "This A is non-B" is equivalent to "'This A' indicates and it is not the case that thisA is B," and "Either 'this A' does not indicate or this A is B" is its contradictory. ARTHUR W. BURRS.

En la primera parte el autor examina criticamente la tricotomia bhsica de 10s signos de Peirce. El simbolo ('rojo') representa su objeto mediante una regla convencional; el indice (el acto de seii&lar)lo representa mediante una relaci6n existential, y un icono (un diagrama) mediante la exhibici6n de su objeto. Peirce confunde la relaci6n indicativa o de indice con la relaci6n de causa-efecto, con la funci6n denotativa de 10s sujetos y con la definicici6n ostensiva. En la segunda parte, analiza el autor la naturaleza de 10s indices, llevando el anhlisis m&s all& del punto a donde lleg6 Peirce. La indicaci6n 'este libro' tiene un sentido indicativo o de indice que se compone del 'sentido simb6lico caracteristico del tipo, m&s la informacidn dnica relativa a la indicacidn, a saber: su situaci6n espacio-temporal y el acto de seiialar del que est&hablando. Un signo con sentido indicativo bien definido puede no indicar bien un objeto, de tal suerte que 'Este A es B' y 'Este A es no-B' no Sean contradictorios. Se hace un an&lisis de 10s contradictorios de ambos.