MEANING, the object of a symbolization, considered from the standpoint of the symbol. Thus the meaning of the figure 2 is the number two, the meaning of the formula (x + y)'= + 2xy is the law that formula represents, and so on indefinitely.The experiences which we undergo possess besides their presented con tent a represented content, and this represented content bears toward them the relation of mean ing. One of the cardinal problems of modern psychology is the determination of the psychical concomitants of this meaning. In accordance with the general nominalistic and associational istic trend of experimental psychology, those who approach the question of meaning from this angle have usually considered that the meaning of an image is conveyed in conscious ness a group of such accompanying sub stantive states as images, sensations and feel ings. They held, that is, that the meaning of "bear* read into a noise in the woods is *car ried by a verbal image and an organic shudder,* and that every experience is surrounded by a fringe of vaguer meaningful states. They would consider that the vehicle of the law of universal gravitation is a visual or auditory verbal image, together with certain organic and kinaesthetic sensations.
All this psychology of meaning suffers from the lack of an antecedent logical analysis. The logical situation best adaptEd to this analysis is that of the relation of a set of mathematical symbols to the theory they represent. The theory is obviously the meaning of the symbols, but it is only to the very slightest extent car ried by the individual symbols themselves. Only the elementary constituents of the system, together with certain of the simpler general notions, are represented by special characters. The structural relations are signified, and must be signified, by the arrangement — that is, the structural relations of the symbolism on the paper.. The essence of the conventional system of algebraic notation lies, not in the use of let ters for numbers, not in the symbolizing of ad dition by + and of multiplication by X, but in the agreement between the laws of the manipu lation of the symbols and the laws of number. Symbolization is primarily the relation toward a system of entities of a similarly order system of arbitrary marks, and only in a derived sense the relation between a mark and the correspond ing entity. The symbol is a symbol only within a symbolism. It is precisely as a symbolism that our verbal images, kinesthetic sensations and other mental states convey a When the mathematician is developing a new theorem, his mental content may be inventoried as a verbal image or two, his sensation of the paper and pencil in front of him, and a few organic sensations. Somehow or other he puts these into an entirely extraneous correlation with the entities which he is examining. This strain behind the eyeballs acquires a temporary association with the unknown function for which he is seeking; that fragmentary visual image of a formula represents a mathematical law; and so on. In his trained mind, the symbolism of his states shapes itself into the de sired conclusion, which he symbolizes anew in the conventional algebraic notation on the paper lying before him. No enumeration of his sub stantive states can ever disclose how the mean ing of the conclusion and the premises is car ried in his mind, for it is not these states them selves, but their arrangements, that are the vehicles of meaning.
This structural nature of the vehicle of meaning is intimately connected with our power to communicate with others. My sensation of red is something that as far as I know may be peculiarly mine. If there were a man who from his birth had seen red where I see green and green where I see red, it would be a matter of the utmost difficulty for me to detect his anomaly. He would learn the name *red* from hearing it applied to the things which appear red to me but green to him, so that his speech would not dis close his peculiarity. It isonly by ob serving that green objects excite in him the expression of the emotions which we consider appropriate to red, or by some similar peculiarity in the associations of his experience of red and green objects, that the interchange of his red and green sensations could even be sus petted. If the interchange were his sole peculiarity, he would always consider himself, and be considered by others, in the light of a normal human being. Accordingly, we have no reason to believe that the sensory qualities or sense-data of normal human beings agree with our own sensory qualities and sense-data, and there is no way of conveying these qualities and data by language. On the other hand, lan guage is the vehicle of meaning and of nothing else. This alone is enough to prove that the meanings do not reside in any special data or qualities in our minds. What language does is to order the mind of the hearer or reader in a manner similar to that of the speaker or writer. In reading a story we pass through a sequence of mental states which has been designed for us by the author, though our individual states are beyond his knowledge. When he uses the word we interpret it in our own way, but we put it in the same sort of relational con text —complementary color of red, intermediate between yellow and blue, etc.—as that which it occupies in his mind. It, therefore, follows that this relational context, which is all that language can convey, is identically the meaning conveyed by language.
The situation when we hear a noise in the bushes and interpret it as °bear') can now be analyzed. The meaning is not carried in the first instance by the verbal image and the shudder. It is true that there is a possible state of consciousness in which the rustle in the bushes, the verbal image, and the shudder are all that is present, but at this stage meaning has not yet appeared. Meaning first appears when we think, not ((bear,* but ((That's a bear.* In this case, the rustle in the bushes stands for "that,)) the shudder or verbal image for abearD and the juxtaposition of the shudder or image with the sound impression for the rela tion expressed in the sentence. The meaning of "bear') is derived from the meaning of the sentence. In other words, the meaning of the sound in the bushes resides, not in its correlates, but in its correlation. (See TFIOUGHT). Con sult James, W., (Principles of Psychology) (New York 1899) • Stout, G. F., of Psychology) (London 1913) ; Titchener, E. B., (Experimental Psychology of the Processes> (New York 1909).