Symbols, signs, and signals

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Abstract
In this address, no attempt to deal with any problem of symbolic technique will be made, for even if a problem of this kind should be found that was suitable to the present occasion, I should probably lack sufficient competence in the handling of symbols to deal with it satisfactorily. It occurred to me, however, that it might be interesting to consider the nature of symbols in general, to point out certain characteristics peculiar to the symbols used by logicians and mathematicians, and to say something concerning the relations of these symbols to the knowledge of Nature. Although developments in the science of logic are not dependent on such an inquiry, it yet provides us with a perspective on the nature and importance of that science which we cannot gain so long as we attend only to the problems arising inside its field.The symbolic relation. Our attempt to gain this perspective may well begin with the trite remark that nothing is intrinsically a symbol, but that anything is a symbol if and only if it symbolizes. Moreover, the relation called symbolizing is not a dyadic but rather a tetradic relation. That is, in order for something A to be a symbol of something B, there must be in addition C, a mind trained in a special way, and D, a certain manner in which that mind is occupied at the time. For although we do say, for instance, that a mark consisting of a little cross is the symbol of addition, the fact is of course that at times when that mark is not present to a mind, it does not symbolize addition or anything else. Moreover, even when it is present to a mind, it does not symbolize addition unless that mind has been trained in a certain manner; for obviously such a mark does not symbolize addition to the mind of a Hottentot or other wholly illiterate person.

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