IDENTIFICATION AND VISUALIZATION 461
tiling which we did not fully grasp or approve. The above relation is rather important, but has not been sufficiently analysed. The problems of introversion and extroversion are connected with it.
The relation between the problems of identification and the number of values found in the empirical world in connection with the number of values ascribed, or assumed., by our semantic processes, is most important.
The following analysis is, by necessity, one-sided, over-simplified., as a fuller analysis would require a separate volume. I consider many problems 'in principle' only; this allows me a briefer treatment necessary for my purpose, but it must be realized that our language and general semantics, which, in practice, we use unconsciously, are extremely complex and involve one-, two-, three-, and oo-valued components, never, as yet, sharply differentiated nor formulated. Investigation shows that the oo-valued semantics is the most general and includes the one-, two-., and few-valued semantics as particular cases. The one-valued semantics of literal identifications are found only among animals, primitive people, infants, and the 'mentally' ill, although more or less serious traces of some identification are found in practically all of us, because these are embodied in the structure of our language and prevent the acquisition of the oo-valued systems necessary for sanity. For my purpose, it is enough to formulate the problems for the complete elimination of primitive identification, and then modern, oo-valued, A semantics follow automatically. Under such conditions, I must concentrate on the vital problem of one-valued identification and treat the two-., and few-valued systems sketchily, 'in principle', although we must realize that the last systems have been made more flexible by the use of many ingenious verbal devices which I do not even mention in the present work.
Let me repeat that the attitudes, flexibility, or fixity., of our s.r depend to a large extent on the structure of language used, which involves also its appropriate general semantics. The 'logic' of our schooldays represents a composite affair, in the main A, and we call it by this last name. This 'logic' can be considered as a two-valued 'logic' because of the fundamental 'law of the excluded third', expressed as 'A is B or not B', by which a third possibility is excluded. But even the traditional 'logic' had to admit in its scheme what was called 'modality'; namely, some degrees of certainty or uncertainty with which a given statement is made. Lately, Lukasiewicz has shown that a three-valued 'logic' can be so formulated as to include modality. Later, he and Tarski generalized it to an n-valued 'logic'. When n tends toward infinity, this 'logic' becomes the 'logic' of probability. If these disciplines are made non-el,