In view of the afore-mentioned difficulties, it will be helpful to begin with a preview of the argument. I start, in this chapter, by formulating a pre-mathematical characterization of the concept of ‘indistinguishability’. This will, of course, have to be reformulated later in mathematically rigorous terms. But that will not become possible, till we have made a thorough semantic analysis of the kinds of statements that can be made in the presence of this unfamiliar relation. This is not a normal part of any mathematical theory, but if the criteria of argument are to be securely grasped, it must be gone into with as much care as the rest. This will form the material of Chapter II, and its end product will be an axiom-schema which will replace the conventional one concerning the conditions under which one symbol may be validly replaced by another. The change in this rule (which normally goes unstated because so much is taken for granted) to a more complex one, constitutes the main trauma of this theory.
KeywordsSemantic Notation Identical Symbol Objective Notation Reidel Publishing Company Rigorous Term
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