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However, these constraints do not tell us how to translate a single statement of the form q is at ; they tell us, given a whole - and very large - collection of statements about immediate experience, how to assign truth-values to those statements so as to yield the right sort of overall world. This is especially striking when we consider what happens when we find we had been mistaken about the location, say, of a certain object, because an experience fails to accord with it: in Carnap's terms, an assignment of sense-qualities to space-time points may have accorded well with experience up to a point, but must now be revised in order best to satisfy the principles governing such assignments.

For, although Quine in earlier years would count set theory - those truths in which the 'e' of set-membership is the only non-logical expression occurring essentially - as logic, he changed his mind later, thus according with the usual view nowadays that the essential occurrence of 'e' is where logic leaves off and set theory, and hence mathematics if mathematics is reduced to set theory, begins (PL 64-6). And unquestionably the actual character of set theory as developed in the twentieth century has had the character of postulation as described above.

Thus Quine writes: The distinction between the legislative and the discursive refers to the act, and not to its enduring consequence . . conventionality is a passing trait, significant at the moving front of science but useless in classifying the sentences behind the lines. It is a trait of events and not of sentences. (WP 119) In fact the same point goes for stipulative definition, the case where some theorist states that something of the form 'x is F iff x is . . ' is advanced as a definition, thereby introducing the predicate F.