Quine remarked that the system of his book exclusive of *200 is a completely safe basal logic. Axioms of this basal logic are given by *100-*105 and *201-*202 in the book. For relation theory and number theory, we need some further axioms to guarantee elementhood of certain entities. In the article, Quine proposed to adopt as axioms f610 and the following two statements:

It has been shown by Lewis and Langford that the postulate B8,

is not deducible in SI. From this it follows that neither are the paradoxes of strict implication deducible in that system. However, the following weaker—but perhaps philosophically equally important—analogues are deducible:

The purpose of this note is to contribute to the discussion of nonextensional languages that is now in progress. A formal language, L, that contains, besides the lower functional calculus, predicates and predicate variables of higher type will here be called nonextensional if the sentence