The only option thus left is to consider non-extensional language. It is a language which allows the distinction between interchangeability in extensional contexts (where predicates are extensionally equivalent) and interchangeability in modal context (where predicates are equivalent necessarily and not due to any actual accident). This is the way how positivist's requirement can be fulfilled. It is through the intervention of necessity operator truths of meaning are distinguished from mere contingent truths as expressed through extensional equivalence. The expression 'necessarily' thus implies the context where only the predicates which are necessarily and not contingently true can be interchanged. The resources of modal language thus enable us to reformulate the two sentences in the following way. The sentence 'A chordate is a renate' is certainly true but it is contingently true since the equivalence is based on the agreement of fact, whereas the sentence 'A bachelor is an unmarried man' cannot be other than being true and hence it is always read as: 'It is necessarily true that a bachelor is an unmarried man'. On the basis of the resources of modal language a notion of interchangeability can be so defined that it will fulfill the requirement of positivist epistemology.

But then Quine questioned this reformulation suggested on the basis of the consideration of modal language. His main criticism is that properties of this language are as problematic as the notion of analyticity which is now placed within the necessity operator of modal language. In fact, Quine states that both necessity and analyticity have the same set of problems. That means the defect that is noticed in one can be equally noticed in another. The reason is that one cannot be defined independently of the other. To elaborate, the notion of 'necessity' cannot be explained independently of the notion of 'analyticity'. The two statements 'Necessarily A is B' and ''A is B' is analytic' have the same epistemological problem. Their mutual dependence can be evidently seen once we take these two notions together. For to decide whether the statement 'A is B' is necessarily true ultimately depends on whether the statement is analytic or not. Thus, analyticity is defined in terms of interchangeability based on the modal notion of necessity and which in turn is defined in terms of analyticity. This way the definition of analyticity becomes inevitable and viciously circular when construed in modal language.

Similarly, Carnap's attempt to define analyticity in terms of semantic rules construed in a formal language is equally defective. Carnap's plea is that a statement 'S' is analytic if and only if it follows from the semantical or syntactical rules of the language. The obvious advantage here is that since rules are explicitly stated, one could, on the basis of that, be able to define the notion of analyticity. But the notion of analyticity to be defined here will not be a general notion of analyticity. It will only be a definition of analyticity for a specific language say 'L'. Quine's point is that such a definition does not serve any epistemological purpose and similar to the notion of interchangeability. This attempt too involves the charge of circularity.