The kind of synonymy which we are after to underpin analyticity is,
Quine says, cognitive synonymy. Although we cannot,
according to Quine, define this precisely, we have a feel for what is
intended; it's something along the lines of a synonymy which preserves
informational content. Quine proffers the following definition
This introduces a new concept: ``necessarily true.'' Are we entitled to it?
(4) Necessarily all and only bachelors are bachelors.
If we take this as a paradigm example of the use of `necessarily' or `necessarily true,' it certainly does seem that (4) is an example of a true sentence. No matter how we reinterpret `bachelor', (4) remains true. So we might suppose that (4) is a logical truth.
Now, what happens if we replace the second occurrence of `bachelor' with `unmarried man'?
(5) Necessarily all and only bachelors are unmarried men.
While it is clear that the embedded sentence, `Bachelors are unmarried men' is true, it's unclear whether (5) itself is true.
If we look once again at (4) we might be inclined to suppose that we were willing to say that it is true because the embedded sentence (All bachelors are bachelors) is a logical truth. If this is so, in order to count (5) as true, we must be able to classify
(3) All and only bachelors are unmarried men
as analytic of the second sort defined above--viz., definitionally true. The problem is, of course, as we have already seen that while we can make tolerable sense of a notion of logical truth, definitional truth eludes us.
To put it another way, if we agree that (5) is true, then we can say that (3) is analytic, and from there conclude that `bachelor' and `unmarried man' are cognitively synonymous. But we have no grounds for supposing that (5) is true until we can provide a definition of `necessarily true.'
Quine proposes the following.
This captures our intuitions about necessary truth, but it depends upon an understanding of that pesky concept of `analyticity,' which is what we were trying to understand in the first place.
Quine's point is that no language which does not provide an account of `analyticity' is entitled to the concept of necessary truth. Of course, we could put it the other way round: no language is entitled to the concept of analyticity unless it provides an account of `necessarily true.' Either way, the problem is that we are able to use one of these terms only if we assume the other.
Quine now turns to Leibniz's notion of substitutivity salva