If we have a set of postulates {P1. P2, ..., Pn}, we can define a postulate as follows
x is a postulate iff x is a member of the set {P1. P2, ..., Pn}.
If we have a category or set of semantical rules,{R1. R2, ..., Rn}, we can define a semantical rule as follows
x is a semantical rule iff x is a member of the set {R1. R2, ..., Rn}.
The problem, of course, is that this is simply stipulative. Suppose that I want to add `All bachelors are unmarried' to my set of analytic-for-L. It's easy, I just add a semantical rule to the effect that if s = `all bachelors are unmarried' then S is true to my set of semantical rules. Does this look fishy? It should.
If I have a formal language which is fully explicit and
well-understood, how just by looking at its statements can I identify
its postulates. Quine's point is that postulates do not form
a ``natural''kind, so to speak. It is an invented kind. To find out
whether statements are postulates, we have to ask which statements
have been posited, stipulated to be postulates.
The word `postulate' is significant only relative to an act of inquiry;we apply the word to a set of statements just in so far as we happen, for the year or the moment, to be thinking of those statements in relation to the statements which can be reached from them by some set of transformations to which we have seen fit to direct our attention (35/73a).
The same is true of semantical rules. R is a semantical rule for truth
conditions iff we stipulate that it is. The rule I gave above is
intended to show just how arbitrary this is.
But from this point of view no one signalization of a subclass of truths of L is intrinsically more a semantical rule than another;and, if `analytic' means `true by semantical rules', no one truth of L is analytic to the exclusion of another (35/73b).
In other words, just redirect your attention and other truths of L too can assume the mantle of analytic.
We might hesitate here--Quine's semantical rules are highly arbitrary and artificial. As linguists we want not these but empirically based semantic rules. Surely, these aren't subject to Quine's criticisms.
What Quine has shown in this section of the paper (§4) is that artificial languages cannot shed light on natural languages. But we suspected that all along. Artificial languages do not contain analytic statements, only statements that have been declared analytic-for-L, or any of a number of other things-for-L.
If we try to map the semantical rules which ``generate'' these classifications onto natural language, we must fail because they are relative to the artificial language which creates them, and because in natural language, what we are looking for are categories which apply to all natural languages, not just to this one or that one. At most we can interpret the formal/artificial language to have application for natural language, but this is to see the mapping as motivated by the natural language, and thus to deprive the artificial constructs of whatever explanatory power they might have.
We had hoped that the artificial languages would be able to bring some of their clarity and fixedness back to natural language to help us explain analyticity and other semantic categories. It turns out that absent an understanding in natural language, we can't interpret artificial languages to give their relativized analyticity a ``translation'' into analyticity (full stop), analyticity in natural language.
Quine's original challenge remains: How are we going to define
semantic rules (or relations) so that analyticity can be understood in
a way that avoids the ``closed curve in space''?