My gripe here concerns section 4 of the paper, "Semantical Rules." Quine writes (page numbers from From a Logical Point of View):
Once we seek to explain 'S-is-analytic-for-L' for variable 'L'..., the explanation 'true according to the semantical rules for L' is unavailing; for the relative term 'semantical rule of' is as much in need of clarification, at least, as 'analytic for.' (34)So Quine is telling us that there is no decent explanation or clarification of the term 'semantical rule of,' if we generalize away from particular languages.
It seems to me that the next question we should ask is: how does Carnap characterize these semantic rules? Is it as unclear as Quine alleges? To answer that, we have to look at an extremely underread book: Carnap's Introduction to Semantics (1942). There Carnap says:
a semantical system [is] ... a system of rules, formulated in a metalanguage and referring to an object language, of such a kind that the rules determine a truth-condition for every sentence of the object language, i.e., a sufficient and necessary condition for its truth. In this way the sentences [of the object language -GFA] are interpreted, i.e., made understandable. (22)What are some of Carnap's examples of semantic rules? (Where English is both the object and metalanguage):
-'Chicago' designates Chicago etc.
-The truth-tables for the usual propositional connectives
Now I want to know what Quine finds unacceptable (unclear, unexplained, 'unintelligible' he says elsewhere in "Two Dogmas") about Carnap's characterization of semantic rules. This isn't just a matter of my pounding or kicking the table and saying 'I really do understand them' -- rather, it seems to me that if Quine is right that these things are unclear, then logic (at least logic that is not purely syntactic/ proof-theoretic) is unclear. In order to specify an artificial language in model-theoretic terms at all, we need to be able to say things like "Modus Ponens is an inference rule in such-and-such language" -- and if that is not clear, then logicans working in model theory are stumbling around in an unintelligible haze. If we cannot (intelligibly) lay down/ identify semantical rules such as this one and the others Carnap mentions, then the logician cannot (intelligibly) specify interpreted languages to study.
Thus concludes my main rant. A couple further things should be said before signing off, though. First: Quine, in "Notes on the Theory of Reference" and elsewhere, says that "'Chicago' designates Chicago," "'Snow is white' is true iff snow is white" and the like are basically comprehensible (p.138 in From a Logical PoV). That this is in tension with Quine's criticism in "Two Dogmas" has been pointed out (in different terms) already, by Marian David in Nous 1996. Second, there is one real difference between the semantic rules Carnap uses and the ones Quine favors and we usually use today, pertaining to hte interpretation of predicates and relation letters. Carnap sets up the following as a semantic rule: 'Blue' designates the property of being blue.
And here Quine would have a (more) direct disagreement with Carnap: Quine rejects intensional languages in general, and properties (for Carnap) are to be understood intensionally. So to generate a clean Quinean argument against semantic rules from the above quotation, we can fall back on Quine's rejection of non-extensional discourse as unclear and unintelligible. But this view of Quine's has won far fewer supporters than his rejection of the analytic-synthetic distinction.