I’m reading Matti Eklund’s really interesting paper “Carnapian Theses in Metaontology and Metaethics”, which raises some of the issues I've addressed recently.
A couple of things. Eklund claims on p. 6 that the internal/external distinction does not require the analytic/synthetic distinction. I disagree because I think a Carnapian should subscribe to something like either of the following arguments.
Suppose that analytic truths are sentences that are true in a language L solely in virtue of L. Every linguistic framework has semantic rules. Linguistic frameworks are languages or language-fragments. If something is true solely in virtue of semantic rules, it is true solely in virtue of language. For some language L, there is at least one sentence that is true in L solely in virtue of L’s semantic rules. Therefore, there is at least one analytic truth in at least one linguistic framework.
Alternatively, suppose that analytic truths are synonyms of logical truths. Every linguistic framework has semantic rules. The semantic rules of a linguistic framework entail all of the synonymy relations between sentences in that framework. For at least one linguistic framework L, at least one logical truth in L has a synonym in L. Therefore, there is at least one analytic truth (which is not just a logical truth) in at least one linguistic framework.
I am presupposing that Carnap is what Eklund calls a “language pluralist”, but I take that to be obvious. I am also presupposing that Carnap thinks true all of the premises of at least one of these arguments, but I think he does. I remember him advocating the view of analyticity in the second argument (Williamson calls it “Frege-analyticity”) somewhere in his correspondence with Quine.
One more thing. Eklund writes: “One less trivial claim would be that ‘there are
numbers’ has different meanings and truth-values in different languages while meaning what it actually means. But this is less trivial at the expense of being committing to some form of relativism, and language pluralism was supposed to be an alternative to relativism.” (11) This isn’t true, since one of the languages might be much more useful than all of the others. If someone can say that there is an objective fact to the effect that we ought to use a language that assigns a certain meaning and value to “there are numbers”, then it seems odd to call her a relativist.