But aren’t philosophers sometimes concerned to know from the armchair the propositional contents of non-metalinguistic sentences, rather than their metalinguistic counterparts? That is, aren’t philosophers sometimes concerned to know, say, that every vixen is a female fox, not just that “Every vixen is a female fox” is true in the language of modern zoology? Knowing that a sentence is true in some language certainly isn’t sufficient for knowing its content, otherwise we would know, for instance, that phlogiston has a real functional role in combustion, and that the sun will rise tomorrow tonk the sun is purple.* Perhaps we might say that we know the content of “Every vixen is a female fox” if we know that it is analytic in our own zoological language and that we ought to be using our own zoological language. Or, to be a little more cautious, we might say that we know the content of "Every vixen is a female fox" if we know that it is analytic in every zoological language L such that (a) we know that L is maximally useful for us and (b) we know that the translation of "Every vixen is a female fox" in L is analytic. But certainly we don’t know what sort of zoological language we ought to be using from the armchair. For instance, we don’t know from the armchair whether the terms “vixen” or “fox” mark useful distinctions.
Still, as long as we understand a chunk of modern zoological theory in its customary linguistic guise, then we are in a position to know from the armchair what language that chunk of zoological theory does use, or what (slightly formalized) language or languages it can be taken to be using, or what language or languages it can be rationally reconstructed as using. This knowledge is a priori in the sense that it is guaranteed by our linguistic competence alone. And, for each of those languages, we are in a position to know from the armchair what the analytic truths are, construed epistemologically. At any rate, if I’m right about how to relativize truth and understanding to languages, then Williamson hasn’t shown that we aren’t in a position to know from the armchair what the analytic truths are, construed epistemologically. If philosophers are sometimes concerned to know from the armchair the propositional contents of non-metalinguistic analytic sentences, then they’re in for a disappointment. But maybe they'll do just fine if they set their sights a little bit lower.
This was Michael Friedman’s idea with the “relativized a priori”, right? Or, if Friedman was right, then this was all Carnap’s idea.
* - Williamson makes roughly this point himself.
I understand “Every vixen is a female fox” and it has some positive epistemic status for me. How does it get that status? … The lazy theorist may try to dismiss the question, saying that it is simply part of our linguistic practice that “Every vixen is a female fox” has positive epistemic status for whoever understands it. But the examples of defective practices [surrounding “phlogiston”, “tonk”, racial pejoratives, and so on] show that it is not simply up to linguistic practices to distribute positive epistemic status as they please. That the practice is to treat some given sentence as having positive epistemic status for competent speakers of the language does not imply that it really has that epistemic status for them. (The Philosophy of Philosophy, 84)