Okay, just a quick post to help consolidate some thoughts.
I've been thinking about conventionalism, the old school badass conventionalism about logical truth that my realist metaphysician's upbringing taught me was a comical boogie man to be shunned.
There are some pretty standard attacks on traditional conventionalism, folk like Quine, Kripke, and Lewy seem leave some folk pretty confident that the matter has been put to bed, and the world has moved on (I suspect that this may not be the case outside of the metaphysical bubble that is Leeds university, but I'm in said bubble, so what are you gonna do about it, eh?). To me these are starting to look like pretty thin reasons for abandoning convention as a source of necessity. The main reason for this is that it's becoming less clear to me that the kind of thing the conventionalists were talking about is the same as the kind of thing that its critics were.
If you want to ground necessity (or logical truth) in convention then it seems that there are a few ways of going about it:
1 - The formal system: In 'Truth by Convention' Quine lays out a formal system in an attempt to derive all the necessities from axioms. He concludes that this cannot be done because you'll never be able to get the truth of all the necessities, a Caroll-esque regress follows.
2 - Identify necessity with analyticity: Folk like Kripke and Putnam put this one to the sword, and rightly so (I reckon).
3 - Go hard-core anti-realist (as opposed to some kind of reductionist anti-realist) about necessity and treat modal claims in the same kind of way that expressivists in (say) morality treat claims like "pulling off Jimmy's face is wrong". When we say "one plus one is necessarily two" we are expressing a commitment to use language in such a way as to never allow anything to count against our belief that 1+1=2. Now, this isn't grounding any special kind of truth. It's not reflecting anything special about the world either. Just as my claim about Jimmy's face doesn't ground or reveal any ethical truth, neither do modal claims. When I say it's wrong to pull off Jimmy's face, I'm expressing my lack of approval for such actions, and my preference that they not be done. When I make claims about necessity, I'm expressing (albeit tacitly) the character and rules of the language I use when reasoning about stuff in the world.
The literature on conventionalists seems to presume that the position the first two. I'm beginning to think that this may be something of an error. I think that maybe (at least some of) the conventionalists had something bit more like 3 in mind. If they didn't, then they probably should have done considering the motivations that led them to be conventionalists in the first place.
Okay, so that's a thought about conventionalism about logical truth. Now I need to start thinking about conventionalism about essential truth. If I can consolidate and back up these thoughts for logical truth then maybe I can start to map out the positions available to the (as of yet seemingly hypothetical) conventional essentialist... I anticipate taxonomical headaches.
P.S. Incidentally, if anyone thinks they can recommend any sources that might highlight this kind of distinction in the literature on conventionalism, please do let me know.