"As such, mathematical truths are mere grammatical conventions, free choices that have no deep meaning."
And just what do you mnake of Quine's "Truth by Convention"?
[Warning: philo-geek talk below]
Short version of a very long discussion...
Quine is an interesting case. His notion of convention in TbC is somewhat in the Poincarean mold -- as far as he shares the view with Carnap and his notion of linguistic tolerance. Although the real similarity here is with Poincare's near contemporary, Pierre Duhem and his holistic approach in which only theories as wholes have meaning. Poincare (who was actually putting forawrd an interestng version of neo-Kantianism -- Janet Folina does the best job of working this out, but I think it is even stronger than what she suggests) still maintained that individual propositions had meaning, but that we needed to arbitrarily pick a language in which to express them.
But the real twist is that in terms of mathematical truth, Quine was not a conventionalist, but a Platonist.
"But the real twist is that in terms of mathematical truth, Quine was not a conventionalist, but a Platonist."
Yeah, the rest of the article is a charitable reading of the Poincare position, but it is a reductio ad absurdem. The end offers a powerful argument, showing that even if you bite the Godel bullet, and reduce math to intuitionism, there is still a problem with viewing Logic as true by convention. The argumetn always seemed(s) quite powerful to me.
"such claims are likely not meaningful"
What in the world would make you say this? Seems perectly meaningful to me.
But what does all this have to do with the work of that other underappreciated genius, Tom Lehrer?
Here is one for you SteveG. The man who funded the American revolution was Hyam Salomon, a Jewish immigrant from Poland who gave away his entire fortune for revolutionaries. He really ought to be in Adam Sandler's Chanukkah song.
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