π, τ, and Quine's pragmatism
Some readers may already be familiar with the π vs. τ debate. If not, I recommend checking out Michael Hartl's τ manifesto and this fantastic short video by Vi Hart. An attempt at a balanced evaluation of π vs. τ can be found here.
For those who don't know, τ is just 2π. The defenders of τ argue (as seen in the above links) that using it instead of π makes many things much clearer and simpler/ more elegant.
Let's assume for present purposes that the τ-proponents turn out, in the end, to be right. I want to ask a further question: what would this then say about Quine's denial of the analytic-synthetic distinction? Quine's denial, virtually all agree, is the claim that all rational belief change is pragmatic, i.e. there is no principled difference between questions of evidence/justification on the one hand, and questions of efficiency and expedience on the other (= between external and internal questions, i.e. between practical questions of which language-form to adopt, and questions of whether a particular empirical claim is supported by the available evidence).
So here's my question: if Quine is right, then is our old friend C=2πr simply wrong (and C=τr right)? If not, how can a Quinean wiggle out of that consequence? And if so (i.e. C=2πr really is wrong), does the Quinean have any way of softening the sting of this apparently absurd consequence?