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I've been reading up on the epistemology of Carnap and Quine. Although Carnap maintains the
analytic/ synthetic distinction, while Quine rejects it, both philosophers hold that any statement
(including analytic) is open to revision. Given this, it is unclear to me why Carnap argues for the
analytic/ synthetic distinction. Please help me illuminate his argument.
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My take on Carnap and analytic truths is that they are those that come from considerations of logic.
Synthetic truths come from empirical data, roughly speaking. Now, a truth which comes from logic is
the result of deduction, usually (or induction on a known series, let us say), and as such follows from
premises, according to the terms defined, the operations employed, etc. Now let's take an analytic
truth like "any triangles' angles add to 180 degrees". This is provable within a particular framework,
Euclidean geometry, as we all know. But as we also all know, at this point, this truth only holds on a
plane. On the surface of a sphere, one must say (as I recall... it's been awhile), "any triangle's angles
add to more than 180 degrees" (I'm just not sure of the "any" in that quote... but I think it's correct).
And on a hypersphere (a surface of negative curvature), we must say, "any triangle's angles add to
less than 180 degrees". So the Euclidean truth must be revised, mustn't it, when one generalizes to
other surfaces than planes, to read, "any planar triangles' angles add to 180 degrees". And so it goes.
But one still can say that those truths are analytic, if that term is indeed meaningful, as Carnap
believed.
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For Carnap, a given statement can be analytic relative to one system or theory, but synthetic relative
to another. Quine's objection in 'Two Dogmas of Empiricism' to the 'dogma' of the analytic/ synthetic
distinction hinges on the fact that we don't know which is the correct theory prior to experience. I.e.
we don't first arm ourselves with a set of concepts and then go about investigating the world.
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