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May 02, 2006

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Chris

Soames's reply is here: http://www-rcf.usc.edu/~soames/replies/Rep_Chicago.pdf

Andreas Stokke

Hi.
I have a question about the way you employ the distinction between 'known' and 'knowable'.

In the post, you say that:
"when one knows a priori that P, one thereby rules out a priori world-states where P is false. But then it follows that if P is a priori knowable, any world-state where P is false can be ruled out a priori, so are not epistemically possible."

Suppose that P is a theorem, i.e. a propositions that has been established as true by an a priori procedure. So we know a priori that P is true. The view seems to imply that in that case, not-P is not knowable a priori. I suppose that you would argue that the proposition Not-P is false is known, and hence knowable, a priori; and therefore true.

This seems to imply that the negations of theorems have a different epistemic status than the theorems themselves. This seems all right as long as we are dealing with cases where the truth of P has been established, i.e. where we have a proof of P. However, what about undecided cases like Goldbach's Conjecture (GC)? We do not know whether GC is true or false (or undecidable). Yet, we want to say that, if we obtain a proof establishing that it has either truth-status, we will know a priori that it has that truth-status.

But since GC has as of yet not been decided, it seems clear that both GC and not-GC (or even 'GC is undecidable') are knowable a priori. But do you not have to say, then, that in the presence of a future proof of either, its opposite shifts from being a priori knowable to being a priori unknowable? Are you happy with that?

Thanks.

djc

Thanks, Chris. I've updated the post now.

Andreas: If GC is provable but not yet proved, then GC is knowable a priori, but ~GC is not knowable a priori. The proof will reveal to us that GC is knowable a priori and that ~GC is not, but they will have had these epistemic statuses (unknown to us) even before we had the proof.

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