[FOM] Question on the Scope of Mathematics
Henrik Nordmark
henriknordmark at mac.com
Tue Jul 27 14:46:33 EDT 2004
>Aatu Koskensilta <aatu.koskensilta at xortec.fi> wrote:
>But the only reason for assuming that provability in ZFC has anything
>to do with
>truth of statements is that ZFC is sound. By your account, this either
>is not a mathematical
>truth, or we should specify a formal system, say MK, in which it can be
>proved.
Well, it depends on what you mean by a "mathematical truth".
I sympathize with Dmytro's position in the sense that if one is working within the framework of ZFC, then the claim that ZFC is sound and is a good formalism lies at the meta-mathematical and not really at the mathematical level. Of course, one can go beyond the framework at hand and justify the claim that ZFC is sound by using stronger systems, but then again the issue of whether these stronger systems are any good is meta-mathematics.
Henrik Nordmark
Institute for Logic, Language and Computation
Universiteit van Amsterdam
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