[FOM] Are proofs in mathematics based on sufficient evidence?
hendrik at topoi.pooq.com
Sun Jul 11 08:53:31 EDT 2010
On Fri, Jul 09, 2010 at 09:32:26PM -0400, Richard Heck wrote:
> No progress is possible here unless we carefully distinguish these
> questions. And, to my mind, the critical question that Vaughn raised
> needs to be formulated in this light. It does seem a characteristic of
> /mathematics/ that proofs are supposed to be /deductively/ valid,
> whereas proofs in other realms do not have to meet that high standard.
> Whether that means there are different notions of proof is not obvious,
> but it makes clear where the issue is.
Because the other notions of proof do not "meet that high standard", you
even find that if you present a long, careful, mathematical, deductively
valid proof to someone whoo follows one of the other notions of proof,
you'll find that he jusn't believe it, because in his experience, long,
detailed proofs often come to wrong conclusions.
Perhaps this is eveidence that they are really other notions of proof.
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