[FOM] Euthyphro and proof
David Auerbach
auerbach at unity.ncsu.edu
Tue Jan 20 22:06:43 EST 2009
That's a very nice name for it. As Socrates sets it up (in terms of
what the gods will) it is plausible that the alternatives are
exhaustive. That doesn't seem to be the case here.
There's logical space to reject both horns. There might be a way to
rephrase the second horn in order to close up the space a bit--ruling
out incorrect proofs that are momentarily accepted. That is, it should
be possible to opt for the spirit of horn two without committing to
the infallibility of the mathematical community. (Not that Socrates
didn't point out an analogous problem...)
David Auerbach
Department of Philosophy & Religion
Box 8103
NCSU
Raleigh, NC 27695-8103
On Jan 20, at 4:21 PM, Timothy Y. Chow wrote:
> One topic that is sometimes debated in the philosophy of mathematics
> is
> whether a (valid) proof is something objective, in the sense that it
> is
> something that is correct or incorrect independently of whether anyone
> believes it to be correct, or whether it is something subjective, in
> the
> sense that correct proofs are simply those that are accepted as such
> by
> the mathematical community.
>
> Keith Devlin uses the terms "right-wing" and "left-wing" to describe
> the
> two sides of this debate.
>
> http://www.maa.org/devlin/devlin_06_03.html
>
> I personally don't care for the terms "right-wing" and "left-wing."
>
> My purpose here is not to argue for one side or the other, but to
> suggest
> that the debate be called a "Euthyphro dilemma." Recall that Socrates
> famously asked Euthyphro whether something is pious because it is
> loved by
> the gods, or whether it is loved by the gods because it is pious.
> Analogously, we can ask whether a proof is correct because it is
> accepted
> by the mathematical community, or whether it is accepted by the
> mathematical community because it is correct.
>
> Tim
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