[FOM] Euthyphro and proof
Timothy Y. Chow
tchow at alum.mit.edu
Tue Jan 20 16:21:27 EST 2009
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.
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.
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