FOM: Hodges' comments on criticisms of Cantor's diagonalization argument
Fred Johnson
johnsonf at lamar.ColoState.EDU
Wed Mar 25 13:36:49 EST 1998
Wilfrid Hodges' article in the Bulletin of Symbolic Logic
(March, '98) raises questions that I think are relevant to
recent discussions:
1) Definition of "Platonism": Does Hodges' statement (p. 14)
put him in the Platonist camp?
The validity of an argument can never depend on you or me
doing some particular thing in the privacy of our
imaginations. (Our imaginations might help us *find* a
valid argument, but that is a different matter.)
2) Priority of the informal notion of proof (and truth and
determinacy): Is Hodges saying that formal proofs are only
as good as the informal proofs that underlie them and that
often these informal proofs are not very good (resting, for
example, on the ambiguous directive "assume x")? If so,
is he right?
Fred Johnson
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