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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