FOM: Franzen on "which undecidables have determinate truth value"

hartry field hf18 at
Thu Feb 26 11:07:50 EST 1998

I appreciate TF's advertisement of my paper.  One clarification about his
summary: on point (i) of the summary, an 'f-decidable' sentence is a
semantic consequence IN THE LOGIC OF FINITENESS of our fullest mathematical

On his critique of my attempt to use empirical assumptions to ground the
determinacy of 'finite': I certainly agree that anyone antecedently
convinced that 'finite' was indeterminate wouldn't be convinced.  But I was
addressing my remarks to those who (like almost everybody) is strongly
inclined to think that 'finite' is determinate, but who at the same time are
puzzled how it COULD be determinate given that (a) our meanings are
determined by our practice and (b) our practice with 'finite' seems
exhausted by what we accept and (c) what we accept has nonstandard models.
(The last part of the paper is an attempt to show how we could learn to live
with the conclusion that 'finite' is radically indeterminate--something I
claim we need to do if the empirical assumptions fail.  This is the context
for the discussion of the incompleteness theorem.) 


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