[FOM] polemic, predicativism, and absolute certainty
Timothy Y. Chow
tchow at alum.mit.edu
Mon Feb 6 19:18:29 EST 2006
Curtis Franks wrote:
> I'd like to point out that in his earliest descriptions of his
> foundational program (I'll quote from his 1922 Hamburg paper), David
> Hilbert articulated the same motivation--"I should like to regain for
> mathematics the old reputation of incontestable truth"--as an
> *objection* to foundational programs that involve a restriction of
> ordinary mathematical techniques. He even specifically picks out
> Predicativism as a foundational program that jeopardizes the objectivity
> of mathematics:
This is an interesting historical fact that I for one wasn't aware of, but
it seems to me that its philosophical importance in the present debate is
limited by its pre-Goedel date. Given that Hilbert's vision is impossible
in its original form, perhaps predicativism is more plausible as a
candidate for "absolute truth" than it might have seemed before Goedel's
theorems.
Tim
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