[FOM] Re: Comment on Church's Thesis (Harvey Friedman)
Alexander Zenkin
alexzen at com2com.ru
Fri Jan 9 15:35:23 EST 2004
-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu]On Behalf Of
Vladimir Sazonov
Sent: Wednesday, January 07, 2004 9:28 PM
To: addamo
Cc: FOM
Subject: Re: [FOM] Re: Comment on Church's Thesis (Harvey Friedman)
addamo wrote:
>
> I don't understand how your comment refers to Church's Thesis.
> Could you make it more explicit?
>
> Do you or anybody know a proof of the undecidability of the Halting
problem
> not depending on Church's Thesis?
Sorry, how is it possible that any mathematical theorem (such as
the undecidability of the Halting problem) may depend on anything
what is not a mathematical theorem or axiom (like Church's Thesis
which is not a mathematical statement)?
Of course, the intuitive meaning of a theorem may depend on some
intuitive (informal) considerations.
[. . .]
Vladimir Sazonov
Solomon Feferman writes in one place, "The ideas of potential vs. actual
infinity are vague but at the intuitive, philosophical level very
suggestive."
Wilfried Hodges writes in one place: " . . .the author observes quite
correctly that the PROOF of Cantor's theorem (on the uncountability of the
real line) depends on acceptance of actual infinity."
How is it possible that not simply mathematical theorem (Cantor's theorem
on the uncountability of continuum), not "the intuitive meaning of the
theorem", but its MATHEMATICAL PROOF may depend on an acceptance of the
"vague, intuitive, philosophical" notion of "actual infinity" "what is
<certainly> not a mathematical theorem or axiom"?
Alexander Zenkin
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