sci.logic
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Re: Turing vs. Godel (Newbie Question)

Subject: Re: Turing vs. Godel Newbie Question
From: Jack Campin - bogus address
Date: Thu, 05 Oct 2006 01:19:57 +0100
Newsgroups: sci.logic
[complicated mess of quotation-within-quotation, but this seems to be
Manna and Waldinger]

> Unless we have a philosophical commitment to intuitionism, maintaining
> constructiveness when it is not required can only make a proof system
> more cumbersome to use. We have seen that certain programs cannot be
> derived from their specifications in a constructive logic, but can be
> derived in a classical logic upon which minimal restrictions have been
> imposed ... ': Zohar Manna and Richard Waldinger, 'Constructive Logic
> considered Obstructive' (typescript, n.d.), 8.

There is a trick that comes out of the theorem-proving-on-top-of-Scheme
community that draws a completely different moral.  You can extend the
Curry-Howard isomorphism to interpret classical logic; Peirce's law
ends up being the type of call-with-current-continuation.  But this
isn't restricting classical logic, it's reinterpreting it.

==============  j-c  ======  @  ======  purr . demon . co . uk  ==============
Jack Campin:  11 Third St, Newtongrange EH22 4PU, Scotland | tel 0131 660 4760
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