Re: Raatikainen's critique of Chaitin
From: Nath Rao (RnNaDthOrMao_at_yahoo.com)
Date: 09/08/04
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Date: Wed, 08 Sep 2004 09:19:35 -0400
KRamsay wrote:
> In article <chl25r$13i$1@charm.magnus.acs.ohio-state.edu>, Nath Rao
> <RnNaDthOrMao@yahoo.com> writes:
> |These discussions always remind me of a position put forth by J-P
> |Changeaux (in the discussions collected in "Conversations about mind,
> |matter and mathematics"): Mathematical objects are really creatures of
> |the human mind, but it is helpful to think of them as real in order to
> |do mathematics. Connes, the other person in these dialogs seems to have
> |been scandalized by this, to judge by his response.
>
> Heh. When I'm feeling most sympathetic to antirealism, I often have
> the feeling that the crucial issue between realists and antirealists is
> the nebulous, nagging perception that somehow thinking things are real
> is more than thinking of them as if they were real.
>
> Keith Ramsay
I agree with that position. Otherwise, the whole discussion is pointless.
BTW, Changeaux, a biologist IIRC, is (I am sure) a realist with regard
to the phenomenal world. I suspect he didn't know enough to ask where
such things as "the" category of (all) C^*-algebras and K-theory
functors live. I just have a problem coming with an answer to such
questions that can be squared with the way people actually think and
talk. [Yes, Grothendieck universes are a way around if you don't mind
excessively strengthening the consensus axiom system, but as A. Levy
pointed decades ago, people talk as if they are referring to "the"
universe, rather than >a< partial universe. The other way out is alien
to most practicing topologists/algebraic geometers etc, and will fail
anyway the moment somebody 'discovers' unavoidably impredicative
functors 'in nature'.]
Nath Rao
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