FOM: Re: Chaitin
silver_1 at mindspring.com
Fri Mar 23 11:08:53 EST 2001
Steve Simpson wrote:
>Chaitin's results are not
>without interest, but claims about their philosophical/foundational
>significance are greatly exaggerated.
I would appreciate any detailed comments you might wish to make
about what interest Chaitin's Theorem really has and what
exaggerations you have found concerning their
philosophical/foundational significance. Rudy Rucker, for one,
considers it to be of greater philosophical interest than Gödel's
Theorem. He says that Chaitin's Theorem gives us more information
than Gödel's. (See the section of _Mind Tools_ on "Algorithmic
Information", beginning on page 279.) What I find of particular
interest (independently of whether Chaitin's Theorem has real content)
is Rucker's connecting Chaitin's Theorem to the philosophical notion
of "conceivability". According to Rucker (p. 290), "a pattern is
'inconceivable' if it is too complex for me to reproduce in detail."
Later, on the same page, he says, "Suppose I think of myself as being
a Turing machine about to make marks on a blank tape. My brain has
only finitely many components, and each of these components can be set
in only finitely many ways...."
It seems to me that certain scientific or maybe pseudo-scientific
notions fire up the public's imagination and are then translated into
modern jargon, which then becomes used to reflect the "general
intellectual interest" of the day. It would be useful to assess the
scientific value of such notions and then to evaluate their
application to diverse fields in the humanities.
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