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From: olaf@cwi.nl (Olaf Weber)
Subject: Re: Penrose and human mathematical capabilities
In-Reply-To: weemba@sagi.wistar.upenn.edu's message of 14 Jul 1995 14:27:38
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Date: Fri, 14 Jul 1995 19:15:47 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:30221 sci.logic:12433

In article <3u5usq$2ji@netnews.upenn.edu>, weemba@sagi.wistar.upenn.edu (Matthew P Wiener) writes:
> In article <DBp80E.IL1@cwi.nl>, olaf@cwi (Olaf Weber) writes:

>> In a sense, Penrose's admission that the best he can do against (II)
>> is to try to convince the reader that it is implausible grants the
>> moral victory to the opposition, for that possibility at least.

> Why is that?  Since he's talking about the real world, the best he can
> do is an implausibility argument.

At that point he's talking about the possibility that mathematical
insight is the result of an algorithmic process in the brain.

Since the _only_ argument he has in favour of his notion that a theory
of quatum gravity is non-algorithmic, non-random, and will explain how
consciousness is produced is that _no_ algorithmic process can underly
what people do, he needs to be more convincing that "I cannot imagine
that this possibility is true".

By the way, Matthew, you should take note that the possibility that
human insight uses an unknowable or unsound algorithm, and can thus be
implemented on a computer, is not rejected by Penrose with a claim
that the underlying computer would have a Goedel limit -- he argues
about properties of such algorithms instead.  Like it or not, that
objection _is_ a red herring.

-- Olaf Weber
