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From: jqb@netcom.com (Jim Balter)
Subject: Re: SRS Theory - Evolution anf Mathematics
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Date: Sun, 29 Sep 1996 19:57:53 GMT
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In article <324E1AC4.4683@dircon.co.uk>,
Chris Gordon-Smith  <gsmith@dircon.co.uk> wrote:
To: gsmith@dircon.co.uk
Subject: Re: SRS Theory - Evolution anf Mathematics
Newsgroups: comp.ai,comp.ai.philosophy,comp.ai.alife
In-Reply-To: <324E1AC4.4683@dircon.co.uk>
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In article <324E1AC4.4683@dircon.co.uk> you write:
>Jim Balter wrote:
>The most straightforward assumption is that we use an unsound algorithm for 
>doing mathematics (and everything else). If you make this assumption then you 
>have to accept that no mathematical propositions we make (even ones like 1 + 
>1 = 2) can be regarded as unassailable. This is not a problem for many of 
>us, because as you say/imply, the idea that we have some kind of direct 
>access to a sort of Platonic world of absolute mathematical truths is 
>unsupported.

1+1 = 2 can be viewed as an analytical truth, a la "all batchelors are unmarried men",
but of course such analycity has been assailed by Quine.

>I guess that most people on this newsgroup would go along with the idea that 
>the mind is an unsound algorithm, and might even find it a source of wonder. 
>However, I think we need to recognise that many (if not most) people are 
>uncomfortable with this because it implies that we are no different, in 
>principle, from machines. 

Oh, it has been well recognized, surely.  Unfortunately, it is mostly those
who reject the arguments because of this discomfort who fail to recognize that
cause.

>> But given that Penrose's
>> argument is not accepted Chalmers, Dennett, Putnam, McCullough, Feferman,
>> McDermott, McCarthy, Minsky, and Churchland, to name just a few, it is
>> anything but unassailable, and people who themselves have not been able to
>> find a flaw in it should not be so arrogant as to think that that fact carries
>> much weight.
>
>Did anyone say they thought it did carry any weight?

Many have, yes.  I wasn't including you among them.
-- 
<J Q B>

