Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!news.mathworks.com!udel!gatech!howland.reston.ans.net!pipex!sunic!trane.uninett.no!eunet.no!nuug!EU.net!uknet!festival!ainews!smaill
From: smaill@ai.ed.ac.uk (Alan Smaill)
Subject: Re: Penrose's new book
In-Reply-To: rickert@cs.niu.edu's message of 23 Oct 1994 15:17:50 -0500
Message-ID: <SMAILL.94Oct29105739@ossian.ai.ed.ac.uk>
Sender: news@aisb.ed.ac.uk (Network News Administrator)
Organization: DAI, University of Edinburgh
References: <389im1$86u@mp.cs.niu.edu> <1994Oct22.005737.2249@math.ucla.edu>
	<38a67l$g8i@mp.cs.niu.edu> <1994Oct22.195802.12955@math.ucla.edu>
	<38egde$p9l@mp.cs.niu.edu>
Date: Sat, 29 Oct 1994 10:57:39 GMT
Lines: 32
Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:21476 sci.philosophy.tech:16209

In article <38egde$p9l@mp.cs.niu.edu> rickert@cs.niu.edu (Neil Rickert) writes:

   Was Penrose talking about abstract matters, or about human
   intelligence?  If all Penrose claims is that a finite computer could
   not emulate a abstract imagined eternal and infinite intelligence not
   restricted by the physical limitations of life on earth, then I will
   grant him that.

No, he claims that an idealised computer (not restricted by time or space)
could not emulate what mathematicians do. (He is not so clear on whether
we should consider mathematical intelligence also without resource
limitations; I presume so.)

This may seem a bit detached from questions of the relation between
real computers and real mathematicians.  Yet I think most AI folk
would regard the statement that "mathematical reasoning can be correctly
modelled by some (traditional, computable) algorithm" as an empirical
statement (one that might logically be true or false).  If you insist
that the task is to model only some finite set of reasoning, then
of course this can be done in a computable way. So to say that this
reasoning is algorithmic is, I think, already to abstract over an
infinite class of problems/inputs.





--
Alan Smaill,                       JANET: A.Smaill@uk.ac.ed             
Department of Artificial           ARPA:  A.Smaill%uk.ac.ed@nsfnet-relay.ac.uk
       Intelligence,               UUCP:  ...!uknet!ed.ac.uk!A.Smaill
Edinburgh University. 
