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Article 1658 of comp.ai.philosophy:
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>From: gar@arp.anu.edu.au (Greg A. Restall)
Newsgroups: sci.philosophy.tech,comp.ai.philosophy
Subject: Re: Consciousness (was Re: Daniel Dennett)
Message-ID: <1991Nov27.032101.23430@newshost.anu.edu.au>
Date: 27 Nov 91 03:21:01 GMT
References: <1991Nov26.135953.5926@husc3.harvard.edu> <1991Nov26.211823.20295@newshost.anu.edu.au> <1991Nov26.212920.5939@husc3.harvard.edu>
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In article <1991Nov26.212920.5939@husc3.harvard.edu> 
zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:

* GAR:
* >The swift move was the `in other words'.  Unfortunately
* >for a logician like myself, I'm not sure of any inference
* >that can take one from the first paragraph to the next.  
* >This is probably due to my limited acquaintance with the 
* >theory of FSAs.  However, I'm prepared to accept that there
* >is a legitimate inference from the claim that the mind is 
* >"computationally isomorphic" to an FSA, and Ultra-intuitionism,
* >if such a move were demonstrated to me.
* 
* No inference was implied; note that I promised merely to suggest an
* argument, not to present it.

True.  I thought that the structure of your suggestion would
hint at the structure of the argument.  That's all.
  
* GAR:
* >Whatever it could be, I have no idea - for it seems to me
* >that the first claim is one in the philosophy of mind, and
* >the second, in the philosophy of mathematics.  And while
* >the philosophy of mathematics espoused by Ultra-intuitionists
* >is intimately tied to the philosophy of mind, it is not
* >clear that the latter could in any way follow from *any*
* >particular philosophy of mind.  After all, on most realist
* >views, numbers exist independently of minds - and independently
* >of what *kinds* of minds there are.
* 
* I agree with nearly all of the above, especially with the claim that the
* philosophy of mathematics espoused by Ultra-intuitionists is intimately
* tied to the philosophy of mind. On the other hand, it seems to me that any
* philosophy of mind that makes a claim of its numerical limitation, should
* be wedded to Ultra-intuitionism.  Last I heard, Yessenin-Volpin was still
* pursuing his research privately, unencumbered by NSF or DOD grants...

*Perhaps* it might be that any philosophy of mind that makes a claim of
its numerical limitation should be wedded to some kind of strict 
finitism in mathematics - (And that is *not* an uninteresting 
perspective.  The best work in finitism in my opinion is coming from
the area of paraconsistent logic.  - It is possible to give finite
models of arithmetic that validate all the Peano axioms - and all
their classical consequences.  See the Meyer & Mortensen article in
the 1984 JSL).   But again, that's not clear.  Isn't this simply
at most an *epistemological* restraint on mathematics?  It still
seems coherent with a realist account of numbers.  All the 
numbers are still out there, behaving as they always have & will,
but we only have access to a particular initial segment of them.

* The conclusion is as follows:
* 
* Given that an FSA is inherently incapable of modeling itself, how can we
* expect an AI theorist to come up with a model of his own intellectual
* processes? 

An FSA cannot model itself.  Does that mean it cannot `come up with
a model of itself'?  `Coming up with models' is a highly intensional 
notion, as you will agree.  It is not to be equated with the simple
notion of modelling from the theory of automata.  

If you are going to make a connection between the notions, it has to be 
made much more rigourous than it stands at present.

* In other words, if so many people in computer science believe themselves to
* be finite state automata, why isn't Yessenin-Volpin besieged with lucrative
* job offers?  (This is *not* a rhetorical question!)

Who knows?  Most probably CS types haven't heard of him.  I'd employ
him, if I had the money.  (Boy!  I'd employ myself, if I had the
money!)

Best,

Greg


  
-- 
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Greg Restall	 	 | Philosophy Department, University of Queensland.
gar@lingua.cltr.uq.oz.au | Queensland, 4072.  Australia.
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