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From: torkel@sics.se (Torkel Franzen)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <1991Jan19.112854.28632@sics.se>
Date: 19 Jan 91 11:28:54 GMT
References: <1991Jan18.083759.19131@sics.se>
	<1991Jan18.191303.6840@bronze.ucs.indiana.edu>
	<1991Jan18.203249.7022@sics.se>
	<1991Jan18.223602.15474@bronze.ucs.indiana.edu>
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In-Reply-To: chalmers@bronze.ucs.indiana.edu's message of 18 Jan 91 22:36:02 GMT

In article <1991Jan18.223602.15474@bronze.ucs.indiana.edu> chalmers@bronze.
ucs.indiana.edu (David Chalmers) writes:

  >It's a fairly subtle point.  I have no idea whether or not we will
  >someday be able to discover enough about the mind to build a TM that
  >accurately simulates it.  But the point is that I don't think you want
  >the refutation of the Lucas argument to rest solely on the claim that we
  >cannot.  Do you think that if in fact we could discover the structure of the
  >mind in this way, the Lucas argument would hold?  It seems tenuous to base
  >the refutation on such a fragile empirical matter.

  Just what do you mean by a refutation of the Lucas argument? What I
mean by refuting the Lucas/Penrose argument is to establish that it is
inconclusive.  I believe this is what is generally meant by refuting
an argument. I am not concerned with either accepting or rejecting
vague speculations about the possibility of our establishing that the
human mind is simulated by some Turing machine. My argument is just
this, that the Lucas/Penrose argument preupposes a claim for which no
justification whatever has been presented, namely the claim that if
the humanly provable statements of arithmetic are exactly the theorems
of a formal system T, it must be possible for human beings to convince
themselves of this fact.

  If we leave the Lucas/Penrose argument to one side and consider on
its own merits the idea of simulating the mathematical activity of the
human mind by a Turing machine or formal system, my general attitude
is that there is no such thing as a well-defined "capacity of the
human mind" for realizing mathematical truths or proving mathematical
statements. The question of the possibility or impossibility of
simulating the human mind by a Turing machine (in the sense and the
area here at issue) is not an empirical question at all, but the
outcome of a misunderstanding of or lack of attention to such concepts
as mathematical provability and mathematical evidence.