In response to the following remark by Nik Weaver:

   > .........Remember, Godel's theorem is a *theorem* ...
   > it exhibits an assertion that cannot be proved true
   > within a given FS, and simultaneously verifies ---
   > proves --- that that assertion actually is true.
   > Empiricism doesn't come in anywhere.

I wrote:

   > There is a way that Godel might have empirical
   > ramifications, however:
   >
   >   Godel's theorem seems to me to prove that Mechanism is
   >   false, that is, that minds cannot be explained as
   >   machines.  So also it has seemed to many other people:
   >   almost every mathematical logician I have put the
   >   matter to has confessed to similar thoughts, but has
   >   been reluctant to commit himself definitely until he
   >   could see the whole argument set out, with all
   >   objections fully stated and properly met.  This I
   >   attempt to do.
   >
   >   Godel's theorem states that in any consistent system which
   >   is strong enough to produce simple arithmetic there are
   >   formulae which cannot be proved-in-the-system, but which
   >   we [STANDING OUTSIDE THE SYSTEM] can SEE to be true...>
   >
   >   Godel's theorem must apply to cybernetical machines,
   >   because it is of the essence of being a machine, that
   >   it should be a concrete instantiation of a formal
   >   system. It follows that given any machine which is
   >   consistent and capable of doing simple arithmetic,
   >   there is a formula which it is incapable of producing
   >   as being true -- but which we [STANDING OUTSIDE THE SYSTEM]
   >   can SEE to be true. It follows that no machine can be a
   >   complete or adequate model of the mind, that MINDS ARE
   >   ESSENTIALLY DIFFERENT FROM MACHINES (J. R. Lucas,
   >   'Minds, Machines and Godel', Philosophy, 36, pp. 112-27).
   >
   >   [emphasis mine]
   >

in response to which Michael Lamport Commons wrote:

   > Not all machines are programmed.  Some use neural
   > networks and stacked neural networks.  They learn
   > the way organism do to a large extent.  They can in
   > principal reflect upon a system and see if it is
   > complete or not.
   >

and Paul Gross wrote:

   >
   > This is true only if your -- or Lucas's --
   > identifications of "machine" and "mind" are
   > unchallengeable. They are not.
   >

Actually, Roger Penrose lists some twenty objections to
the Godelian argument in 'Shadows of the Mind'.  But given
that both Penrose and Lucas have attempted to establish an
empirical assertion (e.g., "minds are essentially different
from machines") based almost exclusively on a single logical
proof, what else would you expect?  For me, the real
Godelian argument against mechanism is to be found, not
so much in the writings of J. R. Lucas and Roger Penrose
as in the simple fact that, subsequent to Godel, just about
every logician in the universe came to appreciate the
futility of Hilbert's program of formalizing mathematical
reasoning.

     Formalism failed for reasoning, but succeeded brilliantly
     for computation (Gregory Chaitin).

As I assume most here are aware, the normal route for
establishing an empirical assertion (e.g., minds are
essentially different from machines) is not to rely on
a logical proof, but rather to MARSHAL EVIDENCE and,
hopefully, to demonstrate that one's favored hypothesis
(e.g., mechanism is false) serves to maximize explanatory
coherence better than any of its competitors (see e.g.,
Pierce, Harman, Lycan, Thagard, etc).

Here goes:

The following is from Derek Parfit's, Reasons and Persons,
(pp. 12, 13):

     A man breaks into my house. The man orders me to open the safe in
     which I hoard my gold. He threatens that, unless he gets the gold
     in the next five minutes he will start shooting my children, one
     by one.

     ....there is a risk that, if he gets the gold, he will kill me
     and my children before he drives away.

     I also have a special drug, conveniently at hand. This drug
     causes one to be, for a brief period, very irrational. Within a
     few seconds of drinking it, it becomes apparent that I am crazy.
     Reeling about the room, I say to the man: 'Go ahead.  I love my
     children. So please kill them.' The man tries to get the gold by
     torturing me. I cry out: 'This is agony. So please go on.'

     Given the state that I am in, the man is now powerless...

     On any plausible theory about rationality, it would be rational
     for me, in this case, to cause myself to become for a period very
     irrational.


ON ANY PLAUSIBLE THEORY???  Perhaps.  But I would think that most
of us would prefer something a bit more substantial than Prof.
Parfit's personal assurance on the matter.  I don't know about
other folks, but its long been my understanding that an outright
logical contradiction is not a particularly good thing to have
in one's theory.  Indeed, its a little difficult for me to
imagine WHAT COULD POSSIBLY MAKE A THEORY LESS ACCEPTABLE!!!

Notice too, that the formalism/determinism generating the
logical contradiction here is not one modeled along the lines of a
propositional logic, nor is it even one dependent on a recursion
(self-reference), but rather the more generalized determinism
of a fixed objective (e.g., maximizing one's long range best
interests) and, as such, circumvents what I construe to be Mike's
objection to the Lucas Godelian argument (e.g., connectionist
machines might not be subject to Godelian limitations).

Also notice that what is being called into question here is
not based on a comparison of minds with machines, but rather
an implicit THEORY that attempts to constrain rationality
within the context of a determined objective (e.g., maximizing
self-interest).  As such, it seems to me that this little
anecdote also circumvents what I take to be Paul's objection.

And for those who are trying to convince themselves the the
foregoing is only anecdotal evidence, or that the only
evidence against mechanism comes in the form of logical
contradictions, think again:

The following was posted to the ev. psych. egroup Jul 23,
2002:

     Cooperation, psychological game theory, and limitations of
     rationality in social interaction

     Andrew M. Colman

     Abstract: Rational choice theory enjoys unprecedented
     popularity and influence in the behavioral and social
     sciences, but it generates intractable problems when
     applied to socially interactive decisions. In individual
     decisions, instrumental rationality is defined in terms
     of expected utility maximization...   Instrumental
     rationality, conventionally interpreted, fails to explain
     intuitively obvious features of human interaction, yields
     predictions starkly at variance with experimental findings,
     and breaks down completely in certain cases...
     ...rationality in social dilemmas IS SELF_DEFEATING.

     http://www.bbsonline.org/Preprints/Colman/


Nik Weaver wrote:

  >
  > What is this math crank stuff doing on an EP list?  This kind of
  > thing usually goes on the sci.math Google discussion groups.
  >

Personally, I think the reason we humans have to expend
so much effort and energy on the survivalistically
bizarre nonphysical need of maximizing self-worth is that we
as a species are beginning to show signs of "standing outside
the system" (Lucas), of transcending the formalism of nature's
fixed objective if you will (maximizing self-interest), and
coming to see our own importance (and therefore the importance
of maximizing our self interest) in a manner that is a bit too
objective (e.g., too rational?) for our own good.  The result
is that we are a species that is expending less and less effort
and energy on trying to stay alive and more and more effort
and energy on trying to maintain REASONS for doing so (needs
for love, achievement, acceptance, purpose, meaning, moral
integrity).  There is indeterminism in nature's most rational
species, as implied by Godel's theorem and the logical
inconsistencies encountered by decision theorists, its just
that it shows up more in the form of a questioning of the
value of maximizing one's self interest (i.e., volatility in
self-worth) rather than in the form of changing one's mind about
what to have for dessert:


     So even if mathematicians are superb cognizers of mathematical
     truth, and even if there is no algorithm, practical or otherwise,
     for cognizing mathematical truth, it does not follow that the power
     of mathematicians to cognize mathematical truth is not entirely
     explicable in terms of their brain's executing an algorithm.  Not
     an algorithm for intuiting mathematical truth -- WE CAN SUPPOSE
     THAT PENROSE HAS PROVED THAT THERE COULD BE NO SUCH THING.  What
     would the algorithm be for, then?  Most plausibly it would be an
     algorithm -- one of very many -- FOR TRYING TO STAY ALIVE ...
     (Dan Dennett review of Roger Penrose's 'The Emperor's New Mind)

     [emphasis mine]


Oops!  Sorry!  Wrong again, old bean. [me again]


     "My ruling passion is the love of literary fame" (David Hume).


     "I have often felt as though I had inherited all the defiance and
all the
     passions with which our ancestors defended their Temple and could
     gladly sacrifice my life for one great moment in history" (Sigmund
     Freud).


     "He, too [Ludwig Wittgenstein], suffered from depressions and for long
     periods considered killing himself because he considered his life
     worthless, but the stubbornness inherited from his father may have
     helped him to survive" (Hans Sluga).


     "The inquest [Alan Turing's] established that it was suicide.  The
     evidence was perfunctory, not for any irregular reason, but because
     it was so transparently clear a case" (Andrew Hodges)



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