From: "Phil Roberts, Jr."
Newsgroups: sci.bio.evolution
Subject: Re: Robot Evolution
Date: Thu, 21 Dec 2006 13:23:10 -0500 (EST)
aatu.koskensilta@xortec.fi wrote:
> Phil Roberts, Jr. wrote:
>
>>I have always thought the Godel argument constitutes a pretty
>>good ARGUMENT against a computational view of the mind.
>
> How?
Godel demonstrated (1931) that for any formal (logical, mathematical,
rule driven, etc.) system capable of simple arithmetic, there is at
least one well-formed sentence or theorem, usually referred to as the
Godel or G sentence, that cannot be proven in the system.
Interestingly enough, because of our ability to attach meaning to the
symbols employed in such a proof, the G sentence is one that we humans
can quite easily "see" to be true in that its semantic interpretation
is simply: 'This sentence can not be proven in this system'. Since
machines (computers) can prove theorems, but cannot prove the Godel
sentence without a logical contradiction, Godel's theorem has served
as the basis for an argument, originally championed by J. R. Lucas
(1961) and more recently by the physicist, Roger Penrose (1989,
1994), that "minds are different from machines" (Lucas).
Interestingly enough, one of the most lucid statements of the
Lucas/Penrose perspective comes from Douglas Hofstadter (1979), who
himself is perhaps one of its most vocal critics:
[quote]
Looked at this way, Godel's proof suggests -- though by no means does
it prove! -- that there could be some high-level way of viewing the
mind/brain, involving concepts which do not appear on lower levels,
and that this level might have explanatory power that does not exist
-- not even in principle -- on lower levels. It would mean that some
facts could be explained on the high level quite easily, but not on
lower levels at all. No matter how long and cumbersome a low-level
statement were made, it would not explain the phenomena in question.
It is analogous to the fact that, if you make derivation after
derivation in [Peano arithmetic], no matter how long and cumbersome
you make them, you will never come up with one for G -- despite the
fact that on a higher level, you can see that [the Godel sentence] is
true.
What might such high-level concepts be? It has been proposed for
eons, by various holistically or "soulistically" inclined scientists
and humanists that consciousness is a phenomenon that escapes
explanation in terms of brain components; so here is a candidate at
least. There is also the ever-puzzling notion of free will. So
perhaps these qualities could be "emergent" in the sense of requiring
explanations which cannot be furnished by the physiology alone
('Godel, Escher, Bach', p. 708).
[unquote]
>
> [moderator's note: And how does this relate to evolutionary
> biology? Keep it on topic, people. - JAH]
>
Because if one assumes, as I do, that 'feelings of worthlessness'
are a maladaptive byproduct of the evolution of rationality,
then they can be construed as an empirical vindication of the
Lucas/Penrose perspective on Godel's theorem, i.e., the assertion
that Godel constitutes an argument that rationality can not be
constrained (captured in its entirety) within a formal (e.g.,
mechanical) system and therefore that "minds are different
from machines" (Lucas). Another way of saying this, is that
they can be construed as evidence that Dawkins was right in
maintaining that:
Darwinism is too big a theory to be confined to the
narrow context of the gene....
As presented in my paper, 'Feelings of Worthlessness' (see URL
below), my assertion that 'feelings of worthlessness' constitute
an empirical vindication of Lucas/Penrose is based on the
following assumptions:
1. That human beings have been programmed by natural selection to survive.
2. That human beings do not survive by blindly responding to stimuli
with no understanding of the overall objective such mechanisms have
been "designed" to achieve, as is likely the case with most other
species, but as the result of a conscious intention to survive often
involving long range planning.
3. That the basis of the conscious intention to survive, at least when
not under the influence of fear, anger, pain, etc., is the value the
organism places on its own existence, i.e., its self-value.
4. That 'feelings of worthlessness' constitute evidence that humans
are beginning to question the value of their existence and therefore
are beginning to question the objective of nature's most basic program.
5. That the same capacity for "standing outside the system" (Lucas)
that allows us to "see" that the Godel sentence is "true" is what is
responsible for our ability to stand outside of nature's program and
question (in the guise of 'feelings of worthlessness') whether it is
one worth completing.
6. That rationality cannot be constrained (captured in its entirety)
within a formal system, not even by Mother Nature herself.
[quote]
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... (Dennett, 1989)
[unquote]
Oops! Sorry! Wrong program, old bean! [My response to Dennett's
failure to notice that, in man, self-worth maximization often trumps
the program "for trying to stay alive".]
[quote]
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).
[unquote]
--
Phil Roberts, Jr.
Feelings of Worthlessness
An Annotated Outline of a Theory of Emotional Instability
http://www.rationology.net