Re: Robot Evolution
- From: "John Edser" <edser@xxxxxxxxxxxxxx>
- Date: Wed, 27 Dec 2006 02:03:30 -0500 (EST)
"Phil Roberts, Jr." philrob@xxxxxxxxxxxxx:-
John Lucas's 'Godel' argument has been much-criticized - and
Penrose's views in this area are essentially a variation on it.
I concede that there is a clear majority who
disagree with the Lucas/Penrose position. On
the other side of the equation, however, we have:
a. Hofstadter, Dennett, Penrose, Clarke and Chaitin,
in various ways acknowledging that Godel at least
SUGGESTS a disconnect between formalism and
mathematical reasoning.
b. Little unanimity as to what exactly is wrong with
the Godel argument, with dozens and dozens of different
sorts of objections, many based on impenetrable
confabulations.
c. Papers still being published criticizing the Godel
argument against mechanism almost 80 years after Godel
first published his theorem.
d. The universal abandonment of Hilbert's program of
formalizing mathematical reasoning by mathematicians
all over the world subsequent to Godel's proof.
e. Intersubjectively reproducible empirical evidence
(feelings of worthlessness) suggesting that not even
Mother Nature herself seems to be able to constrain
rationality within a formalism (the program for
"trying to stay alive").
f. Evidence (e.g., Parfit, 'Reasons
and Persons', p. 12) that any theory that attempts
to constrain rationality within a formal structure
(e.g., a fixed objective) can be shown to sanction
rational irrationality (i.e., can be shown to be
self-defeating).
JE:-
Typically, Karl Popper who provided the missing Darwinian key just remains
ignored:-
http://philsci-archive.pitt.edu/archive/00002662/
Incompleteness is based on the fact that all we can do about ANYTHING is
make competing but entirely refutable guesses and _continuously_ evolve
them. Each _rational_ guess must refute in favor of a better one providing a
lineage of guesses which can explain more and more in an entirely testable
way. It is the mystery of INDUCTION which sits at the heart of this matter.
The truth about ANYTING, including the truth about truth (it always remains
incomplete because it is always based on just an inductive guess) including
what language can express truth (which logic can support the latest testable
against nature theory) do the following:
1) Perceive patterns.
2) Explain the perceived pattern using competing inductions (more than just
the one guess).
3) Reformulate each induction into empirically testable theories which can
be
i) Verified
ii) Non verified
iii) Refuted
by defining at least one different frame of reference for each contesting
theory (each theory employed to explain the same or greater set of facts).
If the proposed theory is just a tautology (circular logic) then it is
proven not to be a theory of anything, e.g. mathematics. If just any two of
the above three exist then only a model of a theory has been provided via
the process of simplification/oversimplification of a valid theory. No model
can validly contest or replace the theory from which is was
simplified/oversimplified.
4) Test all theories on the table until just one is left.
5) When this stands refuted goto 1.
Brief version of what's wrong:
``A mathematician often makes judgments about what
mathematical statements are true. If he or she is not more
powerful than a computer, then in principle one could write
a (very complex) computer program that exactly duplicated
his or her behavior.
Assumes what is being questioned.
JE:-
Mathematics and programming are not at all the same thing. Mathematics
remains a tautology (based on axioms) but computer programs are not they
remain based on human inductions. Put another way: mathematics remains based
on just reversible set intersection while computer programming and what we
call language also requires non eversible _set nesting_.
But any program that infers
Programs don't infer, they model logical relations that
have been found to underly human inferences on most
occasions. As to whether these relations are actually
being followed or simply EMBEDDED IN our inferences remains
to be seen.
JE:-
Put more simply: programs supply the most basic inductive inferences. A
machine must be minimally supplied with the largest nested set. All it can
ever do is mechanically deduce from this (and any others provided).
mathematical statements can infer no more than can be proved
within an equivalent formal system of mathematical axioms
and rules of inference,
True, but Lucas/Penrose assumes we can go beyond this, that
the intuiting of mathematical truth is not simply a matter
of logical proof:
The immediate consequence is that truth cannot be
defined in terms of provability.
JE:-
I contend that refutability and "provability" remain exactly the same thing.
Something can only be refuted when a testable frame of reference becomes
replaced by another, i.e. no refutation exists in a vacuum. Each refuted
idea has to be replaced by another with a larger truth domain (the set of
refutable but non refuted deductions which can flow from it must be larger).
A theory can be considered proven when it provides a UNIQUE verification.
This verification will also constitute a refutation of the old theory, e.g.
Einstein's unique verification of c (the maximal velocity of light in a
vacuum) necessarily refuted Newton's m and t (mass and time).
In any serious
intellectual endeavor we shall be able to formulate
simple mathematical arguments, and thus shall be
subject to Godel's incompleteness theorem.
JE:-
Reasoning is NOT based on just mathematical tautologies, these were and
remain based entirely on reasoning.
However
far we go in formalizing our canons of proof, we
shall be able to devise propositions which are not,
according to those canons, provable, but are none
the less, true. So it is one thing to be provable,
and a different thing to be true. Truth outruns
provability. (J.R. Lucas).
JE:-
Induction outruns deduction via a continuous evolution of inductions via the
Popperian process of refutation.
This argument won't fly if the set of axioms to which the
human mathematician is formally equivalent is too complex
for the human to understand.
What is the basis for the assumption that the intuiting
of mathematical truth is based on a set of axioms, let
alone that they must be too complex to understand?
JE:-
It has no basis. Mathematical axioms are just tautologies which have become
expanded. All of these must be deducible from rational inductions which
alone can form the basis of any empirically testable theories. IOW non
empirical mathematics is entirely deducible from empirical NON mathematics.
These are amazing claims, which Penrose hardly bothers to
defend. Reviewers knowledgeable about Godel's work, however,
have simply pointed out that an axiom system can infer that
if its axioms are self-consistent,
An axiom system can infer?
JE:-
Tautologies can only be expanded.
then its Godel sentence
is true. An axiom system just can't determine its own self-
consistency.
JE:-
Yes, because no tautology is rational, i.e. they remain logical but not
rational.
But then neither can human mathematicians know
whether the axioms they explicitly favor (much less the
axioms they are formally equivalent to) are self-consistent.
Cantor and Frege's proposed axioms of set theory turned out
to be inconsistent, and this sort of thing will undoubtedly
happen again.''
JE:-
Yes: what is the set of all possible sets? Answer: any rational induction
that can evolve via the process of refutation.
Agreed. But we can nonetheless "know" them to be true in
the sense that we all agree we have good reason to believe.
JE:-
No, belief is NOT required, just self consistency relative to at least one
frame of reference which can be empirically tested to refutation.
As to what this has to do with evolution - if humans can
do things no machine can do - or will ever be able to do -
that may impact the hypothesis that machine-based organisms
may replace humans as the dominant life form on earth over
the next century or so.
JE:-
Machines cannot replace humans unless they can think for themselves
(write their own programs _from scratch_)
More importantly, it would mean that there is reason to
suspect that E. O. Wilson may have gotten it wrong in
asserting genetic determinism:
Can the cultural evolution of higher ethical values
gain a direction and momentum its own and completely
replace genetic evolution? I think not. The genes
hold culture on a leash. The leash is very long, but
inevitably values will be constrained in accordance
with their effects on the human gene pool (E. O.
Wilson).
JE:-
Genes (epistatic dependent genetic combinations and NOT independent single
genes) can only limit cultures. OTOH cultures can control (select) genes.
and that Dawkins may have actually gotten it right in
asserting the converse:
We, alone on earth, can rebel against the tyranny of
the selfish replicators" (Dawkins, 1976, p. 215).
JE+-
This is entirely a false gene centric notion (the misuse of an
oversimplified theory). No "selfish replicators" exist in nature
(not a single empirical additive gene fitness has ever been verified in
nature no matter how you define fitness). Only degrees of fertile organism
fitness mutualism empirically exist. These have been chronically mistaken
for "selfishness" and "altruism" providing utterly irrational evolutionary
theories (theories which cannot be tested to refutation. i.e. they remain
"irrefutable" dictates).
However, this particular argment for the qualitative
superiority of humans is simply wrong - and (IMO) rather
obviously so for anyone who knows anything about Godel's
work.
Why then is one of the papers you referenced
written in 2004? Shouldn't this have all been over and
done with decades ago for a flaw that is so "obvious"?
JE:-
If "this particular argument for the qualitative superiority of humans is
simply wrong" then it could NEVER have been written in the first place.
snip<
John Edser
Independent Researcher
edser@xxxxxxxxxxxxxx
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