REPOST OF PHIL ROBERTS POST

From: "Phil Roberts, Jr." 
Date: Thu, 05 Dec 1996 13:29:58 -0500

Jim Balter wrote:
> 
> Phil Roberts, Jr. wrote:
> > 
> >         Godel's Theorem says that in any consistent axiom system rich
> >         enough to generate the arithmetic of the natural numbers, there
> >         are statements we cannot prove in the system, but which can be
> >         _seen_ by other means to be true (Brainstorms, p. 257).
> 
> Dennett does not emphasize "seen", and it is just plain dishonest
> of you to add that emphasis.  Dennett doesn't say how this seeing
> is to be done, or what it means.
>

Curses!  Foiled again.
 
> >         ...what Godel proved, _beyond any doubt_, is that when it comes
> >         to axiomatizing simple arithmetic, there are truths that "we
> >         can see" (Godel) to be true but that can _never_ be formally
> >         proved to be true (Darwin's Dangerous Idea, p. 429).
> 
> And then he immediately says "Actually this claim must be carefully
> hedged: ...".  This hedge includes consistency 

Not an issue.  Lucas acknowledges this.

> He later goes on to say of the idea that we can "see" truths
> that we can't prove, "But although this seems to be what Godel
> himself thought, and it certainly expresses the general popular
> understanding of what Godel's Theorem shows, it is much harder
> to *demonstrate* than first appears".
>

I thought this was my point.  You know, the one you disagreed with:

ROBERTS:
 I think its important to keep in mind the fact that there are actually
 three issues at play here:
 1. The validity of Godel's theorem (including what it says, I suppose).
 2. The validity of Lucas' argument that it applies to material systems,
    and therefore that minds are different from theorem proving machines.
 3. The testability of Lucas' argument.
    Its actually 3 which is where Dennett thinks Lucas and Penrose are most
    vulnerable (ibid, Chapt 15),
BALTER: 
 You have misunderstood Dennett.
 The Lucas argument is not empirical; it's validity or soundness
 does not and cannot depend upon empirical evidence, any more than
 the argument for an infinity of primes.  You are *so* far out of your
 depth ....


I hate to have to keep repeating myself, but in case you missed it the
first time:


LUCAS:

	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 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.


With a little reading between the lines, I believe Lucas can reasonably
be construed as providing an argument (not a proof) that rationality can
not be mechanized (or reduced to logic, for that matter) and, conversely,
that rational creatures are not machines.  Not only should this come as
great news to moralists and libertarians but, more importantly, it is an 
argument which has _empirical_ _implications_ and can therefore be
tested against reality.  Since the Lucas thesis predicts that rational
creatures should be _in_determined (assuming he is right in equating 'being
consistent' with 'being determined' or 'being a machine'), demonstrate that
this is indeed the case and you empirically demonstrate Lucas.  Simple, eh?

Of course, this indeterminism business is a notorious party pooper and AI
buffs have long thought their position secure from such a demonstration.  
Even so, there have been a number of developments in the philosophy of 
science which, I believe, offer a somewhat more enlightened 
perspective from which to approach the matter, and which render the strong
AI position considerably more vulnerable.  The following is from the Manicas
and Secord paper which comprises one of the elements of my Feelings of 
Worthlessness paper (see URL below):


	If we allow for some arbitrariness and overlapping, what Scheffler
	called "the standard view of science" has been undermined from 
	two sides.  The more familiar critique is associated, with
	differences, of course, with Toulmin, Feyerabend, especially Thomas
	Kuhn, Michael Polanyi and many others.  It attacks the "foundationist"
	epistemology of the standard view and its unhistorical notions
	about scientific change and development (Brown, 1977).  This
	critique shattered the "myth of the given," entirely recast the 
	problem of meaning and confirmation in science and powerfully
	argued that science was a social activity.  All this was salutary --
	as far as it went; but as critics saw, the "paradigm" account of
	science precipitously courted irrationalism and failed to make
	clear how science was to be distinguished from non-science
	(Lakatos and Musgrave, 1970).  The dominating neo-positivist
	view of science could not thus be entirely exorcized.

	Concurrent with this strand, there was, however, another strand,
	sometimes overlapping and, on the present view, at least as 
	important.  It can be associated with Michael Scriven, Norwood 
	Hanson and with an effort of great importance by Roy Bhaskar.
	This aspect of the critique of the standard view emphasized 
	the stratification of science and of the world and developes 
	a conception of theory, experiment and explanation which is far
	more coincident with the practice of science than could be 
	sustained by the standard view.  Moreover, it supplements the
	former strand by making it clear that the social conception of
	science and the view of fallibilism which attends it, presupposes
	a view of the world as real, stratified and differentiated.

	Perhaps most fundamental, the new conception rejects the orthodox
	assumption that "the world is so constituted that there are
	descriptions such that for every event, the simple formula 'whenever
	this, than that' apples" (Bhaskar, 1975).  This regulative ideal,
	Laplacean in origin, in turn supports the thesis, derived from Hume,
	that scientific laws are statements of constant conjunctions between
	events.  But for the new view of science, there may be no
	description such that for some event the formula, "whenever this,
	then that" applies.  On this view the world is radically open.

	In the new heuristic, scientific knowledge is much closer to that
	knowledge which is *more familiarly accessible, through common sense,
	literature, and other modes of experience*.


Now then, if these guys are to be taken seriously (and I take them very 
seriously, indeed), it becomes apparent that the appropriate place to look
for the indeterminism predicted by Lucas will not be at the level of the 
individual, but rather at the more abstract level of the species, and the
formalism/determinism which we will want to focus on will not be some
lawlike constant conjunction, but rather the more abstract design constraints
of the only legitmate scientific theory we psychologists have to work with, 
as your buddy, Dennett, also seems to have understood:


	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 algorhithm 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* ...  (Murmers in the Cathedral).


Oops!  Sorry!  Wrong again, old bean.  But then as someone who has wasted 
much of his adult life picketing the Cartesian theatre and doing his best 
to try to intimidate those of us who regularly attend (see my "Is a 
Science.."), we shouldn't be too surprised to find him being quided by his 
personal convictions rather than a crucial piece of empirical evidence 
(feelings of worthlessness).


	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 brief moment of 
	greatness* (Sigmund Freud).


	Since the explanation I have proposed (for worthlessness related
	need and disorder) amounts to the contention that the most 
	rational species (presumably) is begining to exhibit signs of 
	transcending the formalism of nature's fixed objective (accomplished
	in man via intential self-concern), it can reasonably be construed
	as providing evidence and argumentation in support of Lucas/Godel
	(Rational Negativism synopsis: Additional Implications).


-- 

Phil Roberts, Jr.

Feelings of Worthlessness from the Perspective of
So-Called Cognitive Science

http://www.geocities.com/Athens/5476