On 21 Dec 2013, at 17:32, Craig Weinberg wrote:
On Thursday, December 19, 2013 10:13:25 AM UTC-5, Bruno Marchal wrote:
On 19 Dec 2013, at 15:07, Craig Weinberg wrote:
On Thursday, December 19, 2013 5:23:20 AM UTC-5, Bruno Marchal wrote:
Hello Craig,
That is the very well known attempt by Lucas to use Gödel's theorem
to refute mechanism. He was not the only one.
Most people thinking about this have found the argument, and
usually found the mistakes in it.
To my knowledge Emil Post is the first to develop both that
argument, and to understand that not only that argument does not
work, but that the machines can already refute that argument, due
to the mechanizability of the diagonalization, made very general by
Church thesis.
In fact either the argument is presented in an effective way, and
then machine can refute it precisely, or the argument is based on
some fuzziness, and then it proves nothing.
If 'proof' is an inappropriate concept for first person physics,
then I would expect that fuzziness would be the only symptom we can
expect. The criticism of Lucas seems to not really understand the
spirit of Gödel's theorem, but only focus on the letter of its
application...which in the case of Gödel's theorem is precisely the
opposite of its meaning.
The link that Stathis provided demonstrates that Gödel himself
understood this:
So the following disjunctive conclusion is inevitable: Either
mathematics is incompletable in this sense, that its evident axioms
can never be comprised in a finite rule, that is to say, the human
mind (even within the realm of pure mathematics) infinitely
surpasses the powers of any finite machine, or else there exist
absolutely unsolvable diophantine problems of the type
specified . . . (Gödel 1995: 310).
To me it's clear that Gödel means that incompleteness reveals that
mathematics is not completable
OK. Even arithmetic.
in the sense that it is not enough to contain the reality of human
experience,
?
He says the 'human mind', but I say human experience.
Mathematics is not enough for the mind and experience of ... the
machines.
not that it proves that mathematics or arithmetic truth is
omniscient and omnipotent beyond our wildest dreams.
Arithmetical truth is by definition arithmetically omniscient, but
certainly not omniscient in general. Indeed to get the whole
arithmetical "Noùs", Arithmetical truth is still too much weak. All
what Gödel showed is that arithmetical truth (or any richer notion
of truth, like set theoretical, group theoretical, etc.) cannot be
enumerated by machines or effective sound theories.
The issue though is whether that non-enumerablity is a symptom of
the inadequacy of Noùs to contain Psyche, or a symptom of Noùs being
so undefinable that it can easily contain Psyche as well as Physics.
The Noùs is the intelligible reality. It is not computable, but it is
definable. Unlike truth and knowledge or first person experience.
I think that Gödel interpreted his own work in the former and you
are interpreting it in the latter - doesn't mean you're wrong, but I
agree with him if he thought the former, because Psyche doesn't make
sense as a part of Noùs.
That is too much ambiguous. The psyche is not really a part of the
Noùs, which is still purely 3p.
I see Psyche and Physics as the personal and impersonal
presentations of sense,
Machine think the same, with "sense" replaced by arithmetical truth.
Except that the machine has to be confused and for her that truth is
beyond definability, like sense.
and Noùs is the re-presentation of physics (meaning physics is re-
personalized as abstract digital concepts).
The Noùs has nothing to do with physics a priori. It is the world of
the eternal platonic ideas, or God's ideas.
keep in mind the 8 hypostases:
- p (truth, not definable in arithmetic, but emulable in some
trivial sense)
- Bp (provable, believable, assumable, communicable). It splits into
a communicable and non communicable part (some fact about
communication are not communicable)
- Bp & p (the soul, the knower, ... the psyche is here). It does not
split.
- Bp & Dt (the intelligible matter, ... matter and physics is here).
It splits in two.
- Bp & Dt & p (the sensible matter. the physical experience, (pain,
pleasure, qualia) are here. It splits also in two parts.
Physics is the commercialization of sense. Psyche is residential
sense. Noùs is the hotel...commercialized residence.
An excellent book has been written on that subject by Judson Webb
(mechanism, mentalism and metamathematics, reference in the
bibliographies in my URL, or in any of my papers).
In "conscience and mechanism", I show all the details of why the
argument of Lucas is already refuted by Löbian machines, and Lucas
main error is reduced to a confusion between Bp and Bp & p. It is
an implicit assumption, in the mind of Lucas and Penrose, of self-
correctness, or self-consistency. To be sure, I found 49 errors of
logic in Lucas' paper, but the main conceptual one is in that self-
correctness assertion.
Penrose corrected his argument, and understood that it proves only
that if we are machine, we cannot know which machine we are, and
that gives the math of the 1-indeterminacy, exploited in the
arithmetical hypostases. Unfortunately, Penrose did not take that
correction into account.
Gödel's theorem and Quantum Mechanics could not have been more
pleasing for the comp aficionado.
Gödel's theorem (+UDA) shows that machine have a rich non trivial
theology including physics, and QM confirms the most startling
points of the comp physics.
As far as QM goes, it would not surprise me in the least that a
formal system based on formal measurements is only able to consider
itself and fails to locate the sensory experience or the motive
'power on' required to formalize them in the first place.
They don't address that question.
Formal systems are seen as mathematical object, even number, and
they exist independently of us, if you still accept arithmetical
realism.
I accept the realism of arithmetic representation, and that they
exist independently of us humans, but not that they exist
independently of all experience or possibility of aesthetic
presentation. I say no to theoretical realism.
Realism is always defined with respect to some theory.
Arithmetical realism is not independent of experience, as arithmetic
produces them necessarily. They are concomitant.
The consistency objections similarly fail to recognize the core
capacity to discern consistency from inconsistency. It is not
possible to doubt our own consistency without also doubting the
consistency of our doubt.
On the contrary, we, and/or machines, cannot not doubt our
consistency.
But we can't doubt the consistency of doubt.
Not sure what you mean. In fact we can doubt all assertion of
consistency. We cannot doubt that we doubt, but we can doubt of the
consistency of all the proposition. G does not contain any sentence
beginning with a D, and G*, on the contrary is close from
possibilitation (p ====> Dp).
We believe that it is within our power to disbelieve.
What we cannot doubt is our raw consciousness "here-and-now", which
might be the first person view of consistency. Consistency (Dt) and
consciousness have many things in common, but incorrigibility works
only for consciousness. A good first person description of
consciousness would be Dt v t, making it non doubtable and trivial
(which it is from the 1p view). But that is still only a sort of
approximation.
Eliminative physicalism is the embodiment of doubt of our raw
consciousness.
OK. Nice.
Computationalism and emegentism is also used that way by many.
Yes. Alas. But I think that this is specifically and definitely refute
with the UDA (and AUDA). Most people believe that comp is an ally to
materialism, but in fact comp is incompatible with most reasonable
form of materialism. of course primitve matter is a fuzzy notion, so
you can adapt it to be compatible with anything, and that's why in
step 8 we still need a bit of Occam, and that's normal as that has to
be the case when we apply a theory to "reality".
Bruno
http://iridia.ulb.ac.be/~marchal/
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