On 01 Apr 2015, at 13:51, Bruce Kellett wrote:
Bruno Marchal wrote:
On 01 Apr 2015, at 02:35, Bruce Kellett wrote:
I don't think that your arguments that consciousness cannot be
understood in terms of physical supervenience are very convincing.
At all the crucial points you simply appeal to the
computationalist hypothesis -- your argument is, at heart, circular.
At which line of the proof? Comp (even just the Church-thesis)
assumes arithmetical realism only, not plato's theology. This means
that 2+2=4 is independent of me and you.
You build quite a lot into the comp hypothesis. If it is, as you
said above, just the statement that the (human) brain is Turing
emulable, then no assumption of arithmetical realism is involved.
You need it to define computation. Just to *define¨them.
2+2=4 can be true independent of me and you without assuming numbers
have a real independent platonic existence.
Nice. You *are* an arithmetical realist. I defined arithmetical
realism exactly by "2+2=4 can be true independent of me and you".
I have never said anywhere that numbers have a "real independent
platonic existence" (and what would that mean). I gave the theory: it
assumes only:
0 ≠ (x + 1)
((x + 1) = (y + 1)) -> x = y
x = 0 v Ey(x = y + 1)
x + 0 = x
x + (y + 1) = (x + y) + 1
x * 0 = 0
x * (y + 1) = (x * y) + x
With predicate logic. (I can give a simpler theory which does not
assumes even predicate logic, but the one above is easier to
understand by non mathematicians).
I do not do metaphysics, and avoid term like "real", or "true", unless
it is a context where I can defined them mathematically (in logic
"true" is an standard notion, non problematical when concerned with
natural numbers or finitary describable things).
Arithmetic might not be fully axiomatizable (because of Goedel), but
an axiomatized version is plenty rich enough to cope with everyday
things.
You preach the choir. yes, I share with Macintyre and Franzen the idea
that most of math and physics does not go beyond what PA can prove.
But this fails for logic, category, group and ... theology,
metaphysics, etc. In theoretical computer science, we can distinguish
hiearchies of complexities, but also degrees on insolubilities. Some
insoluble problems can be much more insoluble than some others.
It does not mean that a material galaxy does not also exist
independently of me. For this I provide a proof or argument.
I haven't seen any proof of arithmetical realism.
Of course, when used in your sense. But as I insist, arithmetical
realism is just accepting the theory above, and to be precise,
accepting the idea that arithmetical proposition are either true or
false.
And it does not proof that material galaxies don't exist, but that
it cannot be related with the conscious event of seeing some galaxy
through a telescope. It shows that assuming matter is useless to
explain the appearance of matter, once we assume comp.
So don't assume comp.
But then I have to assume miracles, substantial Gods, fairy tales, ...
and so "no" to all doctors.
The the appearance of galaxies tells us something about the universe
in which we live -- a universe explained by matter and related
concepts.
assuming non comp, or eliminating consciousness. Please study the
argument in detail, and if you find a flaw, well it is about time to
make it precise.
It looks to me that you are just not aware of the reasoning.
>> So prime numbers might exist_{math}, but they do not
exist_{phys}.
>
> Sure. I have not verified, but I do think the universal machine
would
> say the same. Physical is a sophisticated internal view of
arithmetic/
> There still might be too much much white rabbits, but prime
numbers
> are not of the type "observable" there.
I think this claim needs some backing up. You have to actually
derive at least some basic physical laws from your UD.
That is done, and sum up in the second part of the sane04 paper,
but it assumes some "maturity" in mathematical logic. Have you read
it. I have already deduce the or a quantum logic of the observable.
I have not read your paper because, as yet you have not given me any
reason to believe that I would find it interesting.
You believe in comp, even explicitly in the arithmetical realist part,
and you are not interested in finding a flaw in a reasoning which
shows that any UTM is a toe, that physics is indifferent for the basic
ontology, etc.
I think that you will find the paper tremendously interesting, if not
shocking, if you believe in both comp and in a primitive or primary
physical universe.
Either you will find a flaw, or you will learn something. (or you will
pretend to have find a flaw but without succeeding to convince anyone
or to make it clear, I mean some people can't stay cold on this).
Deducing some quantum logic is not much of an achievement. What
about an actual physical law? Schroedinger's equation? Conservation
of momentum? The Coulomb force law?
None of those explain the origin of the physical laws, and none of
those provides light on the mind-body problem. If you are interested
in physics, there is no problem. But that is not really the subject
matter here, which is he problem of where are there physical laws, and
how are those laws related to our experiences.
Pointing to prime numbers is not enough.
Please, read the papers and the publication. It has been 30 years
of work. I have defend this without any problem as a PhD in
computer science. It modest, and radical only for people having
faith in primitive matter (a metaphysical hypothesis NOT sustain by
any facts).
I think it is your metaphysical hypothesis that is not sustained by
any facts.
because you thought that arithmetical realism involved some belief in
some metaohysical realm for the numbers. But it is enough to accept
the theory above. It is precisely defined by "believing that 2+2=4
independently of me and you". Only rare sunday philosophers doubt
arithmetical realism. It is the base of 99,999% of all scientific
theories. I made it explicit, sometimes, to explain how FEW I assume.
But you need it to define the notion of computation, universal
machine, etc.
I really don't know where you find a statement by me saying what you
say. I hope you don't repeat what some people says. You must be
serious. If you read the two first page of sane04, I think you would
not have made that attribution.
Physics has accumulated quite an impressive basis of explained facts
over the years.
No doubt on this. Physics remains the local verification criteria,
even with comp. No problem.
If you have a theory how a physical universe can make some machine
dreams more real that their dream emulated by arithmetic, I am all
ears?
The physical universe, described by universal physical laws, can do
that without producing white rabbit miracles.
May be. But once assuming comp, that must be deduced for all machine's
observable.
The dreams emulated by arithmetic are, at the moment, no better than
opium-induced fantasies.
?
No, that are theorem. That is the part that logicians told me to
suppress from my thesis, as being too much simple and at the
undergraduate level of mathematicians.
But I am not astonished, because I see very few scientists are aware
of that. But this is obvious *almost* since Gödel 1931, for the
logician, *almost* although you need the work of others to make that
entirely clear (Hilbert, Bernays, Turing, Church, Löb).
If you agree with comp (which you do, when you take arithmetical
realism in the sense I give), then you can prove that the set of
machine dreams is contained in the set of solutions of the following
set of Diophantine equations, thanks to the work of Putnam, Davis,
Robinson, and Matiyasevitch, and Jones.
You can see this as one description of the bloc mindscape. That work
is not obvious, as it has been hard to define the exponential function
by a diophantine polynomial relation (a lot bet that this was not
possible, but Matiyasevitch eventually got the solution.
(unknowns range on the non negative integers (= 0 included)
31 unknowns: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S,
T, W, Z, U, Y, Al, Ga, Et, Th, La, Ta, Ph, and two parameters: Nu and
X.
BEGIN:
Nu = ((ZUY)^2 + U)^2 + Y
ELG^2 + Al = (B - XY)Q^2
Qu = B^(5^60)
La + Qu^4 = 1 + LaB^5
Th + 2Z = B^5
L = U + TTh
E = Y + MTh
N = Q^16
R = [G + EQ^3 + LQ^5 + (2(E - ZLa)(1 + XB^5 + G)^4 + LaB^5 + +
LaB^5Q^4)Q^4](N^2 -N)
+ [Q^3 -BL + L + ThLaQ^3 + (B^5 - 2)Q^5] (N^2 - 1)
P = 2W(S^2)(R^2)N^2
(P^2)K^2 - K^2 + 1 = Ta^2
4(c - KSN^2)^2 + Et = K^2
K = R + 1 + HP - H
A = (WN^2 + 1)RSN^2
C = 2R + 1 Ph
D = BW + CA -2C + 4AGa -5Ga
D^2 = (A^2 - 1)C^2 + 1
F^2 = (A^2 - 1)(I^2)C^4 + 1
(D + OF)^2 = ((A + F^2(D^2 - A^2))^2 - 1)(2R + 1 + JC)^2 + 1
if the solution of that equation exists or not independently of you
and me, then all machine's dream exists independently of you, me, and
even of the existence or non existence of a physical universe, and
that is why you have to answer how matter can help a machine to
distinguish being in a physical universe, or in such a dream. The
answer is that they can do a test, and I give it.
That polynomial relation is turing universal. It simulates all Turing
machine. For a proof see Matiyasevitch's book:
http://www.amazon.com/Hilberts-10th-Problem-Foundations-Computing/dp/0262132958
Bruno
Bruce
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