On 13 Jun 2014, at 17:07, David Nyman wrote:
You're right, oftentimes they do. But I wouldn't include Bruno in
"people" here (if you see what I mean). Once one assumes the existence
of the UD (or rather its infinite trace) the hard problem then becomes
one of justifying in detail every aspect of the *appearance* of matter
through its interaction with mind. Then, as Bruno is wont to say, the
problem turns out to be (at least) twice as hard as we might have
feared. As to the admissibility of the UD, for me, in the end, it's
just another theoretical posit. As it happens, it strikes me as
sufficiently motivated, because once computation is fixed as the base,
I don't see how one would justify restricting its scope to certain
computations in particular.
By Gödel's traditional textbook presentation of the incompleteness
theorem, the "belief in the UD" is equivalent with the believe in
elementary arithmetic.
The computable facts are those are equivalent with sigma_1 sentences,
and proof for sigma_1 sentences.
Actually p <-> []p is true for them. The löbian number can even prove
p -> []p,
but they still will not prove []p -> p for all sigma_1 propositions.
For example they still not prove <>t = []f -> f (and f = "0=1" which
is trivially sigma_0 and thus sigma_1).
Well, I meant that to believe in the UD is a theorem in arithmetic.
Even a constructive one.
Thanks to many years of research the UD*, which is a sort of splashed
universal machine, dovetailing on all her abilities, can be put in the
explicit form below. You need only to believe in the existence of the
solution of the following universal system of diophantine equations:
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
I don't show this to impress, but to illustrate that arithmetic is
effectively universal at a rather law level of complexity
(polynomials!). This results from the works of Putnam, Davis,
Robinson, Matiyazevich, solving negatively Hilbert tenth problem, and
Jones, getting a not to big universal (and thus Turing complete)
system of polynomials.
Ontologically, you need only to believe in the solutions or non
solutions of those equations.
Of course B^(5^60) is an abbreviation of B * (B * (B * ( ...)))) 5^60
times, when written in the {s, 0, +, *} language.
The solutions of that system emulates all Turing emulable processes.
Each choice of the values of the variables 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 the two parameters: Nu and X will do, or not do. In fact
phi_Nu(X) converges iff the numbers 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
exist verifying the universal diophantine equation. So (even without
CT) anything "computational" is automatically provided by the minimal
arithmetical realism (subtheory of any current physical theory).
In that sense, comp assumes less than any other theory.
If there were a reason why a primitive matter was needed (to select
and incarnate consciousness), there would be number X and Nu which
would emulate validly "Brunos and Davids" finding that reason, and
proving *correctly* that they don't belong only to arithmetic, which
would be false, and that is a mathematical contradiction, even if
those Davids and Brunos are zombies. That makes physicalism just
logically incompatible with mechanism (and that argument is simpler
than step 8).
Bruno
http://iridia.ulb.ac.be/~marchal/
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