On 21 Jan 2017, at 01:16, Brent Meeker wrote:
The number machine Nu must be defined by some specific encoding.
The polynomials depend on X and Nu. So what is an X and Nu for
which they have a solution and what enumeration is phi_mu?
The specific encoding is given by the polynomial itself.
It means simply that if you make the number Nu vary on N, you get all
polynomials enumerating the RE sets. The Nu is variable, and the proof
that such W_nu will go through all RE sets is by the direct encoding
on what is needed for that task, using many previous technic. A
universal polynomial is a bit like coding Lisp in Lisp, a universal
lisp expression.
If you choose Nu = 456, will give the X for which there are a
solution, and those X are the elements of the 476th recursivley
enumerable set W_456, in a universal enumeration (has proved by Jones,
using technic of Robinson and Matiyasevich).
It entails that there is a number Nu such that the set of X is the set
of prime numbers, that there is a number Nu such that the X is the
code of the grap of the function sending x on x^x, etc. Indeed, there
will be an infinitely of number Nu doing that task.
It means also that there is Nu fro which there is no solution at all,
but the verification of this (which is just by addition,
multiplication and number comparison) will mimic exactly (that is
emulate), a Universal dovetailing. But the UD itself will be
implemented in infinitely many different, all encoded in the universal
polynomial equation.
Adding computationalism, there is a number Nu such that the set of X
justifies the existence of the computations supporting the person
Brent reading the current line, again, there is an infinity of one,
leading to the arithmetical inflation of histories (but constrained by
self-reference and its meaning/truth nuances the hypostases) which
limit the possible use of that inflation to refute computationalism).
The UD is used to formulate the "body" problem, not to solve it, as
some people misunderstand sometimes. The "solution" is in the self-
referential "theology" of the universal person.
P.S. I can believe statements are true without believing their
referents exist: "The Mad Hatter is insane and makes hats" is true.
Yes, me too. That is why I can believe that "I am sending you a mail"
is true without believing in a "material" mail, notably. What counts
is not that 2 or 3 exists in any important sense, what counts is that
2+3=5 is true independently of you and me. That is enough for the web
of dreams to be realized in arithmetic. All form of effective
existence are then given by the internal views of the numbers
( embedded in relative numbers sequences). Adding a special Reality
which selects the realities is poor explanation with computationalism,
and akin as invoking an oracle without evidence, and this before
testing the observable reality).
Here the TOE is Robinson arithmetic, so s(s(s(s(0)))) exists just
because RA proves Ex(x=s(s(s(s(0)))), but this is unimportant, we can
use at the bottom any Turing universal machine, in the large but
precise sense of Church, Turing, etc.
Bruno
Brent
On 1/20/2017 9:53 AM, Bruno Marchal wrote:
I think you miss the discovery of purely mathematical, even
arithmetical Turing universal relations. Just for the beauty of it,
I copy again below a system of diophantine relations which defines
a Turing universal system.
Bruno
Only bad faith fears reason.
Only bad reasons fear faith.
The Putnam-Davis-Robinson-Matiyasevich-Jones Polynomial equations:
We have that X is in W_Nu, that is phi_Nu(X) is defined, that is
the number/machine Nu stops on input data X, if and only if the
following system of polynomial equations ha a solution. It is
short, and one degree is very high (560), but we can diminish the
degree to 4, easily, by introducing a lot of other variables
though. We can also limit the syetm to one equation. From this you
can conceive that once you believe that 2+2=4 independently of you,
then such a system polynomial equation has or not solution, but
this encoded the entire universal dovetailing, including the non
computable redundancy.
Nu = ((ZUY)2 + U)2 + Y
ELG2 + Al = (B - XY)Q2
Qu = B^(560)
La + Qu4 = 1 + LaB5
Th + 2Z = B5
L = U + TTh
E = Y + MTh
N = Q16
R = [G + EQ3 + LQ5 + (2(E - ZLa)(1 + XB5 + G)4 + LaB5 + +
LaB^5Q4)Q4](N2 -N)
+ [Q3 -BL + L + ThLaQ3 + (B5 - 2)Q5] (N2 - 1)
P = 2W(S2)(R2)N2
(P2)K2 - K2 + 1 = Ta2
4(c - KSN2)2 + Et = K2
K = R + 1 + HP - H
A = (WN2 + 1)RSN2
C = 2R + 1 Ph
D = BW + CA -2C + 4AGa -5Ga
D2 = (A2 - 1)C2 + 1
F2 = (A2 - 1)(I2)C4 + 1
(D + OF)2 = ((A + F2(D2 - A2))2 - 1)(2R + 1 + JC)2 + 1
*you* emerges from the first person view on all solutions of that
equations.
The physical reality is given by the competition of infinitely many
universal numbers operating below your substitution level.
The bio-psychological reality the same, with finitely many
universal systems operating above your substitution level.
The goal is not doing a new physics. The goal is in applying reason
in metaphysics, and with the computationalist hypothesis, this is
almost ... metamathematics (an "old" name of mathematical logic).
Bruno
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