On 19 Dec 2013, at 22:46, Jason Resch wrote:
> 8. There is no need to build the computer in step 7, since the
executions of all programs exist within the relations between large
numbers.
That would only be true if everything that could exist does exist,
and maybe that's the way things are but it is not obviously true.
It doesn't require that everything to exist, it requires only one
particular program to exist: the universal dovetailer. This program
and its execution exist within mathematics.
Yes, even in arithmetic, and under different important forms. Its many
descriptions exist, and the computation are "truly" emulated in the
truth referred by the theorems concerning those description. That is a
point which met some difficulties for non-logician, as it is
impossible to ever point a computation, without mentioning a
description of it. The computation itself is captured by the truth of
certain arithmetical statements, not by the existence of a description
of those computations. The nuance is subtle, because we infer the
existence of the computation by looking at the existence of some
description of them, and to show that this is equivalent is by no
means a trivial affair, linking the syntax of the theory and its
intended meaning (and that is why we need AR). There is a need to
really study how simple theories (like RA) can represent in some
strong sense the partial recursive function. It is well done in Boolos
and Jeffrey, or in Epstein & Carnielli.
The whole difficulty of step 8 is in this paragraph. Those who believe
that a filmed boolean graph can be thinking commit a confusion between
use and mention (like I have just described).
For example, it is a true statement that the state of this program
after the 10^100th step of its computation has some particular value
X, and it is also a true statement that the 10^100 + 1 step has some
other particular value Y. It is also a true statement that the
program corresponding to the emulation of the wave function for the
Milky Way Galaxy contains John Clark and this particular John Clark
believes he is conscious and alive and sitting in front of a
computer in a physical universe.
OK.
> Hence, arithmetical realism is a candidate TOE.
A candidate certainly, but is it the real deal? Maybe but it's not
obvious.
Right, but it is a scientific question. It will not be easy but we
can refute or confirm the theory by seeing what the UD implies for
the physics that observers see. Everett's theory was a great
confirmation, for without it, conventional QM with collapse (and a
single universe) would have ruled it out. As it stands, there are
several physical concepts that provide support for the UD being a
valid TOE:
Quantum uncertainty
Non clonability of matter
Determinism in physical laws
Actually, this one is the problem. There might still be a too big FPI,
like with the "white rabbits".
Information as a fundamental "physical" quantity
Yes, and even obeying different "information laws" above and below the
substitution level. And this is confirmed by the difference between
quantum information and classical (Shannon) information theory.
(I think there is something I am forgetting, but Bruno can fill in
the gaps)
May be after more coffee :)
What we need to do, or at least what mathematicians should do is to
compare the empiric quantum logics with the quantum logics provided
(by Goldblatt's result) on the (three) arithmetical quantum logic
provided by the arithmetical quantizations (S4Grz1, Z1*, X1*). It fits
up to now, but the program I wrote to test this should be optimized.
We can come back on this.
Bruno
http://iridia.ulb.ac.be/~marchal/
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