On 21 Jun 2016, at 03:44, Jason Resch wrote:
On Mon, Jun 20, 2016 at 8:26 PM, John Clark <johnkcl...@gmail.com>
wrote:
On Mon, Jun 20, 2016 at 3:37 PM, Jason Resch <jasonre...@gmail.com>
wrote:
Is ??? really the floor or does ??? need an explanation too?
Valid questions. As you see the answer is not so clear cut,
But what is clear cut is that the chain on "what caused that?"
questions either comes to an end or it does not. My hunch is it does
come to an end but it's just a hunch, but It's also clear cut that
if it does come to an end Bruno does not know what it is.
Bruno has shown that arithmetic is a viable candidate for explaining
physics: physics as the semi-stable systems of observations that
conscious programs existing in arithmetical reality can have and make.
It is also shown that arithmetic cannot be explained in terms of
anything else, which is kind of like hitting bedrock in terms of
searching for deeper explanations.
Yes. And here, we can limit ourself (and I think we might have to
limit ourself) to "sigma_1 arithmetic", so that the axiom of the TOE
can be just the axiom of Robinson Arithmetic, or of any Turing
Universal system (the short one is the one given by the two equations:
Kxy = x
Sxyz = xz(yz)
The theology, including the testable physics, is the same whatever
sigma_ complete (Turing universal) system is chosen. We could take
superstring theory, but that would made harder to see that we derive
physics without cheating. It is better to take axioms not obviously
coming from physics, like the SK combinators above, and even better,
the RA axioms, which I recall are precisely (taken above some
presentation of classical predicate logic with equality, + the symbol
s, 0, + and * (and parentheses)):
~(0 = s(x))
s(x) = s(y) -> x = y
x = 0 v Ey(x = s(y))
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
In that theory, we can define the Löbian observer, and extract physics
by interviewing them on the "probability one" on the (true) sigma_1
sentences (which represents in arithmetic the "leaves" of the
Universal Dovetailing). The probability one is defined in arithmetic
by either []p & p, or []p & <>t, or []p & <>t & p, with p sigma_1, et
[] denoting Gödel's beweisbar predicate. The three option possible
provides a quantum logic with a neat quantization, as we could expect
(well, as a comp believer should expect at least).
If we do not assume the natural numbers, or something Turing
equivalent, then indeed, we cannot retrieve them at all.
In fact, we cannot prove the existence of a Turing universal system in
any theory which is not a Turing universal system. Accepting Church-
thesis makes our base assumption equivalent with the axiom that a
universal system exist.
Bruno
>>If not and there are only finitely many layers to your
pyramid then I think it more likely that physics =???, physics is
the explanatory floor and mathematics is just the best language
minds can use to describe physics.
> That's a possibility, but it is a belief you learn towards
(at least partially) on faith.
Having a hunch is not the same as having faith. People with
hunches are often correct but never certain, people with faith are
seldom correct but always certain.
It is good to hear that you remain open to either possibility.
Have you read Russell Standish's Theory of Nothing? The e-book is
free from his website, and it shows that quantum postulates can be
derived from simple assumptions relating to a theory of observation
within a plentitude of all possibilities.
Jason
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