On 14 Jul 2014, at 20:43, meekerdb wrote:
On 7/14/2014 10:59 AM, Bruno Marchal wrote:
On 14 Jul 2014, at 02:07, meekerdb wrote:
On 7/13/2014 11:17 AM, Bruno Marchal wrote:
Then, look at my preceding post to you. I don't know for Tegmark,
but computationalism excels in differentiating and relating the
different sort of existence: ontological, epistemological,
observational, communicable or not, theological, etc.
Lists like this that subscribe to everythingism Bruno's "comp"
and Tegmark's MUH completely erase the boundary between math and
physics.
On the contrary, Comp introduces a clear distinction between the
physical, core of all universal being, and the geographical,
which are the contingencies of the normal universal numbers
living above their substitution level.
Physics is done today is just fuzzy about such distinction.
That would be a nice result. How does it differentiate different
sorts existence?
ExP(x) (the arithmetical usual sense. It means that "ExP(x)"
is true if there is number n such that P(n). It is the chosen
ontology, although we could have taken any other first order
specification of a universal base)
Modal nuances:
[]ExP(x)
[]Ex[]P(x)
[]<>ExP(x)
[]<>Ex[]<>P(x)
With either [] (<>) being the box (diamond) of the modal logics G,
G*, S4Grz, , Z, Z*, X, X*, G1, G1*, S4Grz1, Z1, Z1*, X1, X1*.
Notions of physical existences are given by []<>Ex[]<>P(x) in the
S4Grz1, Z1*, and X1* logics. Those logics are quantum logics. They
are graded, as the logic of []p & <><>p, or [][]p & <><><>p, and
any []^n p & <>^m p gives a quantum logic when n < m.
Hmmm. I think I will have to take your course in modal logic before
those become clear to me.
I think I could explain without using the modal logic. At step seven,
it seems that you can intuitively understand that physics is somehow
already reduced to a statistics on all computations, relative to your
state, and the shape of that mathematics gives the core of the
physical laws (for all universal machine).
The modal logic sum up in fact long series of theorems translating
that measure question in arithmetical relations.
I have to go, and tomorrow is still busy, but I will try to say more
later.
Bruno
Brent
In french, the basic ontology is given by the arithmetical
existence of numbers, and the physical existence is given by the
quantization provided by incompleteness on the consistent RE or
sigma_1 extensions, as viewed from some machine points of view.
Physics is the science of measurement of possibly alternated
results (like W and M, in step 3 and 4, and like other
computational states in the step seven generalization where the FPI
is on UD*, or any sigma_1 complete reality).
All the boxes of G, G*, ... X1*, can be defined either in
arithmetic, or in higher level arithmetical term, like the []p & p.
Bruno
Brent
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