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.
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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