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.
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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