The Tuvian Naval Base: Logic, Measure and Universe (memorandum)

NOTICE

DO NOT TRUST THE FOLLOWING
I do not intend to make any "alternative" or "abuse" of well-established results in related areas

Speculations

Logic and probability was united in Boole's time
Jevons' intertemporal consumption optimization model naturally used probabilistic measure as utility
Semantics of classical logic is measure theory
Models corresponding theories form topological groups
Banach-Tarski theorem on paradoxical decomposition must have metamathematical correspondent in forcing theory. Free group F_2 (i.e. propositions) plays crucial role in both arenas
Measure (or truth value) may vary, difference of measure could be zero or some
Independent statements, like existence of certain kind of real numbers, reside as "edge" of certain ergodic ensemble of orbits. Reflecting its dissipative nature, truth value for it may vary
Central orbits, which should have relations to "center" factors in operator ring theory, is computable, or integrable
Everyone knows (or should know) that anyone who rigorously relies on well-specified model is just searching under the street light
Complete probability measure is such street light
We always are able to build another street light
Why our universe ever grow? (in both QFT and logical sense)

Remarks (added)

Banach-Tarski and slightly similar theorem in 2-dimension was considered by John von Neumann. He also wrote a descriptive set theory paper with Kuratowski, I think that's not unrelated
Topology of operator space, or lattice, reflect its computational hierarchy
There are some studies on descriptive set theory in relation with ergodic theory
A talk by Clive Newstead on a recent result by Andreas Blass: "Models of set theory from topological groups" (pdf) (video)

TODO

The Tuvian Naval Base