Preliminaries — definitions of concepts of logical truth and necessity:

Preliminaries — definitions of concepts of logical truth and necessity:

The hierarchy of stable sets, then, consists at least of the empty  set, the set of logical necessities, the set of physical necessities, and the set of all truths. Since any proper subset of the set of logical truths fails to be logically closed, the set of logical truths is the smallest nonempty stable set. Marc Lange

1. Boltzmann’s continuum hypothesis (necessarily incomplete)(admitted by Boltzmann)

2. Boltzmann’s ergodicity (necessarily incomplete as to exact equilibrium)

3. Ramsey’s ergodicity (tends toward equilibrium)

4. Wittgenstein’s foundational logic for mathematics (as interpreted by Ramsey)(sum of all propositions possible represents logical infinity as a fundamental ground of math)(symbolically useful/used as to computer math software)

5. Cantor’s w incompleteness (as per Brower’s intuitionistic logic)(para-consistent logic)(logic is deeper still)

6. Are set-theoretical truths mathematical or logical (why the most basic set is logical)(the non-empty stable set)(logical truths form a stable set under CH and ØCH counterfactual necessity)(stable sets form a heiarchy)

7. Physical necessity and/vs. logical necessity (two definitions of logical necessity —classical and ergodic)(where ergodic applies to non-fixed/non-linear universal logic, i.e., logic of the universal mechanics, not exact universal logic, i.e., what exists in macro structures vs. what exists in micro structures of black holes — as per theory, also QM at super-positioning limit)

8. Godel’s incompleteness of his incompleteness theorem = hypothesis (new discovery sheds new light on Godel’s math being short of its full logic knowledge)

9. Necessary counterfactuals (i.e., by the necessity of a space-time continuum being mathematically un-closable, counterfactuals function as physical necessities for logical necessity, i.e., positive and negative charges of qm fundamental substance matter, except in the possibilities of theoretical black-hole super-positioning mechanics, thus allowing the two positions of logic over math impossibilities)(such a relational logic can’t be written into numbers, at this level of super-positioning)(maybe in the future, it can be mathematized; but, this is un-necessary to absolute foundations of logic, where such logic dictates its own closure by necessity of charge counterfactuals and the c-laws of physics — light, or charge as light velocity-spin collisions, is its own absolute governor on logic’s possibilities and necessities)

Summary of the concept of logical truth and necessity:

Since the time of Thales, Anaximander and Heraclitus we’ve been confronted with the fact of how the mind logically necessarily mechanically functions as to “argument to exhaustion”, or in modern terminology, “counterfactuals”. What is it about us bio-beings that allows us such high level of both logical and mathematical interpretation? I mean; Is it the mind’s eye’s geometric necessary mechanics of scalable intelligence only, or is there a deeper fundamental mechanical necessity in operation? For the last 4 or 5 years, I’ve thought it mainly the bio-organic mechanics of the mind’s eye’s geometric functioning, but I was having trouble grounding such mechanics, other than highly complex compounding of the many truth and proof systems available, but I now see another path — that of a more fundamental counterfactually necessary CH and ØCH logic.

We know the trouble really reared its ugly head with the logic and mathematical crises of the latter part of the 19^th century, when non-linear logic and maths were discovered, placing all fundamental classical logic and math in jeopardy. And, even with all the work done in math and logic since, from Piano axioms, Cantor and ZF set theory and its variants up through Von Neumann, Church-Turing, Godel, Tarski, Cohen, etc., and many other non-standard analyses since, there’s still been the nagging question of incompletenesses, in many areas, especially as to absolute foundations; foundations which could not be fully derived, either from the universal laws, maths or logics, without using the often fudged axioms. What would or could replace the questionable axioms? Many of us have surmised it to be some more basic system of math or logic, not yet discovered, and that is what I’ve discovered — At least, as far as I can see.

I just happened to wake up yesterday morning thinking about “The tensor scalability of imagination”, i.e., “Empires scale up and down over time, mainly by law, money and intelligence; and/or, the lack of intelligence, money and by symmetric and asymmetric law confusions, conflations and changes”; “Quantifiable truth requires a physical ground, even if only qm space”; “Linguistics’ over-formalization of non-fundamental formalization, i.e., Chomsky — Psychology can-not be formalized”; “So far, the only successful “Universal Languages” that’s ever been developed are logic and math; and then, there’s 137+ different formal logics and many more maths”; “Philosophy is a formal methodology of thinking about thinking, as abstraction, conceptualism, logic, etc., and being formal is thus an objective science” — When it dawned on me that what I was looking at was a fundamentally new way of looking at formalizable foundations in logic and math, from a perspective I’d never considered — That of; “The foundation of all quantifiable logic, math and truth systems is the fact that a completed continuum hypothesis is “Impossible of Proof” in any of these systems, thus acts as the counter-factual fact to found such physical realities upon — The Ø symbol is the foundation symbol of all truth proof systems, i.e., “Factual Incompleteness” is the foundation of all truth systems’ proofs.” ØCH extends all the way back to Thales’ counter-factuals, or arguments to exhaustion. Exhaustion only exists due to the incompleteness of ØCH possible. Logic, math and truth systems would not function without ØCH incompleteness, as there’d be no logical or physical counterfactuals to base such systems and thinking upon. CH Completeness must remain incomplete for our knowledge systems to function. The CH is only “Ergodic” — “Tends Toward Equilibrium” — But, ØCH complete — by necessity of logic, math and truth functionality — Otherwise; Counterfactuals could not exist to base any knowledge system upon. All logic, math and truth systems are true up to “Ergodicity”; But, ØCH complete… (Ø meaning “never” here)(CH complete would destroy all possibility of logic, math and truth functionality)(Realize this is just an early summary of my yet pregnant ideas, while the concept is complete in my mind — It’ll take me a while yet to polish and complete it)

ØCH and ØØCH can both be true, as in unified black-holes’ neutron charge non-existence, and all other natural phenomena of universal charges +’s and –’s counterfactual necessities outside black-holes and neutron stars — Thus; Physical necessity is not always logical necessity, allowing for absolute counterfactual facts and truths. The smallest non-empty stable set of pure logic is the ergodic ØCH. E = MC² except at limit — Limit = “Absolute Hydrodynamic Spin-Time Compression” in black-holes, where opposing charges neutralize — When all electrons and atomic structure merge into “Super-Super-Positioning”. No math exists for the above conditions — Only ØCH Logic — The sums and products of truths and counterfactual truths of the propositions involved. These facts alone are the reason logic is the more stable set, over and above set math.

If you follow this at all, give me some honest criticism, as imo, I’m looking at; The #1 Universal Law of ØCH Modal Necessity — CH Counterfactuals Absolutely Must Exist — Which actually changes and enhances the entire foundations of logic, and the logical foundations of math.

P.s.

Sorry for the mostly note infused prelim and summary. I’ll work it into a more condensed and presentable paper later. Just wanted to give you some idea what I’m working on.