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 19th
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.
