Re: Undecidability based on epistemological antinomies V2

On 04/17/2024 10:57 PM, olcott wrote:

On 4/17/2024 9:34 PM, olcott wrote:
"...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof..." (Gödel 1931:43-44)
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is literally true whether or not Gödel meant it literally. Since it <is>
literally true I am sure that he did mean it literally.
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*Parphrased as*
Every expression X that cannot possibly be true or false proves that the
formal system F cannot correctly determine whether X is true or false.
Which shows that X is undecidable in F.
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It is easy to understand that self-contradictory mean unprovable and
irrefutable, thus meeting the definition of Incomplete(F).
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Which shows that F is incomplete, even though X cannot possibly be a
proposition in F because propositions must be true or false.
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A proposition is a central concept in the philosophy of language,
semantics, logic, and related fields, often characterized as the primary
bearer of truth or falsity.
https://en.wikipedia.org/wiki/Proposition
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Most common-sense types have "the truth is the truth is the truth" then
as with regards to logical positivism and a sensitive, thorough, comprehensive, reasoned account of rationality and the fundamental
objects of the logical theory, makes for again a stonger logical positivism, reinvigorated with a minimal "silver thread" to a metaphysics, all quite logicist and all quite positivist, while
again structuralist and formalist, "the truth is the truth is the truth".
Plainly, modeling bodies of knowledge is at least two things,
one is a formal logical model, and another is a scientific model,
as with regards to expectations, a statistical model.
For all the things to be in one modality, is that, as a model of
belief, is that belief is formally unreliable, while at the same
time, reasoned and rational as for its own inner consistency and
inter-consistency, all the other models in the entire modal universe,
temporal.
Axioms are stipulations, they're assumptions, and there are some
very well-reasoned ones, and those what follow the reflections on
relation, in matters of definition of structural relation, and
the first-class typing, of these things.
The axiomless, really does make for a richer accoutrement,
after metaphysics and the canon, why the objects of reason
and rationality, "arise" from axiomless deduction, naturally.
Then, our axiomatics and theory "attain" to this, the truth,
of what is, "A Theory", at all.
One good theory.  (Modeling all individuals and contingencies
and their models of belief as part of the world of theory.)
One good theory, "A Theory: at all", we are in it.
A catalog and schema and dictionary and the finite is only that, though.
"Bigger:  not always worse."