Re: Undecidability based on epistemological antinomies

On 04/17/2024 12:27 PM, olcott wrote:

...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...(Gödel 1931:43-44)
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*I will paraphrase his quote using the simplest terms*
>
Every expression X that cannot possibly be true or false proves that
there is something wrong with a formal system that cannot correctly
determine whether X is true or false.
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>

I like to read it more as Mirimanoff and the extra-ordinary.
In the early 20'th century, Mirimanoff was very influential in
what became set theory.  He was very well-known in the small circle
that is the usual introduction, and should be more, today.
Regularity, a usual ruliality, as Well-Foundedness, has a
delicate interplay and contraposition with Well-Orderedness,
both regular and rulial, yet in the infinite, that the
antinomies sort of make for that for arithmetic, that
both increment is an operator, and division is an operator,
and while they join as they come together in the field,
in the modular, they represent yet opposite concerns.
So, Mirimanoff's extra-ordinary, is another way to look
at Goedel's incompleteness, that the truths about the
objects, i.e. their proofs or models, do have an
extra-ordinary existence, arising from the resolution
of what would otherwise be the contradiction, the paradox,
making for why Goedel's result is as well that there
_is_ an extra-ordinary infinity, plainly courtesy the mind,
and simple ponderance of alternatives in quantifiers
and the basis of fundamental logic.
So, it's not "wrong", instead, it's "better".
I like to think of it this way as I am entirely pleased
about it and it very well follows from what I've studied
of the development of the canon of logic as it was and is,
and, will be.
Warm regards, E.S., bonjour,
--
https://www.youtube.com/@rossfinlayson