Re: Undecidability based on epistemological antinomies V2 --correct reasoning--

On 04/25/2024 10:04 AM, olcott wrote:

On 4/25/2024 6:32 AM, Richard Damon wrote:

On 4/25/24 12:33 AM, olcott wrote:

On 4/24/2024 10:59 PM, Ross Finlayson wrote:
The only thing that I have ever been talking about is True(L,x)
specified as relations between finite strings such that a
correct and consistent True(L,x) can be defined for every
element of human knowledge that can be expressed using language.
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As far as Eastern religion goes Zen/Tao & Advaita.
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Then what is the value of True(L,x) where x is defined as to be the
stagtement: "Not True(L,x)"?
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If it is TRUE, the x is the equivalent of NOT TRUE, or FALSE and thus
your True(L,x) has said a false statement was true.
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If it is FALSE, then x is the equivalent of NOT FALSE, or TRUE, and
thus your True(L,x) has said that a TRUE statement was FALSE.
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If it refuses to answer, then you have lied that it can be defined for
ANY finite string.
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That, our your logic system just can't handle the basics of the problem.

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∃L ∈ Formal_Systems, ∃x ∈ L (True(L, x)  ≡ (L ⊢ x))
∃L ∈ Formal_Systems, ∃x ∈ L (False(L, x) ≡ (L ⊢ ~x))
∃L ∈ Formal_Systems, ∃x ∈ L (Truth_Bearer(L, x) ≡ (True(L, x) ∨ False(L,
x)))
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https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
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I created Minimal Type Theory so that I could concisely encode
actual self-reference. In all the literature it is conventional
to encode self-reference incorrectly.
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LP := ~True(LP)
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Prolog rejects expressions having the same structure as LP
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
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Truth_Bearer(L, LP) == FALSE
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I can understand that that may be what you want,
it's a little more involved what it is.
It's like Einstein the other day made a quote,
and it was about making truth-makers, I saw it
on Wikiquote.
"Whoever undertakes to set himself up as a
judge of Truth and Knowledge is shipwrecked
by the laughter of the gods."
- https://en.wikiquote.org/wiki/Albert_Einstein#Essay_to_Leo_Baeck_(1953)
Now, that goes for all of you all, because,
if it's not courtesy axiomless natural deduction,
and a brief metaphysics and teleology and entelechy
for a broad epistemology of a thorough ontology,
it's not.
So, Peter, on the one hand you're grasping for
some of what basically the foundations, the very
foundations must provide, and, that somehow
there is one, some "true" foundation, "sole" foundation,
that it provides "even given free expansion of
comprehension that quantifier impredicativity
is not a thing", you have to confront that all
fully down in an entire foundation altogether,
to arrive at some of these extended goals you
have in mind for yourself.
Then the rest of you are sort of in a Flat-Earther's
opinionated penury of Russell's retro-thesis.
Of course, overgeneralizations are generally unsound,
if even moreso profoundly of the counterintuition
of failure.
No offense, ..., keine Beleidigung beabsichticht.