From Newsgroup: comp.theory
On 1/5/26 7:06 PM, olcott wrote:
...there is also a close relationship with the rCLliarrCY antinomy,14 ... ...14 Every epistemological antinomy can likewise be
used for a similar undecidability proof...(G||del 1931:40)
This last sentence does mean that the liar antinomy
can be used for for a similar undecidability proof.
This does mean that the essence of all of his complex
machinery can be boiled down to the Liar Paradox.
Why is it that no one has understood this simple
truth in more than 90 years.
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
https://jamesrmeyer.com/ffgit/godel-original-english
Your problem is that you just don't understand what he means by this.
He did NOT just use the Liar Paradox as a premise for his proof, as you
want to try to assert, but the FORM of the statement, with a syntactic
change, changing assertion of truth, to assertion of provability, a
lessor condition that breaks the contradiction but leads to only one
logically valid conclusion.
This comes out of your broken application of "Semantics" in that you
ignore how context affects the meaning of words, particularly in Natural Language statements, which that piece you are quoting was.
And YES, while "the LIAR" is the simplest form of the antinomy that he
uses, more complicated version could also have been used.
The liar states: This sentence is true if and only if it is not true.
This statement is a contradiction, and its only resolution is that it is
not a truth-bearer.
The transformed statement is: This sentence is true if and only if it is
not provable.
That transformed statement is NOT a contradiction, and in addition to
possibly not being a truth-bearer, could also be a True statement, that
just was not provable.
The case of not being a truth-bearer is removed, because the plain
meaning of the statement, that there does not exist a number g that
satisfies a particular defined relationship is a truth-bearer which
obeys the law of the excluded-middle, as a finite number with that
property either exists or it doesn't.
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