From Newsgroup: sci.math

...there is also a close relationship with the rCLliarrCY antinomy,14 ...
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

Even when G||del directly admits that it is
as simple as that and people see that he
admitted it they still deny this.

G := (F re4 G) // where A := B means A "is defined as" B

LP := ~True(LP) // "This sentence is not true".

The Liar Paradox is an epistemological antinomy

epistemological antinomy
An epistemological antinomy is a fundamental,
unresolvable contradiction within human reason,
where two opposing conclusions, each supported
by seemingly valid arguments, appear equally true.
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>

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From Newsgroup: sci.math

On 05/01/2026 16:04, 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...
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

Even when G||del directly admits that it is
as simple as that and people see that he
admitted it they still deny this.

G := (F re4 G) // where A := B means A "is defined as" B

LP := ~True(LP) // "This sentence is not true".

The Liar Paradox is an epistemological antinomy

epistemological antinomy
An epistemological antinomy is a fundamental,
unresolvable contradiction within human reason,
where two opposing conclusions, each supported
by seemingly valid arguments, appear equally true.

For most peopple who care at all onlh care about the result and only
to the extent that that they don't try the impossible. Some people
want to understand G||del's proof or some other proof but for most of
them understanding one proof is enough. Usual alternative proofs are
fairly similar to the original one and only differ on some details.
A significantly simpler proof would be interesting but only if it is
a complete proof.
--
Mikko
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From Newsgroup: sci.math

On 1/5/2026 8:20 AM, Mikko wrote:

On 05/01/2026 16:04, 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...
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

Even when G||del directly admits that it is
as simple as that and people see that he
admitted it they still deny this.

G := (F re4 G) // where A := B means A "is defined as" B

LP := ~True(LP) // "This sentence is not true".

The Liar Paradox is an epistemological antinomy

epistemological antinomy
An epistemological antinomy is a fundamental,
unresolvable contradiction within human reason,
where two opposing conclusions, each supported
by seemingly valid arguments, appear equally true.

For most peopple who care at all onlh care about the result and only
to the extent that that they don't try the impossible. Some people
want to understand G||del's proof or some other proof but for most of
them understanding one proof is enough. Usual alternative proofs are
fairly similar to the original one and only differ on some details.
A significantly simpler proof would be interesting but only if it is
a complete proof.

G||del admits that these simplifications are equivalent.
The only way to totally understand these things is to
boil them down to their barest possible essence. No one
wants to do that because they prefer bluster over truth.
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2