On 22/10/2025 03:51, olcott wrote:The most important aspect of Gödel's 1931 Incompleteness theoremGödel numbers totally hide the underlying semantics.I bet they /do/ !
are these plain English direct quotes of Gödel from his paper:
...there is also a close relationship with the “liar” 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 ...
(Gödel 1931:40-41)
Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF LP := ~True(LP)
00 ~ 01
01 True 00
In both Prolog and Olcott's Minimal Type Theory
a cycle is detected in the evaluation sequence
of the formalized: "This sentence is not true"
Since Gödel said
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
We simply reject G := ¬(F ⊢ G)
before it even gets started.
----
Tristan Wibberley
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| Date | Sujet | # | Auteur | |
| 21 Oct 25 |  UTM Theorem vs the identity function | 12 | Tristan Wibberley | |
| 21 Oct 25 |  Re: UTM Theorem vs the identity function | 8 | Pierre Asselin | |
| 22 Oct 25 |   Re: UTM Theorem vs the identity function | 7 | Tristan Wibberley | |
| 22 Oct 25 |  Re: UTM Theorem vs the identity function | 3 | olcott | |
| 22 Oct 25 | Re: UTM Theorem vs the identity function | 2 | Tristan Wibberley | |
| 22 Oct 25 |  Re: UTM Theorem vs the identity function --- Gödel | 1 | olcott | |
| 22 Oct 25 | Re: UTM Theorem vs the identity function | 3 | Pierre Asselin | |
| 23 Oct 25 | Re: UTM Theorem vs the identity function | 2 | Tristan Wibberley | |
| 23 Oct 25 | Re: UTM Theorem vs the identity function | 1 | Pierre Asselin | |
| 22 Oct 25 | Re: UTM Theorem vs the identity function | 3 | Mikko | |
| 22 Oct 25 | Re: UTM Theorem vs the identity function | 2 | Tristan Wibberley | |
| 23 Oct 25 | Re: UTM Theorem vs the identity function | 1 | Mikko |
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