XPost: comp.theory, sci.math, sci.lang   
   XPost: comp.ai.philosophy   
   From: mikko.levanto@iki.fi   
      
   On 05/01/2026 16:04, olcott wrote:   
      
   > ...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   
   >   
   > Even when Gödel directly admits that it is   
   > as simple as that and people see that he   
   > admitted it they still deny this.   
   >   
   > G := (F ⊬ 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 Gödel'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   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)