XPost: sci.logic, sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 1/19/2026 7:58 AM, Tristan Wibberley wrote:   
   > On 19/01/2026 11:49, Richard Damon wrote:   
   >   
   > ...   
   >   
   >> the concept of Truth being based on Provability just breaks as it   
   >> means some things have undefinable (not just unknowable) truth values,   
   >> they can't even be defined as not-having a truth value, as you can't   
   >                       ^^^^^^^   
   > I'm pretty sure that's not the right word.   
   >   
   >> prove that, but you insist that truth must be provable.   
   >   
   > Unless you're lucky enough to make a statement about them be an axiom of   
   > the system. Then you are hoping you've defined a consistent system but   
   > perhaps you got lucky.   
   >   
   > Is it really true, though, that truth based on provability always breaks   
   > so? It looks like falsity based on non-provability is the problem and   
   > then only in conjunction with some notions of negation and maybe some   
   > notions of conjunction too (obviously the Quine might be the problem but   
   > we know fixed points give us Quines and vice-versa and they're so   
   > important we don't want to lose them).   
   >   
   > What is the negation of "go to the shop" ?   
   > What is the negation of "is so! is not! is so! is not! ..." but "is not!   
   > is so! is not! is so! ..."   
   >   
   > Given positive intuitionist systems (where a system has unprovable   
   > things that are provable in extensions) our truth predicate must leave   
   > anything unprovable that could be an axiom of an extension as neither   
   > true nor false but rather be inapplicable.   
      
   Yes that is the exact idea that I have been presenting   
   since 2020 and possibly earlier.   
      
   Simply defining Gödel Incompleteness and Tarski Undefinability away V12   
   https://groups.google.com/g/comp.ai.nat-lang/c/p_evEnqowPQ/m/0RHg0UjWAAAJ   
      
   Please leave the comp.theory link in because   
   my system applies to sci.math, sci.logic and   
   comp.theory by making:   
      
   "true on the basis of meaning expressed in language"   
   computable from finite strings.   
      
   > A binary Truth predicate (at   
   > minimum) is required to even make sense and maybe it requires a further   
   > restriction argument (a 2nd order logic, then), which Tarski's   
   > indefinability theorem doesn't cover, not by a long way.   
   >   
      
      
      
   --   
   Copyright 2026 Olcott

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

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)