XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 11/28/2025 3:08 PM, Alan Mackenzie wrote:   
   > dart200  wrote:   
   >> On 11/28/25 9:36 AM, Alan Mackenzie wrote:   
   >>> dart200  wrote:   
   >>>> does the logical construction:   
   >   
   >>>> "this sentence is false"   
   >   
   >>>> place a hard limit on our ability to understand truth:   
   >   
   >>>> yes/no???   
   >   
   >>> No, not at all.  Anybody beyond early childhood will recognise it as a   
   >>> mere frivolous distraction from any seeking after the truth.   
   >   
   >> so why does anyone think such a construct places a meaningful limit in a   
   >> formal system then?   
   >   
   > People, in general, don't, apart from one or two exceptions.   
   >   
   >> "this sentence has no proof"   
   >   
   > That is a world apart from "This sentence is false.".  It's the kernel   
   > of Gödel's proof (as you know, of course).  "This sentence has no proof"   
   > turns out to be true and unprovable (for a precisely defined meaning of   
   > "unprovable").   
   >   
      
   *Within A new foundation for correct reasoning*   
      
   (a) Every element of the body of knowledge that can   
        be expressed in language is entirely composed of   
      (1) A finite set of atomic facts   
      (2) Every expression of language that is semantically   
          entailed by (1)   
   (b) a formal language based on Rudolf Carnap Meaning   
        Postulates combined with The Kurt Gödel definition   
        of the "theory of simple types"   
        https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944   
        Where every semantic meaning is fully encoded syntactically   
        as one fully integrated whole not needing model theory   
      
   We have now totally overcome Gödel Incompleteness   
   and Tarski Undefinability for the entire body if   
   knowledge that can be expressed in language. It   
   is now a giant semantic tautology.   
      
   >> "this program loops forever iff it's decided that it halts"   
   >   
   > As you also know, this is the contradiction reached in one of the proofs   
   > of the Halting Theorem.  This is also not the same as "This sentence is   
   > false.", though it is inspired by that nonsense.   
   >   
      
   It is isomorphic.   
      
   > None of these sentences/nonsenses limit our ability to understand truth.   
   > They are part of the truth that we understand.  They delineate   
   > fundamental boundaries of what can be known and proven, in particular   
   > that truth is more subtle than provability.   
   >   
      
   That is bullshit as I have just proven.   
   Within the giant semantic tautology of knowledge that   
   can be expressed in language everything is proven or   
   not an element of this body.   
      
   > This opens the possibility that some mathematical conjectures may be   
   > true but unprovable.  That's just part of existence.   
   >   
   >> --   
   >> a burnt out swe investigating into why our tooling doesn't involve   
   >> basic semantic proofs like halting analysis   
   >   
   >> please excuse my pseudo-pyscript,   
   >   
   >> ~ nick   
   >   
      
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   This required establishing a new foundation   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)