XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 1/22/2026 7:15 PM, Tristan Wibberley wrote:   
   > On 23/01/2026 00:29, olcott wrote:   
   >> On 1/22/2026 6:23 PM, Tristan Wibberley wrote:   
   >>> On 20/01/2026 23:08, Tristan Wibberley wrote:   
   >>>> On 18/01/2026 23:41, olcott wrote:   
   >>>>   
   >>>>> I already just said that the proof and refutation of   
   >>>>> Goldbach are outside the scope of PA axioms.   
   >>>>   
   >>>> So Richard is right that you need a truth value for not being covered:   
   >>>>   
   >>>> True(S, Goldbach) = OutOfScope   
   >>>   
   >>>   
   >>> Oh ho! but is Goldbach definable as a shortcode for a statement of the   
   >>> goldbach conjecture in PA? If there's no such statement then it's out of   
   >>> scope without a truth value for that.   
   >>>   
   >>   
   >> Within proof theoretic semantics the lack   
   >> of a finite proof entails ungrounded thus   
   >> non-well-founded. My system works over the   
   >> entire body of knowledge that can be   
   >> expressed in language. Knowledge excludes   
   >> unknowns as outside of its domain.   
   >   
   > Because, even if a statement can be expressed, whether it is true or   
   > false is determinable by an axiom extension (among other kinds of   
   > extension). So it cannot be said that all systems must assign some kind   
   > of truth value /including/ that its truth is unknown.   
   >   
      
   When the axioms of this system are exactly Russell's   
   set of "basic facts" then the system anchored in proof   
   theoretic semantics and a notion of TRUE can always   
   correctly determine   
   "true on the basis of meaning expressed in language"   
      
   --   
   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)