XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   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.   
      
   --   
   Tristan Wibberley   
      
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    * Origin: you cannot sedate... all the things you hate (1:229/2)