XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/30/2025 3:34 PM, Tristan Wibberley wrote:   
   > On 30/12/2025 20:59, Richard Damon wrote:   
   >> On 12/30/25 3:35 PM, olcott wrote:   
   >>> On 12/30/2025 2:22 PM, Tristan Wibberley wrote:   
   >>>> On 30/12/2025 14:32, olcott wrote:   
   >>>>   
   >>>>> G := (F ⊬ G)   
   >>>>> a sequence of inference steps in F from the axioms   
   >>>>> of F that assert that they themselves do not exist in F.   
   >>>>   
   >>>> You suppose that's what the symbols mean. Yet you know that supposition   
   >>>> is inadmissible per-Se. Cognitive dissonance in action.   
   >>>>   
   >>>   
   >>> The symbols *mean* a self-contradictory expression of language   
   >>> the same sort of thing as: "this sentence is not true".   
   >>   
   >> But it doesn't, as it is satisfiable by a statement that is true but   
   >> unprovable, which just mean the statement is established true by an   
   >> infinite chain of infernce   
   >   
   > Are you using a finite derivation in the meta-system of the limit of a   
   > converging sequence of finite derivations of increasing length (whose   
   > terminals may or may not be the statement being proved but the limit of   
   > whose terminals /is/)?   
   >   
   > And thus you say the statement is true thereby exemplifying a point from   
   > which we may inductively infer a meaning for "true"? Is that "true of   
   > the system in the meta-system" ?   
   >   
      
   True in the system can only really mean provable   
   from the axioms of this same system any other   
   meaning is nonsense.   
      
   --   
   Copyright 2025 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)