XPost: comp.theory, sci.logic, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   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" ?   
      
   --   
   Tristan Wibberley   
      
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