XPost: sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 11/25/2025 9:26 PM, Python wrote:   
   > Le 26/11/2025 à 04:24, olcott a écrit :   
   >> When ALL *objects of thought* are defined   
   >> in terms of other *objects of thought* then   
   >> their truth and their proof is simply walking   
   >> the knowledge tree.   
   >   
   > A definition tree is not a proof system, Peter.   
      
   When you have a narrow-minded view maybe not.   
   When a proof is any process applied to any   
   combination of finite strings (such as a tree   
   of knowledge) that makes its conclusion necessarily   
   true then it is a proof in the most generic sense.   
      
   When we stipulate that "cats"  "animals"   
   then the stipulated relation between those two   
   finite string is the proof that it is true.   
      
   A tree of knowledge works this exact same   
   way yet the relationships can also be their   
   position in the inheritance hierarchy of types.   
      
   > Walking a hierarchy does not make undecidable truths disappear — it just   
   > hides them from your model.   
   >   
      
   A tree of knowledge makes undecidability impossible   
   within the entire body of knowledge that can be   
   expressed in language.   
      
   > If “truth” were just “following links in a tree,” then:   
   >   
   > no arithmetic fact would require a proof,   
   >   
      
   We also have semantic logical entailment from   
   a finite set of atomic facts. This set is not   
   finite.   
      
   > no theorem would be non-trivial,   
   >   
   > no undecidable sentence would exist,   
   >   
   > and mathematics would collapse into a directory structure.   
   >   
   > But mathematics is not a filesystem.   
      
   It makes no difference that G is not provable in PA.   
   Any X is provable in General_Knowledge or it is not   
   a member of General_Knowledge.   
      
   --   
   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)