From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 26.11.2025 klo 5.45:   
   > 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.   
      
   Is the knowledge that G is not provable in PA a member   
   of General_Knowledge?   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)