XPost: comp.theory, sci.math, sci.math.symbolic   
   XPost: comp.lang.prolog   
   From: news.x.richarddamon@xoxy.net   
      
   On 1/22/26 12:40 PM, olcott wrote:   
   > Well-founded proof theoretic semantics where True(L, x)   
   > is anchored in provability from the axioms of formal   
   > system L seems to eliminate the undecidability that   
   > model theoretic semantics encounters when truth is   
   > measured from outside of the formal system in a separate   
   > model.   
      
   But GOdel's proof wasn't based on a truth outside the system.   
      
   The proof was based outside the system, but only about things actually   
   in the system.   
      
   Your problem is you don't seem to understand the rule of context, and   
   ignore what is actually being said.   
      
   There *IS* no number g that satisfies that relationship that he build IN   
   PA. There is also no proof in PA of this fact.   
      
   THere is also no proof in PA that you can't prove the fact.   
      
   THus, your "proof theoretic semanrtics" just don't know what to do about   
   the statement, it is outside their ability to process, and thus make the   
   system just incomplete in its own reasoning. They can't even say it is   
   outside its ability, as it just can't show that either.   
      
   >   
   > This is the *FORMAL* epistemology of:   
   > "true on the basis of meaning expressed in language"   
   >   
      
   Which just can't handle mathematics, as you STILL can't explain how you   
   get from the meaning of the words:   
      
   The sum of the squares of the length of the two sides of a right triange   
   is equal to the square of the length of the hypotenuse.   
      
      
   So, I guess you aren't talking about the problems people actually want   
   to handle.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)