XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/29/2025 1:21 PM, Pierre Asselin wrote:   
   > In sci.logic Tristan Wibberley  wrote:   
   >> On 29/12/2025 13:37, Richard Damon wrote:   
   >   
   >>> Incompleteness is a property of a given Formal System, it says that   
   >>> there exist a statement that is true in that system, but can not be   
   >>> proven in that system.   
   >   
   >> What do you mean by "proven" here. Do you mean "derived" ?   
   >   
   > I think Richard misspoke slightly. The undecidable statement is   
   > true *in the intended interpretation* of the formal system   
   > (In Goedel's case, the natural numbers with addition and multiplication).   
   >   
   > Truth "in the formal system" isn't really defined. You need an   
   > interpretation.   
   >   
      
   Unless (as I have been saying for at least a decade)   
   the formal language directly encodes all of its   
   semantics directly in its syntax. The Montague   
   Grammar of natural language semantics is the best   
   known example of this.   
      
   --   
   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)