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   comp.ai.philosophy      Perhaps we should ask SkyNet about this      59,235 messages   

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   Message 58,877 of 59,235   
   olcott to Pierre Asselin   
   Re: have we been misusing incompleteness   
   29 Dec 25 13:32:01   
   
   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)   

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