XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 11/30/2025 8:17 AM, Alan Mackenzie wrote:   
   > [ Newsgroups: trimmed ]   
   >   
   > In comp.theory olcott  wrote:   
   >> On 11/29/2025 3:24 PM, Alan Mackenzie wrote:   
   >>> dart200  wrote:   
   >   
   > [ .... ]   
   >   
   >>>> godel's proof does not prove anything about any other premise than   
   >>>> one particular sentence that is essentially "this truth has no proof"   
   >>>> ...   
   >   
   >>> That's a misunderstanding.  That proof proves that there is such an   
   >>> unprovable sentence in any logical system bar the simplest.  Since   
   >>> neither the sentence nor its negation can be proven, you can extend the   
   >>> system by adopting that sentence or its negation as a new axiom.  The new   
   >>> system you've just created will likewise have an unprovable sentence.   
   >   
   >> If it is a logic sentence and it cannot be proven or refuted   
   >> because its proof or refutation requires an infinite number   
   >> of steps then it is not an element of the body of knowledge.   
   >> https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)   
   >   
   > Possibly.  In which case, the "body of knowledge" is a somewhat   
   > restricted, partial collection of our knowledge.  One of the things you   
   > cannot do with it is arithmetic.  Hence it doesn't stand as a basis for   
   > doing mathematics, science, or philosophy.   
   >   
      
   No one can show how Gödel's incompleteness applies to the   
   formal system of The entire body of general knowledge that   
   can be expressed in language semantically. In other   
      
   YOU MUST MAKE SURE TO PAY COMPLETE ATTENTION TO EACH PF THESE WORDS   
   The entire body of general knowledge that can be expressed in language   
   The entire body of general knowledge that can be expressed in language   
   The entire body of general knowledge that can be expressed in language   
      
   The entire body of general knowledge that can be expressed in language   
   can perform any mathematical operation that can be performed.   
      
   THESE WORDS PROVE THAT THEY ARE COMPLETELY TRUE ENTIRELY   
   ON THE BASIS OF THEIR MEANING   
      
   Within the body of knowledge expressed in language   
   that is encoded in Rudolf Carnap Meaning Postulates   
   and arranged in a type hierarchy such that every   
   possible semantics is directly expressed in the syntax   
   of the formal language anything that cannot be proven   
   is not a member of this body.   
      
   There is nothing left out of the body of general   
   knowledge knowledge that can be expressed as language.   
   Its formal language is powerful enough that anything   
   that anyone can ever say can be formalized in this   
   language.   
      
   > [ .... ]   
   >   
   >>>> --   
   >>>> a burnt out swe investigating into why our tooling doesn't involve   
   >>>> basic semantic proofs like halting analysis   
   >   
   >>>> please excuse my pseudo-pyscript,   
   >   
   >>>> ~ nick   
   >   
   >> --   
   >> 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.   
   >   
      
      
   --   
   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)