XPost: comp.theory   
   From: polcott333@gmail.com   
      
   On 12/29/2025 12:42 PM, 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.   
   >>   
   >> Godel's proof build a meta-system that constructs a statement that   
   >> exists in the base system, and which is true in that base system, but   
   >> can not be proven in the base system, only the meta-system.   
   >   
   > What do you mean by "proven" here. Do you mean "derived" ? Normally we   
   > say a proposition is true in a system when we mean the proposition is a   
   > theorem of the system; it has a derivation in the system: a finite   
   > sequence of statements that each is derivable from the axioms and   
   > earlier statements in the sequence by application of a deductive rule of   
   > the system--where the deductive rules are transitive so that's also   
   > application of /some/ deductive rules--and which ends with the   
   > proposition that's being derived.   
   >   
   > If there is a derivation then it is provable in the base system, if   
   > there /isn't/ a derivation then it is /not/ true in that base system   
   > (which is different from saying its contrapositive is true in that base   
   > system).   
   >   
   >   
      
   Yes you are correct here. Even though it is dead-obvious   
   that you are correct everyone indoctrinated with Godel   
   1931 Incompleteness will disagree.   
      
   --   
   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-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)