XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 1/1/2026 8:45 PM, André G. Isaak wrote:   
   > On 2026-01-01 16:48, Richard Damon wrote:   
   >> On 1/1/26 6:13 PM, Tristan Wibberley wrote:   
   >>> On 01/01/2026 22:40, Richard Damon wrote:   
   >>>   
   >>>> But it IS a theorem of the base system, as it uses ONLY the   
   >>>> mathematical   
   >>>> operations definable in the base system. What makes you think it   
   >>>> isn't a   
   >>>> Theorem in the base system.   
   >>>   
   >>> It has no derivation in the base system, if it had you wouldn't think   
   >>> the base system were incomplete.   
   >>>   
   >>   
   >> It has no PROOF in the base system.   
   >   
   > Which means it is not a theorem of the base system. A theorem is a   
   > statement which can be proven in a particular system.   
   >   
      
   This is the kind of clarity that we need.   
   True in the base system essentially means   
   a theorem of the base system.   
      
   >> The statement is surely a statement in the base system.   
   >   
   > Sure, but being a statement and being a theorem are two different things.   
   >   
   >> It is shown to be true there, by a proof in the meta-system.   
   >   
   > It is shown to be true in the base system, but only within the   
   > metasystem. Within the base system it cannot be so shown, which   
   > precludes it from being a theorem. That's the entire point of Gödel:   
   > truth and theoremhood cannot be made to coincide except in very trivial   
   > systems.   
   >   
   >> I think you are confused about what you talk about.   
   >   
   > I think you are both somewhat confused here.   
   >   
   > André   
   >   
      
      
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   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
   
      
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