XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 1/2/2026 12:20 AM, Tristan Wibberley wrote:   
   > On 02/01/2026 00:23, Richard Damon wrote:   
   >> On 1/1/26 7:12 PM, Tristan Wibberley wrote:   
   >>> On 01/01/2026 23:50, Richard Damon wrote:   
   >>>> On 1/1/26 6:17 PM, Tristan Wibberley wrote:   
   >>>>> On 01/01/2026 22:42, Richard Damon wrote:   
   >>>>>> On 1/1/26 5:13 PM, Tristan Wibberley wrote:   
   >>>>>>> On 01/01/2026 00:35, Richard Damon wrote:   
   >>>>>>>   
   >>>>>>>> THe statement G exist   
   >>>>>>>   
   >>>>>>>   
   >>>>>>> Ah, I'm not so easily convinced   
   >>>>>>>   
   >>>>>>>   
   >>>>>>   
   >>>>>> What did he do that might allow it not to exist?   
   >>>>>>   
   >>>>>> He constructs it by the rules of F, and shows that for it to not be   
   >>>>>> true, F must be inconsistant.   
   >>>>>>   
   >>>>>> You can't just complain that you don't think something exists, when it   
   >>>>>> was constructed by the system.   
   >>>>>   
   >>>>>   
   >>>>> There's no symbol "G" in the system.   
   >>>>>   
   >>>>>   
   >>>>   
   >>>> Sure there is, as system allow the creation of names for objects in   
   >>>> them.   
   >>>>   
   >>>> Name a system that meets the basic requirements that doesn't allow the   
   >>>> creation of a "name" for a statement in the system.   
   >>>   
   >>> Nope. The name is not a statement of the system, it's a statement of a   
   >>> related system such as a meta-system or extension.   
   >>>   
   >>>   
   >>   
   >> No, G is the statement created in the system, using the mathematical   
   >> relationship defined in terms of operations in the system build in the   
   >> meta system.   
   >>   
   >> G HAS to be in the system, so the PRR can refer to it.   
   >>   
   >> OR, are you saying that in the system of arithmetic, we can't talk about   
   >> a variable "x" as it isn't defined in the system?   
   >   
   >   
   > Godel's system P has variable objects, but no indeterminates. And it's   
   > namespace of Godel numbers is full up. You can do /some/ things like   
   > definitions using existential and universal quantification but the   
   > character of the propositions is different than a definition of a new   
   > symbol due to the Godel numbering; you have to be careful and not throw   
   > statements around like Goedel's introductory simile based on PM.   
   >   
      
   His paper is a convoluted mess hiding this simple fact   
   ...We are therefore confronted with a proposition which   
   asserts its own unprovability. 15 … (Gödel 1931:40-41)   
      
   Gödel, Kurt 1931.   
   On Formally Undecidable Propositions of   
   Principia Mathematica And Related Systems   
      
      
   --   
   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   
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