XPost: comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   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.   
      
   --   
   Tristan Wibberley   
      
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