XPost: comp.theory, sci.logic, sci.math   
   From: chris.m.thomasson.1@gmail.com   
      
   On 11/29/2025 5:10 PM, Richard Damon wrote:   
   > On 11/29/25 7:35 PM, Chris M. Thomasson wrote:   
   >> On 11/29/2025 4:17 PM, Richard Damon wrote:   
   >>> On 11/29/25 6:53 PM, Chris M. Thomasson wrote:   
   >>>> On 11/29/2025 1:27 PM, Richard Damon wrote:   
   >>>> [...]   
   >>>>> Godel proved that such a system can't exist if it can represent the   
   >>>>> properties of the Natural Number.   
   >>>   
   >>> So, where do you have a "provability operator" that will tell you if   
   >>> a given theory is in fact provable.   
   >>   
   >> Nope. That is not possible. Think of the integer 0. I can prove that   
   >> it has, wrt n-ary, n positive children, and n negative children. For   
   >> example, 2-ary, two (+) and two (-). Say n is a natural number:   
   >   
   > And that was the pre-condition Olcott made of his logic system, that it   
   > have a provability operator.   
   [...]   
      
   PO is a nut bar with extra nuts?   
      
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