XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 3/6/2026 9:51 PM, Ross Finlayson wrote:   
   > On 03/06/2026 03:42 PM, Tristan Wibberley wrote:   
   >> On 06/03/2026 20:00, Richard Damon wrote:   
   >>> Yes, systems simple enough to work with JUST proof theoretic semantics   
   >>> don't have deciability.   
   >>>   
   >>> They don't have full arithmetic either.   
   >>   
   >> Can you show that? I feel perhaps I don't correctly understand what   
   >> "proof theoretic semantics" refers to.   
   >>   
   >   
   > Usually enough it might be related to "model theoretic semantics",   
   > as about that proof-theory and model-theory are equi-interpretable.   
   >   
   > Then often that points back to Proclus and "QED" and "QEF",   
   > quod erat demonstrandum and quod erat fasciendam,   
   > about specifics and generalities.   
   >   
      
   It seems that you are saying that an equivalent arithmetic can   
   be constructed in proof theoretic semantics. That would be   
   correct. The only thing that the PTS version lacks is undecidability.   
      
   >   
   > Among strong mathematical platonists it would relate to particular   
   > well-known features of mathematics like geometry and number theory.   
   >   
   > And that's all, ....   
   >   
   >   
      
      
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