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sci.logic

Logic -- math, philosophy & computationa

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Message 262,634 of 262,912

olcott to Mikko

Re: The Halting Problem asks for too muc

20 Jan 26 12:35:45

   [continued from previous message]   
      
   Truth in PA is proof‑theoretic. These were historically   
   conflated only because proof‑theoretic semantics did not   
   exist. With Curry’s notion of internal truth, PA’s truth   
   predicate is simply:   
      
   ∀x ∈ PA ((True(PA, x)  ≡ (PA ⊢ x))   
   ∀x ∈ PA ((False(PA, x) ≡ (PA ⊢ ~x))   
      
      
   --   
   Copyright 2026 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-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)

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