XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 1/3/2026 10:58 AM, Tristan Wibberley wrote:   
      
   We begin by postulating a certain non void, definite   
   class {E} of statements, which we call elementary   
   statements...   
      
   The statements of {E} are called elementary statements   
   to distinguish them from other statements which we may   
   form from them or about them in the U language...   
      
   A theory (over {E}) is defined as a conceptual class   
   of these elementary statements. Let {T} be such a theory.   
   Then the elementary statements which belong to {T}   
   we shall call the elementary theorems of {T}; we also   
   say that these elementary statements are true for {T}.   
   Thus, given {T}, an elementary theorem is an elementary   
   statement which is true. A theory is thus a way of   
   picking out from the statements of {E} a certain   
   subclass of true statements…   
      
   The terminology which has just been used implies that   
   the elementary statements are not such that their truth   
   and falsity are known to us without reference to {T}.   
      
   Curry, Haskell 1977. Foundations of Mathematical   
   Logic. New York: Dover Publications, 45   
   https://www.liarparadox.org/Haskell_Curry_45.pdf   
      
   In other words: ∀x ∈ T ((True(T, x) ≡ (E ⊢ x))   
      
   >   
   > Then I should have used examples such as "Theorem of the theory proper   
   > of a system".   
   >   
      
      
   --   
   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-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)