XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: polcott333@gmail.com   
      
   On 1/8/2026 4:22 AM, Mikko wrote:   
   > On 07/01/2026 13:54, olcott wrote:   
   >> On 1/7/2026 5:49 AM, Mikko wrote:   
   >>> On 07/01/2026 06:44, olcott wrote:   
   >>>> All deciders essentially: Transform finite string   
   >>>> inputs by finite string transformation rules into   
   >>>> {Accept, Reject} values.   
   >>>>   
   >>>> The counter-example input to requires more than   
   >>>> can be derived from finite string transformation   
   >>>> rules applied to this specific input thus the   
   >>>> Halting Problem requires too much.   
   >>   
   >>> In a sense the halting problem asks too much: the problem is proven to   
   >>> be unsolvable. In another sense it asks too little: usually we want to   
   >>> know whether a method halts on every input, not just one.   
   >>>   
   >>> Although the halting problem is unsolvable, there are partial solutions   
   >>> to the halting problem. In particular, every counter-example to the   
   >>> full solution is correctly solved by some partial deciders.   
   >>   
   >> *if undecidability is correct then truth itself is broken*   
   >   
   > Depends on whether the word "truth" is interpeted in the standard   
   > sense or in Olcott's sense.   
   >   
      
   *The Haskell Curry Foundations of Mathematical Logic sense*   
      
   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   
      
   "relative to a set of axioms and semantic commitments"   
      
   All "true on the basis of meaning expressed in language"   
   can be computed from a set of finite string axioms.   
      
   The formal language directly encodes all semantics   
   syntactically. There is no separate model theory or   
   meta-language. ∀x ∈ T ((True(T, x) ≡ (T ⊢ 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)