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|    sci.logic    |    Logic -- math, philosophy & computationa    |    262,912 messages    |
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|    Message 262,397 of 262,912    |
|    olcott to Tristan Wibberley    |
|    Re: have we been misusing incompleteness    |
|    05 Jan 26 08:22:57    |
   
   XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 1/5/2026 1:46 AM, Tristan Wibberley wrote:   
   > On 03/01/2026 22:27, olcott wrote:   
   >> On 1/3/2026 3:06 PM, Tristan Wibberley wrote:   
   >>> On 03/01/2026 17:30, olcott wrote (quoting Curry):   
   >   
   >>>> In other words: ∀x ∈ T ((True(T, x) ≡ (E ⊢ x))   
   >>>   
   >>> Curry would not approve of you formalising that without defining the   
   >>> system in which you formalise it.   
   >>   
   >> You have to read my quote of Curry to see that he   
   >> already defined {T} and {E}.   
   >   
   > You forget the history of the posts of who you're talking to.   
   >   
      
   No everyone else erases the full quote and   
   then paraphrases it incorrectly.   
      
   >   
   >> {E} is merely my own notion of atomic facts,   
   >> previously called base facts.   
   >   
   > I think not. Elementary statements   
      
   are stipulated to be true that exactly the   
   same thing as my own atomic facts. The only   
   thing that matters is that they are stipulated   
   to be true, thus TRUE IN THE SYSTEM EXISTS   
   WITHOUT NEEDING ANY INTERPRETATION THROUGH A   
   META-SYSTEM.   
      
   Adding extraneous details does not form any   
   rebuttal.   
      
   > are those made from predicates   
   > adjoining terms but not adjoining other statements. Your atomic facts   
   > are nullary predicates, or unary predicates adjoined to primitive terms,   
   > or binary predicates adjoining terms to some world (perhaps if the world   
   > is represented by a term - we reach the limits of my ready   
   > understanding), etc...   
   >   
   >   
   >>> His notions of U-language and   
   >>> A-language and progressive refinement of the U-language were carefully   
   >>> thought through leading to his incredible written lucidity, and the   
   >>> immense benefit of reading his work carefully from the start.   
   > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^   
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   >   
   > TAKE NOTE and also read his Theory of Formal Deducibility   
   >   
   >   
      
      
   --   
   Copyright 2026 Olcott
|
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