XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 11/29/2025 4:44 PM, Kaz Kylheku wrote:   
   > On 2025-11-29, olcott  wrote:   
   >> On 11/29/2025 3:39 PM, Kaz Kylheku wrote:   
   >>> On 2025-11-29, olcott  wrote:   
   >>>> On 11/29/2025 2:23 PM, Kaz Kylheku wrote:   
   >>>>> On 2025-11-29, olcott  wrote:   
   >>>>>> On 11/29/2025 11:53 AM, Kaz Kylheku wrote:   
   >>>>>>> On 2025-11-29, olcott  wrote:   
   >>>>>>>> Any expression of language that is proven true entirely   
   >>>>>>>> on the basis of its meaning expressed in language is   
   >>>>>>>> a semantic tautology.   
   >>>>>>>   
   >>>>>>> A tautology is an expression of logic which is true for all   
   >>>>>>> combinations of the truth values of its variables and propositions,   
   >>>>>>> which is, of course, regardless of what they mean/represent.   
   >>>>>>   
   >>>>>> I did not say tautology. I said semantic tautology.   
   >>>>>> I am defining a new thing under the Sun.   
   >>>>>   
   >>>>> The existing tautology is already semantic. You have to know the   
   >>>>> semantics (the truth tables of the logical operators used in the   
   >>>>> formula, and the workings of quantifiers and whatnot) to be able to   
   >>>>> conclude whether a formula is a tautology.   
   >>>>>   
   >>>>   
   >>>> Try and show how Gödel incompleteness can be   
   >>>> specified in a language that can directly encode   
   >>>> self-reference and has its own provability operator   
   >>>> without hiding the actual semantics using Gödel numbers.   
   >>>   
   >>> The numbers are essential, because Gödel Incompleteness is   
   >>> about number theory.   
   >>>   
   >>   
   >> The generalization Gödel incompleteness applies to   
   >> every formal system that has arithmetic or better.   
   >   
   > And there you are, trying to take the numbers out of it.   
   >   
   >>> The Gödel Theorem involves a proof in which a certain number,   
   >>> the "Gödel number" that may be called G, is asserted to have   
   >>> a number-theoretical property.   
   >>>   
   >>   
   >> G := (F ⊬ G) // G says of itself that it is unprovable in F   
   >   
   > No, it doesn't; that is an outside interpretation of what it is saying.   
      
   That is EXACTLY what the above expression says.   
      
   > Gödel's sentence says that a certain number isn't a theorem-number.   
   >   
      
   Which he says is merely his enormously convoluted way of saying this   
      
   ...We are therefore confronted with a proposition which asserts its own   
   unprovability. 15 … (Gödel 1931:40-41)   
      
   Gödel, Kurt 1931.   
   On Formally Undecidable Propositions of Principia Mathematica And   
   Related Systems   
      
   If you think that I am wrong then don't fucking guess   
   show exactly what his sentence actually says without   
   the ruse of Gödel numbers in a language has its own   
   self-reference operator and provability operator.   
      
   I say it says this:   
   G := (F ⊬ G) // G says of itself that it is unprovable in F   
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   This required establishing a new foundation   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)