XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 12/7/2025 4:39 AM, Mikko wrote:   
   > olcott kirjoitti 6.12.2025 klo 14.24:   
   >> On 12/6/2025 2:37 AM, Mikko wrote:   
   >>> olcott kirjoitti 5.12.2025 klo 18.41:   
   >>>> On 12/5/2025 2:48 AM, Mikko wrote:   
   >>>>> olcott kirjoitti 3.12.2025 klo 17.59:   
   >>>>>> On 12/3/2025 4:41 AM, Mikko wrote:   
   >>>>>>> olcott kirjoitti 2.12.2025 klo 16.00:   
   >>>>>>>> On 12/2/2025 2:53 AM, Mikko wrote:   
   >>>>>>>>> olcott kirjoitti 1.12.2025 klo 19.15:   
   >>>>>>>>>> On 12/1/2025 5:02 AM, Mikko wrote:   
   >>>>>>>>>>> olcott kirjoitti 29.11.2025 klo 23.59:   
   >>>>>>>>>>>   
   >>>>>>>>>>> G := (F ⊬ G) // G says of itself that it is unprovable in F   
   >>>>>>>>>>>   
   >>>>>>>>>>> With a reasonable type system that is a type error:   
   >>>>>>>>>>> - the symbol ⊬ requires a sentence on the right side   
   >>>>>>>>>>> - the value of the ⊬ operation is a truth value   
   >>>>>>>>>>> - the symbol := requires the same type on both sides   
   >>>>>>>>>>> - thus G must be both a sentence and a truth value   
   >>>>>>>>>>>   
   >>>>>>>>>>> But G cannot be both. A sentence has a truth value but it   
   >>>>>>>>>>> isn't one.   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> % This sentence cannot be proven in F   
   >>>>>>>>>> ?- G = not(provable(F, G)).   
   >>>>>>>>>> G = not(provable(F, G)).   
   >>>>>>>>>> ?- unify_with_occurs_check(G, not(provable(F, G))).   
   >>>>>>>>>> false.   
   >>>>>>>>>>   
   >>>>>>>>>> It is an expression of language having no truth value   
   >>>>>>>>>> because it is not a logic sentence.   
   >>>>>>>>>>   
   >>>>>>>>>> https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)   
   >>>>>>>>>   
   >>>>>>>>> Yes, that is the exxential difference between the two G's.   
   >>>>>>>>> The expession F ⊬ G has a truth value because it is either   
   >>>>>>>>> true or false   
   >>>>>>>>   
   >>>>>>>> I propose that is a false assumption.   
   >>>>>>>   
   >>>>>>> If you want to propose anygthng like that you should   
   >>>>>>> (a) specify what is the assumption you want to propose as false   
   >>>>>>> (b) why should that assumption be considered false   
   >>>>>>> (c) what assumption would be true or at least less obviously false   
   >>>>>   
   >>>>>> ?- G = not(provable(F, G)).   
   >>>>>> G = not(provable(F, G)).   
   >>>>>> ?- unify_with_occurs_check(G, not(provable(F, G))).   
   >>>>>> false.   
   >>>>>>   
   >>>>>> G is neither True nor False its resolution remains stuck   
   >>>>>> in an infinite loop.   
   >>>>>>   
   >>>>>> BEGIN:(Clocksin & Mellish 2003:254)   
   >>>>>> Finally, a note about how Prolog matching sometimes differs from the   
   >>>>>> unification used in Resolution. Most Prolog systems will allow you to   
   >>>>>> satisfy goals like:   
   >>>>>>   
   >>>>>> equal(X, X).   
   >>>>>> ?- equal(foo(Y), Y).   
   >>>>>>   
   >>>>>> that is, they will allow you to match a term against an   
   >>>>>> uninstantiated   
   >>>>>> subterm of itself. In this example, foo(Y) is matched against Y,   
   >>>>>> which appears within it. As a result, Y will stand for foo(Y),   
   >>>>>> which is   
   >>>>>> foo(foo(Y)) (because of what Y stands for), which is   
   >>>>>> foo(foo(foo(Y))),   
   >>>>>> and so on. So Y ends up standing for some kind of infinite structure.   
   >>>>>> END:(Clocksin & Mellish 2003:254)   
   >>>>>   
   >>>>> As even (a) is not answered we must interprete the above to mean   
   >>>>> that you retracted your proposal.   
   >>>   
   >>>> If you understood the above you would understand   
   >>>> that I already answered (a) in 100% complete detail.   
   >>>   
   >>> Apparently "that" in your "I propopose that is a false assumption"   
   >>> refers to my "yes" response to your previous posting. But that   
   >>> response does not oresent any assumption.   
   >>>   
   >>> As everyone can see, you did not indentify the assumption.   
   >>>   
   >>>> The assumption that is false is that G is not   
   >>>> semantically incoherent.   
   >>>   
   >>> That assumption is not present in any plase that the word "that"   
   >>> could refer to.   
   >>   
   >> I explained all of the details of how G is   
   >> semantically incoherent and you understood none of it.   
   >   
   >   
   > The question (a) is still unanswered, apparently because the answer   
   > would reveal that your claim the equestion is about is false.   
   >   
      
   (a) specify what is the assumption you want to propose as false   
   That Gödel 1931 Incompleteness exists as anything   
   besides a misconception.   
      
   I thought that when I proved that it is a misconception   
   that you would be able to infer the incorrect assumption   
   on the basis of this proof. Also if you could not infer   
   this then you lack the prerequisites to understand what   
   I am saying.   
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning" computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)