XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   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.   
      
   --   
   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   
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