XPost: sci.logic, sci.lang, alt.philosophy   
   XPost: comp.theory   
   From: polcott333@gmail.com   
      
   On 1/3/2026 1:40 PM, Richard Damon wrote:   
   > On 1/3/26 10:32 AM, olcott wrote:   
   >> On 1/3/2026 8:09 AM, Richard Damon wrote:   
   >>> On 1/3/26 12:09 AM, olcott wrote:   
   >>>> On 1/2/2026 9:18 PM, Richard Damon wrote:   
   >>>>> On 1/2/26 8:30 PM, olcott wrote:   
   >>>>>> On 1/2/2026 5:43 PM, Richard Damon wrote:   
   >>>>>>> On 1/2/26 6:10 PM, olcott wrote:   
   >>>>>>>> On 1/2/2026 3:31 PM, Richard Damon wrote:   
   >>>>>>>>> On 1/2/26 4:24 PM, olcott wrote:   
   >>>>>>>>>> On 2/22/2018 11:56 AM, Pete Olcott wrote:   
   >>>>>>>>>>> On 2/17/2018 12:42 AM, Pete Olcott wrote:   
   >>>>>>>>>>>> a Collection is defined one or more things that have one or   
   >>>>>>>>>>>> more properties in common. These operations from set theory   
   >>>>>>>>>>>> are available: {⊆, ∈}   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> An BaseFact is an expression X of (natural or formal)   
   >>>>>>>>>>>> language L that has been assigned the semantic property of   
   >>>>>>>>>>>> True. (Similar to a math Axiom).   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> A Collection T of BaseFacts of language L forms the ultimate   
   >>>>>>>>>>>> foundation of the notion of Truth in language L.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> To verify that an expression X of language L is True or   
   >>>>>>>>>>>> False only requires a syntactic logical consequence   
   >>>>>>>>>>>> inference chain (formal proof) from one or more elements of   
   >>>>>>>>>>>> T to X or ~X.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> True(L, X) ↔ ∃Γ ⊆ BaseFact(L) Provable(Γ, X)   
   >>>>>>>>>>>> False(L, X) ↔ ∃Γ ⊆ BaseFact(L) Provable(Γ, ~X)   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Copyright 2018 (and many other years since 1997) Pete Olcott   
   >>>>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> Truth is the set of interlocking concepts that can be   
   >>>>>>>>>>> formalized symbolically.   
   >>>>>>>>>>>   
   >>>>>>>>>>> All of formalized Truth is only about relations between   
   >>>>>>>>>>> finite strings of characters.   
   >>>>>>>>>>>   
   >>>>>>>>>>> This exact same Truth can be equally expressed (tokenized) as   
   >>>>>>>>>>> relations between integers.   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> 2026 update   
   >>>>>>>>>> "true on the basis of meaning expressed in language"   
   >>>>>>>>>> is entirely expressed as relations between finite strings   
   >>>>>>>>>> of characters.   
   >>>>>>>>>>   
   >>>>>>>>>> This by itself makes   
   >>>>>>>>>> "true on the basis of meaning expressed in language"   
   >>>>>>>>>> reliably computable.   
   >>>>>>>>>>   
   >>>>>>>>>   
   >>>>>>>>> No, not until you can do the first, which you can't unless you   
   >>>>>>>>> make you system "small".   
   >>>>>>>>>   
   >>>>>>>>> All you are doing it proving you don't understand what you are   
   >>>>>>>>> talking about.   
   >>>>>>>>   
   >>>>>>>> That is exactly what someone would say that doesn't   
   >>>>>>>> understand what I am talking about.   
   >>>>>>>   
   >>>>>>> YOU don't know what you are talking about,   
   >>>>>>>   
   >>>>>>>>   
   >>>>>>>> I coined the term ignorance squared back in 1998.   
   >>>>>>>> One cannot discern one's own ignorance because   
   >>>>>>>> this requires the missing knowledge to see the difference.   
   >>>>>>>   
   >>>>>>> And you are just ignorance cubed.   
   >>>>>>>   
   >>>>>>>>   
   >>>>>>>> Here is the same idea in much greater depth   
   >>>>>>>> https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics)   
   >>>>>>>>   
   >>>>>>>   
   >>>>>>> Right, and Hilbert was proven WRONG, and admitted it.   
   >>>>>>>   
   >>>>>>   
   >>>>>> It sure would seem that way to everyone that did   
   >>>>>> not devote half their life to finding complete clarity.   
   >>>>>   
   >>>>> No, he was proven WRONG, and he admitted it.   
   >>>>>   
   >>>>   
   >>>> He may have admitted it but he was not actually   
   >>>> been proven wrong.   
   >>>   
   >>> Sure he was.   
   >>>   
   >>> Can you actually prove he was right?   
   >>>   
   >>   
   >> Yes   
   >   
   > Then why haven't you?   
   >   
   > Your current arguements have all been based on bad definitions.   
   >   
   >>   
   >>> Not just based on an argument that starts by assuming him right.   
   >>>   
   >>>>   
   >>>>>>   
   >>>>>> All of computation can be construed as applying finite   
   >>>>>> string transformation rules to finite string inputs.   
   >>>>>   
   >>>>> Yes, but some results are not computable.   
   >>>>>   
   >>>>>>   
   >>>>>> Anything that cannot be so derived is outside of   
   >>>>>> the scope of computation.   
   >>>>>   
   >>>>> You don't understand what you are talking about.   
   >>>>>   
   >>>>> Yes, if it can't be described as a transformation it is out of scope.   
   >>>>>   
   >>>>   
   >>>> See that you proved that you do understand   
   >>>> what I am talking about.   
   >>>   
   >>> So, you don't know what a transformation is.   
   >>>   
   >>> Halting *IS* a transformation of input to output, just not a   
   >>> computable transformation.   
   >>>   
   >>   
   >> All deciders essentially: Transform finite string   
   >> inputs by finite string transformation rules into   
   >> {Accept, Reject} values.   
   >>   
   >> The ultimate measure the actual sequence of steps that   
   >> the actual finite string input specifies to HHH(DD)   
   >> is DD simulated by HHH according to the semantics of C.   
   >   
   > Nope. The problem is you HHH doesn't simulated its input according to   
   > the semantics of C, in part because the input you try to give doesn't   
   > have meaning by the semantics of C, since it deosn't define HHH.   
   >   
      
   That DD is simulated by HHH according to the semantics   
   of C has been proven to be a sufficient definition of   
   HHH for 100 LLM conversations across four different LLMs.   
      
   >>   
   >> This is the correct finite string transformations for   
   >> HHH to apply to its actual finite string input DD.   
   >   
   > No, it shows that you logic is just unsound, as are you.   
   >   
      
   DD simulated by HHH  the ultimate measure of   
   the actual behavior that the actual input to HHH(DD)   
   actually specifies.   
      
   >>   
   >> There exists no finite string transformation rules   
   >> that HHH(DD) can apply to its input to derive the   
   >> behavior of its caller DD() executed in main.   
   >>   
   >   
   > Because there is only one finite string transformation that HHH can   
   > apply, the ones it was defined to do, and thus that can not be used as   
   > the meaning of the string.   
   >   
   >> Therefore the requirement that HHH do this is a   
   >> requirement that its outside the scope of computation.   
   >   
   > Nope, it shows your reasoning is outside the scope of logic.   
   >   
      
   Four different LLM systems have agreed in fifty brand   
   new different conversations that the halting problem   
   is requiring a result that is outside the scope of   
   finite string transformations applied to finite string   
   inputs.   
      
   Examining these actual dialogues conclusively proves   
   that all assessments are made only by applying correct   
   semantic entailment to standard definitions.   
      
   >>   
   >>>>   
   >>>>> But not all transformations are computable, as some need an   
   >>>>> infinite number o them.   
   >>>>>   
   >>>>   
   >>>> Right like Goldbach conjecture.   
   >>>   
      
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