XPost: sci.logic, alt.philosophy, comp.theory   
   XPost: comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 1/3/2026 7:42 PM, Richard Damon wrote:   
   > On 1/3/26 7:09 PM, olcott wrote:   
   >> On 1/3/2026 5:37 PM, Richard Damon wrote:   
   >>> On 1/3/26 5:57 PM, olcott wrote:   
   >>>> On 1/3/2026 4:38 PM, Richard Damon wrote:   
   >>>>> On 1/3/26 3:36 PM, olcott wrote:   
   >>>>>> 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.   
   >>>>>   
   >>>>> WHich just shows that those LLMs are wrong.   
   >>>>>   
   >>>>   
   >>>> All deciders essentially: Transform finite string   
   >>>> inputs by finite string transformation rules into   
   >>>> {Accept, Reject} values.   
   >>>   
      
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