XPost: sci.logic, sci.lang, alt.philosophy   
   XPost: comp.theory   
   From: polcott333@gmail.com   
      
   On 1/3/2026 8:47 PM, Richard Damon wrote:   
   > On 1/3/26 9:42 PM, olcott wrote:   
   >> On 1/3/2026 8:33 PM, Richard Damon wrote:   
   >>> On 1/3/26 8:48 PM, olcott wrote:   
   >>>> 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   
      
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