XPost: sci.logic, sci.lang, alt.philosophy   
   XPost: comp.theory   
   From: polcott333@gmail.com   
      
   On 1/3/2026 9:39 PM, Richard Damon wrote:   
   > On 1/3/26 9:53 PM, olcott wrote:   
   >> 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.   
      
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