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|    Message 262,325 of 262,912    |
|    olcott to Richard Damon    |
|    Re: The ultimate foundation of [a priori    |
|    02 Jan 26 17:10:20    |
   
   XPost: sci.lang, alt.philosophy, comp.theory   
   XPost: comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   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.   
      
   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.   
      
   Here is the same idea in much greater depth   
   https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics)   
      
   --   
   Copyright 2026 Olcott
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