XPost: comp.theory   
   From: polcott333@gmail.com   
      
   On 2/7/2026 10:33 AM, Richard Damon wrote:   
   > On 2/7/26 10:10 AM, olcott wrote:   
   >> On 2/7/2026 8:46 AM, Richard Damon wrote:   
   >>> On 2/7/26 9:22 AM, olcott wrote:   
   >>>> On 2/7/2026 7:50 AM, Richard Damon wrote:   
   >>>>> On 2/7/26 8:10 AM, olcott wrote:   
   >>>>>> On 2/7/2026 4:25 AM, Mikko wrote:   
   >>>>>>> On 06/02/2026 17:30, olcott wrote:   
   >>>>>>>> On 2/6/2026 3:01 AM, Mikko wrote:   
   >>>>>>>>> On 05/02/2026 18:55, olcott wrote:   
   >>>>>>>>>   
   >>>>>>>>>> Changing the foundational basis to Proof Theoretic Semantics   
   >>>>>>>>>> Tarski Undefinability is overcome   
   >>>>>>>>>>   
   >>>>>>>>>> x ∈ Provable ⇔ x ∈ True // proof theoretic semantics   
   >>>>>>>>>   
   >>>>>>>>> A definition in terms of an undefined symbol does not really   
   >>>>>>>>> define.   
   >>>>>>>>   
   >>>>>>>> It is an axiom: ∀x (Provable(x) ⇒ True(x))   
   >>>>>>>   
   >>>>>>> There are theories where every sentence is provable but it is not   
   >>>>>>> possiible to interprete any theory so that every sentence is true.   
   >>>>>>>   
   >>>>>>   
   >>>>>> Proof Theoretic Semantics enables   
   >>>>>> "true on the basis of meaning expressed in language"   
   >>>>>> to be reliably computable for the entire body of knowledge.   
   >>>>>>   
   >>>>>>   
   >>>>>   
   >>>>> No it doesn't, but then you never understood what truth is, or   
   >>>>> really what knowledge is.   
   >>>>>   
   >>>>   
   >>>> "true on the basis of meaning expressed in language"   
   >>>> expressions of language are defined in terms of other   
   >>>> expressions of language thus truth is computed on the   
   >>>> basis of relations between finite strings.   
   >>>   
   >>> In other words, you admit your definition is self-referenetial, and   
   >>> by your own claims, not a basis for logic.   
   >>>   
   >>   
   >> It is an acyclic directed graph.   
   >   
   > So, what part of language has meaning without reference to anything else?   
   >   
   > You just said that your expressions are defined in terms of other   
   > expressions. Which ones are definable without reference to anything else?   
   >   
      
   It is all a huge semantic tautology, even the   
   stipulated "atomic facts" specify relations   
   between finite strings.   
      
   >>   
   >>> But, by the actual meaning of the words, Godel's G is something that   
   >>> can be expressed in the language of PA, and has meaning, but is a   
   >>> statement that must be true in PA, but can not be proven in PA.   
   >>>   
   >>> If your "definition" doesn't do that, you need to show where it makes   
   >>> it not so.   
   >>>   
   >>>>   
   >>>>> You don't understand what Languages is as you think words are   
   >>>>> pliable and can be changed.   
   >>>>>   
   >>>>> You are just showing you are just a natural liar.   
   >>>>   
   >>>>   
   >>>   
   >>   
   >>   
   >   
      
      
   --   
   Copyright 2026 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable for the entire body of knowledge.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)