XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 2/7/2026 2:56 PM, Richard Damon wrote:   
   > On 2/7/26 11:46 AM, olcott wrote:   
   >> 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.   
   >   
   > In other words, NO, you can't explain what you mean and need to keep   
   > changing it because you don't understand what you are talking about.   
   >   
   > A system that is one bing semantic tautology means it is basically   
   > worthless as everything is just redundently true   
   >   
      
   When we understand that every expression that is "true on the basis of   
   meaning expressed in language" derives all of its meaning by its   
   relation to other expressions of language then we can see that the   
   expressions PTS rejects really are semantically meaningless. We can   
   anchor this even more by stipulating that these relations are semantic   
   entailment specified syntactically.   
      
      
   --   
   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)