XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 2/11/2026 6:17 PM, André G. Isaak wrote:   
   > On 2026-02-11 16:41, olcott wrote:   
   >> On 2/11/2026 5:30 PM, André G. Isaak wrote:   
   >>> On 2026-02-11 14:27, olcott wrote:   
   >>>> On 2/11/2026 2:43 PM, André G. Isaak wrote:   
   >>>>> On 2026-02-10 21:59, olcott wrote:   
   >>>>>> We completely replace the foundation of truth conditional   
   >>>>>> semantics with proof theoretic semantics. Then expressions   
   >>>>>> are "true on the basis of meaning expressed in language"   
   >>>>>> only to the extent that all their meaning comes from   
   >>>>>> inferential relations to other expressions of that language.   
   >>>>>> This is a purely linguistic PTS notion of truth with no   
   >>>>>> connections outside the inferential system.   
   >>>>>>   
   >>>>>> Well-founded proof-theoretic semantics reject expressions   
   >>>>>> lacking a "well-founded justification tree" as meaningless.   
   >>>>>> ∀x (~Provable(T, x) ⇔ Meaningless(T, x))   
   >>>>>   
   >>>>> Proof-theoretic semantics makes no such claim. That's your claim   
   >>>>> and you should stop attributing it to others.   
   >>>>>   
   >>>>> André   
   >>>>>   
   >>>>   
   >>>> That is a correct paraphrase of the claims that it   
   >>>> always does make. Try and show otherwise.   
   >>>   
   >>> Not even remotely.   
   >>>   
   >>> And the burden of proof is on you to justify your claims. Please   
   >>> quote someone working on PTS who claims that ∀x (~Provable(T, x) ⇔   
   >>> Meaningless(T, x))   
   >>>   
   >>> André   
   >>>   
   >>   
   >> That is fair.   
   >>   
   >> 1.2 Inferentialism, intuitionism, anti-realism   
   >> Proof-theoretic semantics is inherently inferential,   
   >> as it is inferential activity which manifests itself   
   >> in proofs. It thus belongs to inferentialism (a term   
   >> coined by Brandom, see his 1994; 2000) according to   
   >> which inferences and the rules of inference establish   
   >> the meaning of expressions   
   >   
   > That doesn't support your position, either the quote above or the entire   
   > section in which it is embedded. You're imagining things which simply   
   > aren't there.   
   >   
   > André   
   >   
      
   When we understand that linguistic truth (just like   
   an ordinary dictionary) expressions of language only   
   get their semantic meaning from other expressions of   
   language then we directly understand entirely based on   
   the meaning of words that when no such connection exists   
   then no semantic meaning is derived.   
      
   Proof Theoretic Semantics is doing this same thing   
   whether you ever understand it or not.   
      
   As I have been saying for many years before I ever   
   heard the term Proof Theoretic Semantics expressions   
   of language derive all of their semantic meaning   
   from semantic connections to other expressions of   
   language. Also as I have been saying for many years   
   these connections can be formalized syntactically   
   in several different ways   
      
      
   --   
   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)