XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: mikko.levanto@iki.fi   
      
   On 10/02/2026 15:37, olcott wrote:   
   > On 2/10/2026 3:06 AM, Mikko wrote:   
   >> On 09/02/2026 17:36, olcott wrote:   
   >>> On 2/9/2026 8:57 AM, Mikko wrote:   
   >>>> On 07/02/2026 18:43, olcott wrote:   
   >>>>>   
   >>>>> Conventional logic and math have been paralyzed for   
   >>>>> many decades by trying to force-fit semantically   
   >>>>> ill-formed expressions into the box of True or False.   
   >>>>   
   >>>> Logic is not paralyzed. Separating semantics from inference rules   
   >>>> ensures that semantic problems don't affect the study of proofs   
   >>>> and provability.   
   >>>   
   >>> Then you end up with screwy stuff such as the psychotic   
   >>> https://en.wikipedia.org/wiki/Principle_of_explosion   
   >>   
   >> That you call it psychotic does not make it less useful. Often an   
   >> indirect proof is simpler than a direct one, and therefore more   
   >> convincing. But without the principle of explosion it might be   
   >> harder or even impossible to find one, depending on what there is   
   >> instead.   
   >   
   > Completely replacing the foundation of truth conditional   
   > semantics with proof theoretic semantics then an expression   
   > is "true on the basis of meaning expressed in language"   
   > only to the extent that its meaning is entirely comprised   
   > of its inferential relations to other expressions of that   
   > language. AKA linguistic truth determined by semantic   
   > entailment specified syntactically.   
   >   
   > Well-founded proof-theoretic semantics reject expressions   
   > lacking a "well-founded justification tree" as meaningless.   
   > ∀x (~Provable(T, x) ⇔ Meaningless(T, x))   
      
   Usually it is thought that an expression can be determined to be   
   meaningful even when it is not known whether it is provable. For   
   example, the program fragment   
      
      if (x < 5) {   
        show(x);   
      }   
      
   is quite meaningful even when one cannot prove or even know whether   
   x at the time of execution is less than 5.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)