XPost: sci.logic, comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 11/02/2026 04:30, Richard Damon wrote:   
   > On 2/10/26 8:37 AM, 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))   
   >>   
   >> By combining the ideas from about seven papers together   
   >> we can derive: ∀x (Provable(x) ⇒ True(x))   
   >>   
   >> Makes "true on the basis of meaning expressed in language"   
   >> reliably computable for the entire body of knowledge.   
   >>   
   >>   
   >   
   > The problem is that trying to do that (the way you are trying to define   
   > it) just removes the ability to define mathematics.   
   >   
   > Since Mathematics is part of our current "Knowledge", it means you claim   
   > of result is just a lie.   
      
   Isn't mathematics extensively semantical, though? It could therefore   
   include not only knowledge but also fantasy which we apply to thought   
   objects easily.   
      
   Consider the common teaching that universal-quantification means an   
   expression is true for each sentence when, in fact, it doesn't have to   
   be so. An abstract formal system (whose semantics, AFAICS, are limited   
   to identifiability between systems of otherwise meaningless thought   
   objects and distinction between them within a system) and a syntactical   
   system can exclude the fantasy when its primitive frame is set out just   
   right.   
      
   What I don't know is whether it can include all the knowledge and none   
   of the fantasy.   
      
      
   --   
   Tristan Wibberley   
      
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