XPost: comp.theory   
   From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 14.11.2025 klo 16.49:   
   > On 11/14/2025 3:09 AM, Mikko wrote:   
   >> On 2025-11-14 00:56:17 +0000, Tristan Wibberley said:   
   >>   
   >>> On 13/11/2025 09:05, Mikko wrote:   
   >>>> On 2025-11-12 14:45:34 +0000, olcott said:   
   >>>>   
   >>>>> ... formalized in Minimal   
   >>>>> Type Theory as LP := ~True(LP).   
   >>>>> (where A := B means A is defined as B).   
   >>>>>   
   >>>>> https://philpapers.org/rec/OLCREO   
   >>>>>   
   >>>>> Can someone review my actual reasoning   
   >>>>> elaborated in the paper?   
   >>>>   
   >>>> If you want to use the term "formal language" you must prove that   
   >>>> there is a Turing machine that can determine whether a string is a   
   >>>> valid sentence of your language. If no such Turing machine exists   
   >>>> you have no justifiction for the use of the word "formal".   
   >>>   
   >>> It looks, at a glance, like his system has no theorems with loops in   
   >>> them. The system is "safe" and very small.   
   >>   
   >> It does not look small. It seems to have very many postulates, perhaps   
   >> infinitely many. The intent is that it be complete so it probably is   
   >> only paraconsistent or perhaps even inconsistent.   
   >>   
   >   
   > My system rejects expressions of language that cannot   
   > possibly be resolved to a truth value because they have   
   > pathological self-reference(Olcott 2004)   
   >   
   > G ↔ ¬Prov(⌜G⌝)   
      
   That can be evaluated ir sufficient defitions are given. In particular,   
   the value of Prov('G') must be determinable. The value of G must be   
   either true or false, so even if it is not given or determinable it is   
   possible to evaluate the expression for both values. If the result is   
   the same then that is the value of the expression, otherwise the given   
   information is insufficient.   
      
   > LP := ~True(LP)   
      
   That is a definition. THe purpose of a definition is not to specify a   
   truth value. Languages that permit definitions the use of the same LP   
   on both sides of := is usually a syntax error.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)