XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 2/9/2026 10:43 AM, Tristan Wibberley wrote:   
   > On 09/02/2026 14:57, Mikko wrote:   
   >> Logic is not paralyzed. Separating semantics from inference rules   
   >> ensures that semantic problems don't affect the study of proofs   
   >> and provability.   
   >   
   > Would you agree that inference rules are a formalisation of some semantics.   
   >   
   > a) in a sense   
   > b) yes, properly   
   >   
   > ?   
   >   
   > And then a syntactical system is one in which there remains no   
   > unformalised semantics (or, indeed, pragmatics), not even identification   
   > of thought objects.   
   >   
      
   By the theory of simple types I mean the doctrine which says that the   
   objects of thought (or, in another interpretation, the symbolic   
   expressions) are divided into types, namely: individuals, properties of   
   individuals, relations between individuals, properties of such   
   relations, etc. (with a similar hierarchy for extensions), and that   
   sentences of the form: " a has the property φ ", " b bears the relation   
   R to c ", etc. are meaningless, if a, b, c, R, φ are not of types   
   fitting together. Mixed types (such as classes containing individuals   
   and classes as elements) and therefore also transfinite types (such as   
   the class of all classes of finite types) are excluded. That the theory   
   of simple types suffices for avoiding also the epistemological paradoxes   
   is shown by a closer analysis of these. (Cf. Ramsey 1926 and Tarski   
   1935, p. 399)."   
      
   Semantics can be expressed entirely syntactically.   
   The most formal way to say this is that when all   
   expressions of language derive all of their semantic   
   meaning from other expressions of language, then all   
   knowledge that can be expressed in language is merely   
   relations between finite strings.   
      
   https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944   
      
      
   --   
   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)