XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 11/25/2025 3:40 AM, Mikko wrote:   
   > olcott kirjoitti 25.11.2025 klo 2.53:   
   >> Eliminating undecidability and mathematical incompleteness   
   >> merely requires discarding model theory and fully integrating   
   >> semantics directly into the syntax of the formal language.   
   >>   
   >> The only inference step allowed is semantic logical   
   >> entailment and this is performed syntactically. A formal   
   >> language such as Montague Grammar or CycL of the Cyc   
   >> project can encode the semantics of anything that can   
   >> be expressed in language.   
   >   
   > The resulting theory is not formal unless both the definition of   
   > semantics and the definition of semantic logical entailment are   
   > fully formal.   
   >   
   >   
      
   https://plato.stanford.edu/entries/montague-semantics/   
   https://en.wikipedia.org/wiki/CycL   
   https://en.wikipedia.org/wiki/Ontology_(information_science)   
      
   *This was my original inspiration*   
   Kurt Gödel in his 1944 Russell's mathematical logic gave the following   
   definition of the "theory of simple types" in a footnote:   
      
   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.   
      
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)