XPost: sci.logic, comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 11/26/2025 5:37 AM, Mikko wrote:   
   > olcott kirjoitti 25.11.2025 klo 16.21:   
   >> 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.   
   >   
   > That is a constraint on the language. Note that individuals of all sorts   
   > are considered to be of the same type.   
      
   An individual house, person, orange, piece of pie,   
   is not a group of houses, people, oranges, pieces of pie.   
      
   > For properies and relation the   
   > alternative would be that a predicate is false if any of the arguments   
   > are of wrong type. For functions it is harder to find a reasonable value   
   > if an argument is of wrong type.   
   >   
      
   (General_Knowledge ⊨ x)  means True(x)   
   (General_Knowledge ⊨ ~x) means False(x)   
   ~True(x) & ~False(x) means x is not an element of General_Knowledge   
      
   > This is of course irrelevant to the point that the resulting theory is   
   > not formal unless both the definition of semantics and the definition of   
   > semantic logical entailment are fully formal.   
   >   
      
      
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   This required establishing a new foundation   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)