XPost: sci.logic, comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 11/28/2025 2:58 AM, Mikko wrote:   
   > olcott kirjoitti 27.11.2025 klo 17.31:   
   >> On 11/27/2025 1:56 AM, Mikko wrote:   
   >>> olcott kirjoitti 26.11.2025 klo 17.39:   
   >>>> 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. 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.   
   >>>>>   
   >>>>> 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.   
   >>>>   
   >>>> The body of knowledge is defined in terms of Rudolf Carnap Meaning   
   >>>> Postulates and stored in a knowledge ontology inheritance hierarchy.   
   >>>>   
   >>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) where   
   >>>> the predicate Married(x) is defined in terms of billions of other   
   >>>> things such as all of the details of Human(x).   
   >>>   
   >>> That, too, is 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.   
   >   
   >> In Olcott's Minimal Type Theory Rudolf Carnap Meaning   
   >> Postulates directly encode semantic meaning in the syntax.   
   >   
   > if the encoding is not fully formally specified the theory is not   
   > formal.   
   >   
   >> The meaningless finite string "Bachelor" is defined as   
   >> a semantic predicate through other already defined terms   
   >> ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x)))   
   >> Adapted by Olcott from Rudolf Carnap Meaning postulates.   
   >>   
   >> And encoded in the syntax of Olcott's Minimal Type Theory   
   >> https://philarchive.org/archive/PETMTT-4v2   
   >   
   > That page only tells how to define a sentence in terms of other   
   > sentences. As it does not permit any arguments on the left side of :=   
   > the expression ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x)))   
   > is syntactically invalid.   
   >   
      
   ∀x ∈ Human (Bachelor(x) ↔ (Male(x) ∧ Adult(x) ∧ ~Married(x)))   
      
      
        
         
         
        
        
         
          
         
         
          
           
            
           
           
            
           
          
          
           
            
           
          
         
        
      
      
      
   --   
   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)