XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 11/29/2025 4:17 AM, Mikko wrote:   
   > olcott kirjoitti 28.11.2025 klo 17.51:   
   >> 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)))   
   >   
   > That is a different sentence. The syntax rules of   
   >      https://philarchive.org/archive/PETMTT-4v2   
   > are different for := and =.   
   >   
      
   It is equivalent. The term Bachelor(x) is still defined by   
   Male(x) ∧ Adult(x) ∧ ~Married(x) ∧ Human(x) thus never   
   circular at all as Willard Van Orman Quine insisted.   
      
      
   --   
   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)