XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: mikko.levanto@iki.fi   
      
   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 =.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)