XPost: sci.logic, comp.theory, sci.math   
   From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 27.11.2025 klo 17.43:   
   > On 11/27/2025 2:00 AM, Mikko wrote:   
   >> olcott kirjoitti 26.11.2025 klo 17.54:   
   >>> 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.   
   >>   
   >> In the type system Gödel called minimal all of those would be   
   >> individuals and therefore of the same type.   
      
   > Then Gödel would be wrong.   
      
   No, what he said was perfectly true about what the words meant   
   at the time. Your preferences may differ but there is no right   
   or wrong in matters of taste.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)