XPost: sci.logic, comp.theory, sci.math   
   From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 28.11.2025 klo 17.54:   
   > On 11/28/2025 3:01 AM, Mikko wrote:   
   >> 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.   
   >   
   > There is a correct mapping of finite strings   
   > to the semantic meaning that they specify.   
      
   Yes, amd accoprding to that mapping what Gödel said is true.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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