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