XPost: sci.logic, comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   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. Another way to interpret   
   this would be that house has the "∈" relation to houses.   
   The syntax of Olcott's Minimal Type Theory can express this directly.   
      
   https://philarchive.org/archive/PETMTT-4v2   
      
      
   --   
   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)