XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   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.   
      
   individual means one.   
   a group of individuals is not one individual   
      
   --   
   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)