XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 11/29/2025 4:20 AM, Mikko wrote:   
   > 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.   
   >   
      
   % This sentence cannot be proven in F   
   ?- G = not(provable(F, G)).   
   G = not(provable(F, G)).   
   ?- unify_with_occurs_check(G, not(provable(F, G))).   
   false.   
      
   ...We are therefore confronted with a proposition which asserts its own   
   unprovability. 15 … (Gödel 1931:40-41)   
      
   That thereby makes itself semantically unsound.   
      
   --   
   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)