XPost: sci.logic, comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 11/29/2025 1:27 PM, Ross Finlayson wrote:   
   > On 11/29/2025 09:57 AM, olcott wrote:   
   >> 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.   
   >>   
   >   
   > OR, it proves there is the extra-ordinary, since it's only a   
   > reading of Goedelian incompleteness.   
   >   
   > Then, since somebody like Skolem makes for model-relativism   
   > with regards to ordinality and cardinality, then there are   
   > matters of book-keeping about that there's an abitrarily larger   
   > bound than any given bound, in the un-bounded, as to why that   
   > of course each finite language on finite inputs is decide-able,   
   > just like any rational approximation is construct-ible (if incomplete).   
   >   
   >   
   > The point about Montague semantics instead of Herbrand semantics   
   > is a bad idea, since it essentially ties itself to a bounded   
   > interpretation of interpretability itself. Similarly the   
   > "monotonicity" and "entailment" are not well-defined in   
   > system of "quasi-modal" logic, instead only "modal, temporal,   
   > relevance" logic, for example about Chrysippus and Ross Anderson.   
   >   
   >   
      
   The simpler easier to understand notion of Montague   
   Semantics is Rudolf Carnap meaning postulates that   
   when anchored in what is essentially a type hierarchy   
   can mathematically formalize any expression of   
   language that can ever be said and can completely   
   eliminate the ambiguity of the meaning of words   
   by using GUIDs for the placeholder of each unique   
   sense meaning. This seems to may "interpretation"   
   no longer needed.   
      
   --   
   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)