XPost: sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 11/25/2025 8:43 PM, Python wrote:   
   > Le 26/11/2025 à 03:41, olcott a écrit :   
   >> On 11/25/2025 8:36 PM, André G. Isaak wrote:   
   >>> On 2025-11-25 19:30, olcott wrote:   
   >>>> On 11/25/2025 8:12 PM, André G. Isaak wrote:   
   >>>>> On 2025-11-25 19:08, olcott wrote:   
   >>>>>> On 11/25/2025 8:00 PM, André G. Isaak wrote:   
   >>>>>>> On 2025-11-25 18:43, olcott wrote:   
   >>>>>>>> On 11/25/2025 7:29 PM, André G. Isaak wrote:   
   >>>>>>>>> On 2025-11-25 17:52, olcott wrote:   
   >>>>>>>>>> On 11/25/2025 6:47 PM, Kaz Kylheku wrote:   
   >>>>>>>>>>> On 2025-11-25, olcott  wrote:   
   >>>>>>>>>>>> Gödel incompleteness can only exist in systems that divide   
   >>>>>>>>>>>> their syntax from their semantics ...   
   >>>>>>>>>>>   
   >>>>>>>>>>> And, so, just confuse syntax for semantics, and all is fixed!   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> Things such as Montague Grammar are outside of your   
   >>>>>>>>>> current knowledge. It is called Montague Grammar   
   >>>>>>>>>> because it encodes natural language semantics as pure   
   >>>>>>>>>> syntax.   
   >>>>>>>>>   
   >>>>>>>>> You're terribly confused here. Montague Grammar is called   
   >>>>>>>>> 'Montague Grammar' because it is due to Richard Montague.   
   >>>>>>>>>   
   >>>>>>>>> Montague Grammar presents a theory of natural language   
   >>>>>>>>> (specifically English) semantics expressed in terms of logic.   
   >>>>>>>>> Formulae in his system have a syntax. They also have a   
   >>>>>>>>> semantics. The two are very much distinct.   
   >>>>>>>>>   
   >>>>>>>>   
   >>>>>>>> Montague Grammar is the syntax of English semantics   
   >>>>>>>   
   >>>>>>> I can't even make sense of that. It's a *theory* of English   
   >>>>>>> semantics.   
   >>>>>>>   
   >>>>>>   
   >>>>>> *Here is a concrete example*   
   >>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x)   
   >>>>>> where the predicate Married(x) is defined in terms of billions   
   >>>>>> of other things such as all of the details of Human(x).   
   >>>>>   
   >>>>> A concrete example of what? That's certainly not an example of 'the   
   >>>>> syntax of English semantics'. That's simply a stipulation involving   
   >>>>> two predicates.   
   >>>>>   
   >>>>> André   
   >>>>>   
   >>>>   
   >>>> It is one concrete example of how a knowledge ontology   
   >>>> of trillions of predicates can define the finite set   
   >>>> of atomic facts of the world.   
   >>>   
   >>> But the topic under discussion was the relationship between syntax   
   >>> and semantics in Montague Grammar, not how knowledge ontologies are   
   >>> represented. So this isn't an example in anyway relevant to the   
   >>> discussion.   
   >>>   
   >>>> *Actually read this, this time*   
   >>>> 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   
   >>>>   
   >>>> That is the basic infrastructure for defining all *objects of thought*   
   >>>> can be defined in terms of other *objects of thought*   
   >>>   
   >>>   
   >>> I know full well what a theory of types is. It has nothing to do with   
   >>> the relationship between syntax and semantics.   
   >>>   
   >>> André   
   >>>   
   >>   
   >> That particular theory of types lays out the infrastructure   
   >> of how all *objects of thought* can be defined in terms   
   >> of other *objects of thought* such that the entire body   
   >> of knowledge that can be expressed in language can be encoded   
   >> into a single coherent formal system.   
   >   
   > Typing “objects of thought” doesn’t make all truths provable — it   
   only   
   > prevents ill-formed expressions.   
   > If your system looks complete, it’s because you threw away every   
   > sentence that would have made it incomplete.   
      
   When ALL *objects of thought* are defined   
   in terms of other *objects of thought* then   
   their truth and their proof is simply walking   
   the knowledge tree.   
      
   --   
   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   
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