XPost: sci.math, comp.theory   
   From: agisaak@gm.invalid   
      
   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   
      
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