XPost: comp.lang.prolog, comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 12/7/2025 4:55 AM, Mikko wrote:   
   > olcott kirjoitti 6.12.2025 klo 14.45:   
   >> On 12/6/2025 3:19 AM, Mikko wrote:   
   >>> olcott kirjoitti 5.12.2025 klo 19.40:   
   >>>> On 12/5/2025 3:13 AM, Mikko wrote:   
   >>>>> olcott kirjoitti 4.12.2025 klo 16.10:   
   >>>>>> On 12/4/2025 3:07 AM, Mikko wrote:   
   >>>>>>> olcott kirjoitti 3.12.2025 klo 18.11:   
   >>>>>>>> On 12/3/2025 4:53 AM, Mikko wrote:   
   >>>>>>>>> olcott kirjoitti 26.11.2025 klo 17.13:   
   >>>>>>>>>> On 11/26/2025 3:05 AM, Mikko wrote:   
   >>>>>>>>>>> olcott kirjoitti 26.11.2025 klo 5.24:   
   >>>>>>>>>>>> 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.   
   >>>>>>>>>>>   
   >>>>>>>>>>> When ALL subjects of thoughts are defined   
   >>>>>>>>>>> in terms of other subjects of thoughts then   
   >>>>>>>>>>> there are no subjects of thoughts.   
   >>>>>>>>>>   
   >>>>>>>>>> I am merely elaborating the structure of the   
   >>>>>>>>>> knowledge ontology inheritance hierarchy   
   >>>>>>>>>> tree of knowledge.   
   >>>>>>>>>   
   >>>>>>>>> When ALL subjects of thoughts are defined in terms of other   
   >>>>>>>>> subjects   
   >>>>>>>>> of thoughts the system of ALL subjects of thoughts is either empty   
   >>>>>>>>> or not a hierarchy. There is no hierarchy where every member is   
   >>>>>>>>> under   
   >>>>>>>>> another member.   
   >>>>>>>>   
   >>>>>>>> *I have always been referring to the entire body of general   
   >>>>>>>> knowledge*   
      
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