XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 12/13/2025 5:05 AM, Mikko wrote:   
   > olcott kirjoitti 8.12.2025 klo 21.05:   
   >> On 12/8/2025 3:08 AM, Mikko wrote:   
   >>> olcott kirjoitti 7.12.2025 klo 19.15:   
   >>>> On 12/7/2025 4:50 AM, Mikko wrote:   
   >>>>> olcott kirjoitti 6.12.2025 klo 14.46:   
   >>>>>> On 12/6/2025 3:21 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   
      
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