XPost: sci.logic, comp.theory, sci.math   
   From: mikko.levanto@iki.fi   
      
   On 15/12/2025 17:49, olcott wrote:   
   > On 12/15/2025 3:52 AM, Mikko wrote:   
   >> On 13/12/2025 17:55, olcott wrote:   
   >>> 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   
      
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