XPost: comp.lang.prolog, comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   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*   
   >>>>>   
   >>>>> Your condition that ALL objects of thought can be defined in terms of   
   >>>>> other objects of thought is false about every non-empyt collection of   
   >>>>> objects of thjought, inluding the entire body of general knowledge,   
   >>>>> unless your system allows circular definitions that actually don't   
   >>>>> define.   
   >>>   
   >>>> Yes circular definitions can be defined syntactically   
      
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