XPost: comp.theory, sci.math   
   From: mikko.levanto@iki.fi   
      
   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   
   > and are rejected as semantically unsound.   
      
   The usual way is to rehject them as syntactically invalid.   
      
   If you accept circular definitions as syntactically correct even if   
   semantically unsound the you can have a nonempty collection of unsound   
   objects of thought so that ALL objects of thought in that collection   
   are defined (circularly) in terms of other objects of thought. But   
   every object of thought defined in terms of an unsound object of   
   thought is also unsound.   
      
   > % This sentence is not true.   
      
   You mean the one on the foloowing line?   
      
   > ?- LP = not(true(LP)).   
   > LP = not(true(LP)).   
      
   The answer by the Prolog system means that it is true according to   
   the Prolog rules.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)