XPost: sci.math, comp.theory   
   From: mikko.levanto@iki.fi   
      
   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.   
      
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)