XPost: sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   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   
   that is why he called it Montague Grammar. This is   
   all anchored in Rudolf Carnap meaning postulates   
   that dead obviously encode English semantics   
   directly in the syntax.   
      
   https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf   
   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).   
      
   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, etc. (with a similar hierarchy for extensions), and that   
   sentences of the form: " a has the property φ ", " b bears the relation   
   R to c ", etc. are meaningless, if a, b, c, R, φ are not of types   
   fitting together.   
      
      
   > Somewhere along the line you've come up with this strange notion that   
   > Montague somehow did away with the distinction between syntax and   
   > semantics, but that is simply not true. I recommend you actually read   
   > some Montague rather than simply relying on your own, flawed,   
   > interpretations of wikipedia.   
   >   
   > André   
   >   
      
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   This required establishing a new foundation   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)