XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/29/2025 1:53 PM, Richard Damon wrote:   
   > On 12/29/25 2:32 PM, olcott wrote:   
   >> On 12/29/2025 1:21 PM, Pierre Asselin wrote:   
   >>> In sci.logic Tristan Wibberley   
   >>>  wrote:   
   >>>> On 29/12/2025 13:37, Richard Damon wrote:   
   >>>   
   >>>>> Incompleteness is a property of a given Formal System, it says that   
   >>>>> there exist a statement that is true in that system, but can not be   
   >>>>> proven in that system.   
   >>>   
   >>>> What do you mean by "proven" here. Do you mean "derived" ?   
   >>>   
   >>> I think Richard misspoke slightly. The undecidable statement is   
   >>> true *in the intended interpretation* of the formal system   
   >>> (In Goedel's case, the natural numbers with addition and   
   >>> multiplication).   
   >>>   
   >>> Truth "in the formal system" isn't really defined. You need an   
   >>> interpretation.   
   >>>   
   >>   
   >> Unless (as I have been saying for at least a decade)   
   >> the formal language directly encodes all of its   
   >> semantics directly in its syntax. The Montague   
   >> Grammar of natural language semantics is the best   
   >> known example of this.   
   >>   
   >   
   > But it can't, as any system that defines symbols, can have something   
   > outside it assign additional meaning to those symbols.   
   >   
      
   "true on the basis of meaning expressed in language"   
   can be expressed as relations between finite strings.   
      
   > There may be SOME meaning within the system, but, with a sufficiently   
   > expressive system, additional meaning can be imposed.   
   >   
   > An Montague grammer is out of scope here, as we are talking FORMAL   
   > langauges and system, not Natural Language,   
   >   
      
   "We are therefore confronted with a proposition which   
   asserts its own unprovability." (Gödel 1931:39-41)   
      
   By using an enormously convoluted process with   
   Gödel numbers hiding his actual claim:   
      
   There exists a sequence of inference steps from   
   the axioms of a formal system that prove that   
   they themselves do not exist.   
      
   readers are simply conned into believing that   
   Gödel Incompleteness is coherent and true.   
      
   > Something which seems beyound your ability to understand, since you   
   > brainwashed youself to not understand the basics of this.   
      
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)