XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 11/29/2025 2:48 PM, Alan Mackenzie wrote:   
   > [ Followup-To: set ]   
   >   
   > In comp.theory olcott  wrote:   
   >> On 11/29/2025 5:55 AM, Alan Mackenzie wrote:   
   >   
   >>> In comp.theory olcott  wrote:   
   >>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:   
   >   
   >>>>> In comp.theory olcott  wrote:   
   >>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:   
   >   
   >>> [ .... ]   
   >   
   >>>>>> *Within A new foundation for correct reasoning*   
   >   
   >>>>>> (a) Every element of the body of knowledge that can   
   >>>>>>        be expressed in language is entirely composed of   
   >>>>>>      (1) A finite set of atomic facts   
   >>>>>>      (2) Every expression of language that is semantically   
   >>>>>>          entailed by (1)   
   >>>>>> (b) a formal language based on Rudolf Carnap Meaning   
   >>>>>>        Postulates combined with The Kurt Gödel definition   
   >>>>>>        of the "theory of simple types"   
   >>>>>>        https://en.wikipedia.org/wiki/History_of_type_theo   
   y#G%C3%B6del_1944   
   >>>>>>        Where every semantic meaning is fully encoded syntactically   
   >>>>>>        as one fully integrated whole not needing model theory   
   >   
   >>>>>> We have now totally overcome Gödel Incompleteness   
   >>>>>> and Tarski Undefinability for the entire body if   
   >>>>>> knowledge that can be expressed in language. It   
   >>>>>> is now a giant semantic tautology.   
   >   
   >>>>> You can't "overcome" these theorems, since they're not obstacles.   
   >>>>> They're fundamental truths.   
   >   
   >>>> I just showed the detailed steps making both of   
   >>>> them impossible in the system that I just specified.   
   >>>> A counter-example is categorically impossible.   
   >   
   >>> Your construction is impossible, as proven by Gödel's Incompleteness   
   >>> Theorem.   
   >   
   >>> You didn't "show" anything.  You just waved your hands and expect   
   >>> everybody to accept your continually repeated falsehoods.   
   >   
   >   
   >> You can claim that my idea is impossible.   
   >   
   > I no longer remember which idea that is.   
   >   
   >> It is impossible to show that my idea is impossible.   
   >   
   > Given that your ideas strongly tend to violate firmly established   
   > mathematical results, there is no such impossibility as you assert.  Note   
   > that if you hold established results to be false, you have the burden of   
   > proof.  At no time in this newsgroup have you met this obligation.   
   >   
   >> A mere dogmatic assertion provides zero actual evidence   
   >> that I am incorrect.   
   >   
   > I don't need to provide evidence.  As just written, the burden of proof   
   > is on your side.   
   >   
   >> A consistent finite set of basic facts of the world is possible.   
   >   
   > There are many such finite sets, but none of them are complete, and they   
   > cannot be complete.  This was demonstrated by mathematicians in the early   
   > 20th century.   
   >   
      
   The current complete finite set of atomic facts   
   of general knowledge that can be expressed in   
   language exist right now. They just aren't written   
   does all in the same place.   
      
   >> This consistent finite set of basic facts of the world are   
   >> encoded in Rudolf Carnap Meaning Postulates thus fully   
   >> encoding all of these semantic meaning directly in the formal   
   >> language. The Meaning Postulates are arranged in a knowledge   
   >> ontology similar to a type hierarchy. The only inference   
   >> steps are semantic logical entailment performed syntactically.   
   >   
   > This is a will o' the wisp, as much as Frege's or Russell and Whitehead's   
   > much more modest attempts to formalise all of mathematics were.   
   >   
      
   So you can't even begin to imagine the body of general knowledge   
   that can be expressed in language.   
      
   >> You can declare that I must be wrong because it contradicts   
   >> what others have said, yet you cannot point out any actual   
   >> in any of the steps because there are none.   
   >   
   > As I keep saying, the burden of proof is on your side.   
      
   I cannot prove that every element of an infinite set   
   has a certain property exception by proving that it   
   it categorically impossible that these elements do   
   not have that property.   
      
   For example every element of the set of general   
   knowledge that can be expressed in symbolic language   
   can be written down.   
      
   >  The three   
   > mathematicians just mentioned failed because what they were attempting   
   > was fundamentally impossible.  That was not yet understood in the early   
   > years of the twentieth century, but it is firm knowledge now.  What you   
   > are insisting can be done is a superset of these impossibilities.   
   >   
      
   Every element of the set of general knowledge that   
   can be expressed in symbolic language is a semantic   
   tautology thus can be proven true entirely on the   
   basis of relations between finite strings.   
      
   > There is a lot of hubris involved here, and seemingly not a little   
   > personal insecurity, in someone who cannot accept reality as it is.   
   >   
   >>>>>>>> "this program loops forever iff it's decided that it halts"   
   >   
   >>>>>>> As you also know, this is the contradiction reached in one of the   
   proofs   
   >>>>>>> of the Halting Theorem.  This is also not the same as "This sentence is   
   >>>>>>> false.", though it is inspired by that nonsense.   
   >   
   > [ .... ]   
   >   
   >>>>>>> None of these sentences/nonsenses limit our ability to understand   
   >>>>>>> truth.  They are part of the truth that we understand.  They   
   >>>>>>> delineate fundamental boundaries of what can be known and proven,   
   >>>>>>> in particular that truth is more subtle than provability.   
   >   
   >>>>>> That is bullshit as I have just proven.   
   >   
   >>>>> Every time you use the word "proven" you appear to be lying.  I can't   
   >>>>> recall any occurrence where you were telling the truth.   
   >   
   >>>> When a counter-example to my claim is categorically   
   >>>> impossible then I have proven this claim even if   
   >>>> you fail to understand that this is the generic   
   >>>> way that all actual proof really works.   
   >   
   >>> It has nothing to do with my understanding, and a great deal to do with   
   >>> your lack of it.  You have not proven that a counter example to whatever   
   >>> it is you're talking about is "categorically impossible".   
   >   
   >> You could not point out any specific error in the   
   >> details that I specified. You can only assert mere   
   >> baseless dogma that you believe that I am incorrect.   
   >   
   > The "details" you "specified" were just hand-waving nonsense, not based   
   > on any firm logical or mathematical results.  Therefore they can be   
   > justifiably disregarded.   
   >   
      
   *This is a new foundation for semantics*   
   Every element of the set of general knowledge that   
   can be expressed in symbolic language is a semantic   
   tautology thus can be proven true entirely on the   
   basis of relations between finite strings.   
      
      
   [continued in next message]   
      
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