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Re: A new foundation for correct reasoning +++

Cross-posted to 3 groups.

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On 11/29/2025 2:48 PM, Alan Mackenzie wrote:
> [ Followup-To: set ]
> 
> In comp.theory olcott <polcott333@gmail.com> wrote:
>> On 11/29/2025 5:55 AM, Alan Mackenzie wrote:
> 
>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
> 
>>>>> In comp.theory olcott <polcott333@gmail.com> 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_theory#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.

>>> You can't, since you lack the prerequisites to understand what
>>> constitutes a proof, and you lack the mathematical foundations to be
>>> able to construct one.
> 
>> I don't give a rat's ass about your narrow minded learned by rote
>> definitions of a proof are.
> 
> Neither do I.  Not relevant, since I don't have any such learned by rote
> definitions of a proof.
> 

I make sure to never have such.
I only know things on the basis that they are proven
to be inherently true.

>> The most generic form of a proof is essentially a semantic tautology.
> 
> That's neither here not there, being too abstract to be of use.
> 

It shows that natural preexisting order of all knowledge.

>>>>>> Within the giant semantic tautology of knowledge that
>>>>>> can be expressed in language everything is proven or
>>>>>> not an element of this body.
> 
>>>>> Your scheme is limited indeed, in that it is not powerful enough to
>>>>> represent unprovable propositions.
> 
>>>> In other words "the entire body of knowledge that
>>>> can be expressed in language" uses big words that
>>>> you cannot understand?
> 
>>>> What is left out of:
>>>> "the entire body of knowledge that can be expressed in language" ?
> 
>>> Arithmetic, for a start.
> 
>> So you are trying to get away with saying that
>> knowledge of arithmetic cannot be expressed in language?
> 
> I'm saying that any system of knowledge in which Gödel's Incompleteness
> Theorem doesn't apply is either inconsistent or incapable of doing
> arithmetic.
> 

You are merely spouting off dogma with no understanding
of how I showed that this does not work.

He used Gödel numbers to hide the underlying
semantics in a language that could not directly
specify either provability or self-reference.

G says of itself that it is unprovable in F
G := (F ⊬ G)

>>> If that allegedly "entire body of knowledge"
>>> was capable of doing arithmetic, Gödel's Incompleteness Theorem would
>>> apply to it.
> 
>> Arithmetic is merely insufficiently expressive, the body of knowledge
>> that can be expressed in language knows that.
> 
> No, the body of knowledge that can be represented as you envisage
> wouldn't come up to the level of a stone-age person.
> 

Since it directly formalizes the semantics of anything
that anyone can possible ever say how can this be true?

>>> That is a proof by contradiction that such a body of
>>> knowledge cannot exist.
> 
>> Not at all.
> 
> How can you say that?  You don't understand proof by contradiction,
> remember?
> 
>> Arithmetic is merely insufficiently expressive.
>> While you attempt to come up with counter-examples know
>> that dogma does not count.
> 
> I don't know what you mean by dogma.  I'm talking about proven results
> like 2 + 2 = 4.  You're just ignorant, because you don't have the
> background needed to test these results, but you reject them just because
> you don't like them.  You're an idiot, in other words.
> 
>> A counter-example would be an element of knowledge
>> that can be expressed in language that:
>> (a) Cannot be expressed in language.
>> (b) Is not true. (All knowledge is true)
> 
> That would indeed be a counter example.  But given there is no suspicion
> that such a construct of knowledge could be complete, no proof, no
> attempt at a proof, there is nothing to give a counter example to.
> 

G := (F ⊬ G) // G says of itself that it cannot be proved in F
Gödel says the same thing so verbosely that no one has any
idea that it all boils down to this: G := (F ⊬ G)

>> That is what I mean by counter-examples are
>> categorically impossible
> 
> Your complete system of knowledge is categorically impossible.
> 
>> -- 
>> 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.
> 


-- 
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.

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Thread

A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-28 16:03 -0600
  Re: A new foundation for correct reasoning +++ Richard Damon <Richard@Damon-Family.org> - 2025-11-28 17:33 -0500
  Re: A new foundation for correct reasoning +++ Alan Mackenzie <acm@muc.de> - 2025-11-28 22:54 +0000
    Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-28 17:14 -0600
      Re: A new foundation for correct reasoning +++ Alan Mackenzie <acm@muc.de> - 2025-11-29 11:55 +0000
        Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-29 09:18 -0600
          Re: A new foundation for correct reasoning +++ Alan Mackenzie <acm@muc.de> - 2025-11-29 20:48 +0000
            Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-29 15:31 -0600
              Re: A new foundation for correct reasoning +++ Richard Damon <Richard@Damon-Family.org> - 2025-11-29 17:04 -0500
        Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-01 06:19 -0600
          Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-02 11:56 +0200
            Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-02 08:07 -0600
              Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-03 13:17 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-03 10:13 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-04 11:29 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-04 08:18 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-05 11:03 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-05 11:31 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:39 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-06 06:53 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-07 13:08 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-08 13:56 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-14 13:05 +0200

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