My unique take on Gödel 1931 Incompleteness (also self-referential)
Any expression of the language of formal system F that asserts its
own unprovability in F to be proven in F requires a sequence of
inference steps in F that prove they themselves do not exist.

It is not at all that F is in any way incomplete.
It is simply that self-contradictory statements cannot be proven
because they are erroneous.

*The most important aspect of Gödel's 1931 Incompleteness theorem are*
*these plain English direct quotes of Gödel from his paper*
....there is also a close relationship with the “liar” antinomy,14 ...
....14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
....We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...
(Gödel 1931:43-44)

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

*Antinomy* (Greek αντι-, against, plus νομος, law) literally means the
mutual incompatibility, real or apparent, of two laws. It is a term
*often used in logic and epistemology*, *when describing a paradox or*
*unresolvable contradiction*
https://www.newworldencyclopedia.org/entry/Antinomy

Quoted from above
....14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...

Why would Gödel say this?

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 10/17/23 12:14 AM, olcott wrote:
> My unique take on Gödel 1931 Incompleteness (also self-referential)

Unique because it is incorrect.

> Any expression of the language of formal system F that asserts its
> own unprovability in F to be proven in F requires a sequence of
> inference steps in F that prove they themselves do not exist.

And your problem is that you just don't understand Godel statement,
which is that G asserts that there does not exist a Natural Number g,
that satisfies a particular Primative Recursive Relationship.

Such a statement MUST be True of False, as either such a number exists,
or it doesn't (try to argue against that statement)

>
> It is not at all that F is in any way incomplete.

DEFINITION: A System is complete if, and only if, it can prove all true
statements in it with a proof in it.

Result of the proof: In F, we can show that the statement G must be
true, and also that this can not be proven in F, therefore, F must be
incomplete.

The proof being, in essence, that we constructed (in Meta-F) the PRR
such that it will be satisifed by a number that encodes a proof of the
statement in F. He shows that the basic properties of the Natural Number
allow him to do this.

Since, if such a number exists, G would be false, but G is also proven
in F, and you can't prove a statement that is false, this can not be the
case.
Thus, we can prove IN META-F, which is the only place that can do that
proof, that such a number can't exists, and thus G is proven (in Meta-F)
to be True, and by the rules of construction Meta-F, it must also be
true in F. Also, we can show (in Meta-F) that there can't be a proof of
that statement in F, as that proof would generate a number g. Again,
this truth in Meta-F, by the rules of constructing it, transfers to F.

> It is simply that self-contradictory statements cannot be proven
> because they are erroneous.

And it isn't self-contradictory. it CAN'T be, because there is a
non-contradictory answer, that G is True but not Provable.

This shows that any system with a axiom that says that all true
statements are provable (or that the system is complete) can NOT handle
the axioms that create the full properties of the natural numbers
without becoming inconsistant.

Of course, you can't understand that, because your own logic appears to
have gone inconsistant a long time ago, so you don't allow yourself to
think about such results, or you would need to admit you have been wrong
all these years.

>
> *The most important aspect of Gödel's 1931 Incompleteness theorem are*
> *these plain English direct quotes of Gödel from his paper*
> ...there is also a close relationship with the “liar” antinomy,14 ...
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...
> ...We are therefore confronted with a proposition which asserts its own
> unprovability. 15 ...
> (Gödel 1931:43-44)

Which is all logic in Meta-F, that is PROVEN from the statement that
existed in F, when examined in the light of the knowledge of the Meta
system.

>
> Gödel, Kurt 1931.
> On Formally Undecidable Propositions of Principia Mathematica And
> Related Systems
>
> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>
>
> *Antinomy* (Greek αντι-, against, plus νομος, law) literally means the
> mutual incompatibility, real or apparent, of two laws. It is a term
> *often used in logic and epistemology*, *when describing a paradox or*
> *unresolvable contradiction*
> https://www.newworldencyclopedia.org/entry/Antinomy
>
> Quoted from above
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...
>
> Why would Gödel say this?
>

Because he is smarter than you and knows how to transform statements.

Your just repeating yourself is shown your stupidity. You seem to think
that the disinformational technique of repeating the lie until people
think it is true is valid logic.

You are just showing your stupidity.

Note, his comment is about the logic he does in META-F to build the
Primitive Recursive Relationship (which is what was based on the
TRANSFORMED epistemological antinomy).

You apparently can't comprehend meta-logic, likely because you don't
actually understand plain logic.

You are just too stupid.

On 10/16/2023 11:14 PM, olcott wrote:
> My unique take on Gödel 1931 Incompleteness (also self-referential)
> Any expression of the language of formal system F that asserts its
> own unprovability in F to be proven in F requires a sequence of
> inference steps in F that prove they themselves do not exist.
>
> It is not at all that F is in any way incomplete.
> It is simply that self-contradictory statements cannot be proven
> because they are erroneous.
>
> *The most important aspect of Gödel's 1931 Incompleteness theorem are*
> *these plain English direct quotes of Gödel from his paper*
> ...there is also a close relationship with the “liar” antinomy,14 ...
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...
> ...We are therefore confronted with a proposition which asserts its own
> unprovability. 15 ...
> (Gödel 1931:43-44)
>
> Gödel, Kurt 1931.
> On Formally Undecidable Propositions of Principia Mathematica And
> Related Systems
>
> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>
>
> *Antinomy* (Greek αντι-, against, plus νομος, law) literally means the
> mutual incompatibility, real or apparent, of two laws. It is a term
> *often used in logic and epistemology*, *when describing a paradox or*
> *unresolvable contradiction*
> https://www.newworldencyclopedia.org/entry/Antinomy
>
> Quoted from above
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...
>
> Why would Gödel say this?
>

Gödel refers to: "a proposition which asserts its own unprovability"
Gödel says: ...Every epistemological antinomy can likewise be used
for a similar undecidability proof...

I have provided: "a proposition which asserts its own unprovability"
and I have shown how this is an {epistemological antinomy}.

Thus in my simple version we can see WHY a proposition that asserts
its own unprovability in F cannot be proven in F. It is because such
a proposition is an {epistemological antinomy} in F.

So far the only "rebuttals" have be empty denigration and
ad hominem personal attacks. The lack of any reasoning
showing any mistake is construed as there is no mistake
that can be found.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 10/17/23 11:18 AM, olcott wrote:
> On 10/16/2023 11:14 PM, olcott wrote:
>> My unique take on Gödel 1931 Incompleteness (also self-referential)
>> Any expression of the language of formal system F that asserts its
>> own unprovability in F to be proven in F requires a sequence of
>> inference steps in F that prove they themselves do not exist.
>>
>> It is not at all that F is in any way incomplete.
>> It is simply that self-contradictory statements cannot be proven
>> because they are erroneous.
>>
>> *The most important aspect of Gödel's 1931 Incompleteness theorem are*
>> *these plain English direct quotes of Gödel from his paper*
>> ...there is also a close relationship with the “liar” antinomy,14 ...
>> ...14 Every epistemological antinomy can likewise be used for a
>> similar undecidability proof...
>> ...We are therefore confronted with a proposition which asserts its
>> own unprovability. 15 ...
>> (Gödel 1931:43-44)
>>
>> Gödel, Kurt 1931.
>> On Formally Undecidable Propositions of Principia Mathematica And
>> Related Systems
>>
>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>
>>
>> *Antinomy* (Greek αντι-, against, plus νομος, law) literally means the
>> mutual incompatibility, real or apparent, of two laws. It is a term
>> *often used in logic and epistemology*, *when describing a paradox or*
>> *unresolvable contradiction*
>> https://www.newworldencyclopedia.org/entry/Antinomy
>>
>> Quoted from above
>> ...14 Every epistemological antinomy can likewise be used for a similar
>> undecidability proof...
>>
>> Why would Gödel say this?
>>
>
> Gödel refers to: "a proposition which asserts its own unprovability"

Yes, which is a proposition proved in META-F.

> Gödel says: ...Every epistemological antinomy can likewise be used
> for a similar undecidability proof...

Right, from any epistemogoical antinomy, he can TRANSFORM it from an
antinomy into a statement about provability, and thus prove the
statement must be true.

A statement that, if true, shows it can not be true is a contradiction.

A statement that, if trye, shows it can not be proven, is not. A an
proven statement must be true and can not be false, but an unproven (or
unprovable statement) might still be true.

>
> I have provided: "a proposition which asserts its own unprovability"
> and I have shown how this is an {epistemological antinomy}.

Again, the statement is in META-F, not F.

>
> Thus in my simple version we can see WHY a proposition that asserts
> its own unprovability in F cannot be proven in F. It is because such
> a proposition is an {epistemological antinomy} in F.

And the statement you are talking about wasn't in F, so your arguement
is just based on a LIE.

>
> So far the only "rebuttals" have be empty denigration and
> ad hominem personal attacks. The lack of any reasoning
> showing any mistake is construed as there is no mistake
> that can be found.
>

Nope, You aren't reading the actual rebuttal.

YOUR lack of any actual reasoning, or even attempt to rebut the errors I
am pointing out shows that your logic has nothing to stand on.

You don't even seem to know what an ad hominem attack is, that would be
a claim that your are WRONG because you are STUPID (or the like). That
is NOT what I have been saying, I have been showing that your are STUPID
because you continue to be WRONG, and I show WHY you are wrong.

Your inability to understand that just shows how stupid you are.