Refuting Gödel:

[LeoMota]

I have written a book refuting Gödel, so far no one has been able to counter my argument.
Basically, he took an x not belonging to himself. However, there is nothing that does not belong to itself; he should have at least demonstrated the existence of such an x.

https://www.amazon.com/dp/B0CS8SX7KW

Salam

[mickthinks]

You think you’ve refuted Gödel.

[Age]

I have written a book refuting Gödel, so far no one has been able to counter my argument.
Basically, he took an x not belonging to himself. However, there is nothing that does not belong to itself; he should have at least demonstrated the existence of such an x.

https://www.amazon.com/dp/B0CS8SX7KW

Salam

Does the word 'himself' here refer to "godel" itself?

If yes, then saying and claiming that 'he' ["godel} took an 'x' not belonging to "himself/godel", is very, very different from saying and claiming that 'there is nothing that does not belong to itself'.

See, if "godel" took an 'x' not belonging to 'itself' [the 'x' itself] is very, very different from "godel" taking an 'x' not belonging to "himself" ["godel" itself].

So, which one, or which way, are you actually meaning here?

[Age]

You think you’ve refuted Gödel.

How do you 'know' that "leomota" only 'thinks' that it has refuted "godel"? After all "leomota" might actually 'know' that it has refuted "godel".

Just like the one that 'knew' that it had refuted the 'geocentric' view or belief. Some might have claimed that that one only 'thinks' it has refuted, or disproved, the 'geocentric' view, model, or belief. But, in Truth that one had actually refuted, or disproven, that 'old view', 'old model', or 'old belief'.

Do you 'know', or 'think', that "leomota" 'knows' or 'thinks' that it has refuted "godel"?

In other words do you 'know' or 'think' what you said and wrote here?

[alan1000]

I know - or at least I think I know - or at least I know that I think I know - that this thread may have originated with an intelligible idea.

[wtf]

I have written a book refuting Gödel

I read a book on Gödel once, but it was incomplete.

[Atla]

How can you refute someone who literally has "God" in his name?

[Harbal]

I have written a book refuting Gödel, so far no one has been able to counter my argument.

Is it really because they haven't been able to, or is it just that they haven't bothered to? There is a subtle difference.

[godelian]

I have written a book refuting Gödel, so far no one has been able to counter my argument.
Basically, he took an x not belonging to himself. However, there is nothing that does not belong to itself; he should have at least demonstrated the existence of such an x.

https://www.amazon.com/dp/B0CS8SX7KW

Salam

The abstract of your book seems to suggest that Gödel's argument is akin to the liar paradox:

https://www.amazon.com/dp/B0CS8SX7KW

The focus of this work is to question whether the liar paradox represents something valid whose existence can be confirmed. Faced with a negative answer, we proceed to a critique contrary to the results obtained by Kurt Gödel, as he uses this paradox in the demonstrations of his famous theorems.

Liar paradox: "This statement is not true"

The liar paradox cannot be expressed in first-order arithmetic -- the system from which Gödel proves his theorems -- because of Alfred Tarski's undefinability of the truth. The true() predicate cannot be defined.

Gödel's sentence: "This statement is not provable"

Gödel goes to great length demonstrating how he defines the provable() predicate. Gödel creates an abstract database of all proofs indexed by logic sentence along with a lookup function that allows him to ascertain that a particular logic sentence has a proof. Hence, unlike the true() predicate, the provable() predicate can effectively be defined and implemented. In my opinion, Gödel does not make use of the liar paradox.

Jill Humphries concluded something similar:

https://projecteuclid.org/journals/notr ... 82658.full


Notre Dame Journal of Formal Logic
Volume XX, Number 3, July 1979
NDJFAM

GODEL'S PROOF AND THE LIAR PARADOX
JILL HUMPHRIES

Given this distinction between heterological and diagonal procedures, it can be shown that Gδdel's arguments are not related to the liar paradox.

Gödel's diagonal procedure is in fact just a database implemented using only arithmetic. That is why his database construction may appear confusingly hard. In fact, it is just a simple database.

Similarly, Gödel numbering is an encoding procedure -- using arithmetic operations only -- that we would not use in practice either, because it looks confusingly hard while practical modern encodings such as UTF-8 and MathJax are much simpler, much more efficient, and achieve exactly the same goal.

Gödel could only use arithmetic for implementing a system that would be trivially easy to implement if he had been allowed to use any imperative programming language. He was unfortunately not allowed to do that, because in that case, his theorems would not prove anything about first-order arithmetic.