On: How Gödel's Proof Works (2020)

[GoblinSlayer]

That won't work. Gödel number encodes a paradox, but a halting execution of a TM is not a paradox, so can't be written as a Gödel number.

[pfdietz → GoblinSlayer]

Your word salad is not even wrong. For example:

> Gödel number encodes a paradox

WTF do you mean by this?

[GoblinSlayer → pfdietz]

A statement that can't be proved true or false and thus demonstrates incompleteness of logic.

[pfdietz → GoblinSlayer]

How is that a paradox? And how does that imply the correct argument I gave doesn't work? (It doesn't imply that.)

[GoblinSlayer → pfdietz]

Paradox is a statement that can't be proved true or false; "this statement is false" is an example of Gödel statement. The argument doesn't work, because execution of a Turing machine can't be expressed as a Gödel number.

[pfdietz → GoblinSlayer]

> Paradox is a statement that can't be proved true or false

No it isn't.

> execution of a Turing machine can't be expressed as a Gödel number

Yes it can.