A statement that can't be proved true or false and thus demonstrates incompleteness of logic.
How is that a paradox? And how does that imply the correct argument I gave doesn't work? (It doesn't imply that.)
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.
> 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.
How is that a paradox? And how does that imply the correct argument I gave doesn't work? (It doesn't imply that.)
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.
> 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.