Can someone please explain how "I am lying" is a Liars paradox? and how the truth values are toggling here?

Question

I want to understand why the statement “I am lying” is a liars paradox as I unable to to toggle between the truth values for this statement.  Thanks in advance.

Comments

Suppose, "I'm lying" is said by someone.

Consider, his/her statement is True, but he's/she's saying "I'm lying", so this must be a False statement.

Consider, his/her statement is False, ie NOT(I'm lying) $\equiv$ True $\equiv$ "I'm not lying", so his/her statement should be True.

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Since, you have posted a question about Liar Paradox, you must have to read about “Gödel's incompleteness theorems” by a famous mathematician “Kurt Gödel” and see how beautiful the mathematics is...

Answer 1

The statement is "I am lying". Now statement implies the statement is false, but then the statement means ⌝(false) = true. Then this means the person is not lying when he/she actually meant he/she is lying. This is paradoxial since the truth values are toggling