I reckon the trick to understanding the 'truth' ( or, ahem, 'depth' ) in a paradox, which is a thing that is supposedly both true and false, is to recognise context, generally time.
Find where the same symbols are used to represent different patterns. I.e. the same word or concept is applied in a different context whereby it's meaning changes.
Otherwise, there is no 'depth', and it's just a meaningless statement.
Assuming a statement could be said to have meaning.
Fallacy is stronger than truth.
I always lie.
Aha! Faulty premise. It's possible to know truth?
Perhaps one should not apply binary logic to a problem involving measures of degrees? Or degrees to binary statements.
I think Ying-Yangs are cool.
Damn. I'm using English again.
I wish I could think with something else.
I know nothing.
Haha. It says "No me quitta pas". But it means "Ne me quitte pas".