Question

Just a small remark that occurred to me (for now) about yesterday’s lecture:
According to what you said, the sentence “I am a liar” says that everything I say is false, and therefore this sentence too is false, and that creates a paradox. But in the end you see that there is no paradox, because “I am not false” = there is at least one statement of mine that is true, and that does not have to be this statement.
 
I didn’t understand why you resolve this paradox in such a distant and indirect way. You assume that “I am a liar” = “all my statements are false,” but that is not correct. “I am a liar” = “I am usually a person who lies,” because obviously nobody in the world lies all the time, no doubt about it. So you can say that this sentence that he says about himself (“I am a liar”) is true, meaning that he often lies, but not here.
And really, even “All the inhabitants of Crete are liars” — I don’t see a paradox in that either (even without getting to your solution): all the inhabitants of Crete are usually liars, but what I am saying now is true.