My preferred resolution to the Liar Paradox is Prior's, summarized here
. The idea is that the liar sentence, like all sentences, asserts its own truth. So a sentence that asserts both its truth and its falsity must be false.
One of the nice things about Prior's resolution is that it can be easily applied to many similar paradoxes, for instance Curry's paradox. Consider the sentence "If this statement is true, then 1+1=3." Or if you prefer, statement 1: "If statement 1 is true, then 1+1=3." Suppose that statement 1 is true. Then what statement 1 says is that if it is true, then 1+1=3. So supposing it is true, 1+1=3. In other words, it is correct to say that if statement 1 is true, then 1+1=3 would be true. In other words, "If statement 1 is true, then 1+1=3" is a true statement. But that is precisely statement 1. So statement 1 is true. But statement 1 says that if it's true 1+1=3. We have just shown that statement 1 is true. So we can conclude that 1+1=3. Can you apply Prior's resolution to solve this?