I am a liar.

Alright NS, here's a little brain-stretching for everyone.

So the other day in my philosophy class (kinda a logic/reasoning type class) we were talking about arguments, and we got into something called self-inconsistent statements. I thought this was interesting, so I decided to share.

Arguments are called "consistent" if they don't contradict one another. Certain arguments, though, contradict themselves. For example, if I were to say (like the thread title) something like:

 "I am a liar"

or "This statement is false"

 it would be hard to interpret. Think about those for a second. Go with the second statement - the text says that it itself is false. But if it really is false, then it would be true. This would then make it false, and so on. Same thing with the first - if it is true, I am telling the truth which means I'm not a liar, but if I am a liar it would be false.  Does that make them true or false? Or are they neither?

A similar issue comes up in something called Russell's paradox, in a branch of math called set theory. You don't need to know any math to understand it, though. In set theory, you can have a set containing pretty much anything. For example, you could have set A={1} containing the number one, or B={1,2} containing one and two.

To solve certain problems in math (which aren't important here), a "universal set" was proposed, which was supposed to contain every set (U={A,B,...}). But then the question arose: Does a universal set, containing all other sets, contain itself? It must, because if it didn't it wouldn't be universal. If it does, though, it is easy to see that any universal set is inside another universal set, making it not universal anymore. So can there even be a universal set?

Can these paradoxes be resolved? Do either of them make sense?
What do you think?