As for paradoxes, I like the ones that happen because they happen - they use this all the time in Doctor Who. It's also in the Artemis Fowl book Time Paradox, where they have to go back in time to do something, but if they had never gon back in time they would not have had a need to. It was self-causing - which begs the question, how did it come to happen?
Wait, does his nose grow if he believes what he is saying is true?
I think you mean 'if he believes what he is saying is false'
@Lachlan Easton: I must not be understanding the "damned if you do, damned if you don't" thing then, what does it mean? It sounds nothing like a catch-22 to me, in fact it doesn't really seem like anything special, just a lose-lose situation.
In the book Catch-22, a pilot is found sane if they request a psych evaluation and thus fit to fly (damned if you do), and if they don't request an evaluation they have to fly anyway (damned if you don't).
Actually, it is a catch-22, but in a different sense than explained by LE: the problem (being found unfit to fly) is rendered unsolvable by attempting to solve it (requesting to be grounded).
The trick, though, is to get other people to request that you be grounded. I gather smearing yourself in your own waste and running naked across the base shouting "they're in my brain!" ought to do it.
Why is that not a valid analogy? The quote implies that there are two decisions and which ever you take, there will be negative consequences. In LE's example: the pilot wants to be grounded from flight, the only way for him to do that is to be declared insane. In order for him to be declared insane he must be analyzed by a psychologist. In order for him to be analyzed by a psychologist, he must have an appointment, and the only way he can do that is by requesting one. So his decisions are ask or not ask. If he asks he will still have to fly (negative consequence), if he does not ask he still has to fly (negative consequence).
On the topic of time travel and its paradoxes, I have a hunch one can only travel forward in time and not backward. Have you seen any time travelers from the future yet? I've seen lots from the past, including myself.
Paradox: A statement or group of statements that leads to a contradiction or a situation which defies intuition. No-win situation: Real choices do exist, but no choice leads to success.
"Your damned if you do, and your damned if you don't" is a no-win situation.
The 'Catch-22' pradox is situation in which someone is in need of something that can only be had by not being in need of it. So catch-22 can put you in a no-win situation but a no-win situation isn't always a catch-22. e.g. I have enough money to pay the rent but can't buy food or I buy food, don't pay the rent and get evicted.
a catch-22 paradox isn't always a no-win situation. For example; I need to pay the arrears on the mortgage to release equity in the house but I need to release equity in the house to pay the arrears on mortgage. There is no 'damned if you do, damned if you don't' here.