Member Rara Avis
Self-creating contradiction has some promise, Eddie. But I'm not sure it's a great deal more helpful than simply looking for the paradox. Let's look at a less obvious example.
Every rule has an exception.
If we define the statement as a rule, which isn't a stretch I think, then this is certainly a self-referencing statement. Is it true, false, or a paradox? If it's true, then there must be an exception to this rule, too, meaning it can't be true. It's a paradox, or as you say, a self-creating contradiction. But, if the statement is false? Then there's no contradiction and no paradox. Unfortunately, this falls in the class of "exhaustive" sets where it's impossible to prove it false. The best we can probably hope to do is find a rule with no "known" exception, and that's not good enough to prove that this maybe-a-paradox rule is false. In short, I don't really know if it's a paradox.
Any self-referencing statement, I think, is automatically suspect. But how suspect?
Brad, you pretty much got it, at least to my understanding. Russell's treatment was to allow anything within a given set to only reference things within lower order sets. With this method, he disallowed direct self-referencing (within the same set) and also prevented indirect self-referencing ("The following sentence is true. The preceding sentence is false."). Of course, it had this nasty little side-effect - I could no longer talk about me.
Gödel showed that the elimination of paradoxes necessarily introduced inconsistency. We "might" be able to get rid of paradoxes, but we really don't want to. That's cool. But I'd still like to understand a bit more about their nature.