Kurt Gödel

Gödel was a German mathematician during the early part of this century, and who is most well known for his Incompleteness Theorem, which poses a philosophical question in terms of mathematics. For more about him and what he did, I recommend Gödel, Escher, Bach as an interesting read.

For what's it worth, here's one way to look at what he stated: You cannot have a system of logic that is both complete and self-consistent. A complete system is one that contains every possible expression. A self-consistent system is one that contains no contradictions.

The classic example that makes all this clear is: "this statement is a lie" (also referred to as the Epimendes Paradox). If the statement is true, then the statement is a lie (since that's what the statement asserts); if it's a false statement, then, being a lie, it is a true statement about itself.

It's a paradox all right.

So, English is a language that is complete (you can state anything in English, including a paradox) but it's not self-consistent (you can state things which are logical contradictions). There was a big push in the first part of this century to "prove" or demonstrate that all of math was a "rigorous" system - that if you proved something with math, it was "really proved" - there was no chance that some fundamental problem with mathematics itself would render a proof meaningless. Basically, science and philosophy have spent the last century merging, as they have both spent their energies exploring the same fundamental sorts of questions about meaning and absoluteness. But that's a whole 'nother class.