As far as I know, "synonym" has no synonyms in the English language. It probably does in other languages, but I don't know what they are.

This means that synonym is a word that does not describe itself; words that do not describe themselves are heterological.

Naturally, the question arises: Is "heterological" heterological?

If it is, then this means that it doesn't describe itself---except that it does describe itself, because we already said that it was heterological.

So it must not be heterological; but then, it must describe itself, and therefore be heterological. Paradox!

In fact, this is Russell's paradox, one of the deepest paradoxes in intuitionist set theory, in disguise:
R = \{x | x \notin x\}

I bet you didn't think that a little joke about synonyms would lead to such heady stuff!



This post was originally written by Patrick Julius
University of Michigan · Undecided · 10 Aug 2007