Wednesday, December 1, 2010

True Lies

This sentence is false.

The alert reader will be a little perplexed by that claim for if it is true then it must be false, and vice-versa. Statements like this are called paradoxes. This particular paradox is a version of what's called the Liar's Paradox. It's hard to see how a paradox could be true or false and yet it's hard to say exactly what it is that's wrong with the sentence.

There are lots of different kinds of paradoxes. Some are verbal like the one above, some are visual, like the art of M.C. Escher :
And some are situational like the paradoxes of an ancient Greek named Zeno.

Philosopher Graham Priest has an interesting piece at The Opinionator blog on paradoxes and modern attempts to resolve them. It turns out that some people think that though a paradox involves a contradiction some of them are nevertheless true. I have serious reservations about this because it seems to violate a logical principle called the law of non-contradiction which is a bedrock of rational thought. Even so, the article is very interesting, at least for the logically minded, and may even be correct. Give it a look.