The Liar's Paradox

My last post on programs halt and bang concluded that bang(bang) halts if, and only if, it doesn't halt, which is clearly a contradiction. This occurs because the self-reference creates a paradox. A classic example of this is the statement:

This sentence is false

Because the sentence references itself, if is both true and false at the same time. This is called the Liar's Paradox, which gets it's name from Psalm 116:11 in which David says:

I said in my alarm, "Every man is liar!"

Again, however you read the statement, you get a contradiction because the sentence is self-referential because the speaker is himself a man. 

I thought this was an interesting little complement to our class discussions on proving something uncomputable by trying to compute it and creating a contradiction.