The liar paradox

This is something I came across just recently. Someone says something along the lines of: ‘I am lying’ or ‘this statement is false.’ Our task is to decide whether what they’re saying is true or false. If it’s true, then … it can’t be true, so it must be false. But if it’s false … then it’s true!

See http://www.iep.utm.edu/par-liar/ for some really interesting discussion on this.

For me, the answer is ‘neither’. These just aren’t statements that can be categorised as true or false, and perhaps the difficulty we have with such conundrums merely reflects the fact that our language has not evolved to flag up any such problems; a sentence can be illogical or nonsensical and still make sense semantically.

This put me in mind of the way in which interviewers on the TV or radio will sometimes try to trap their subjects (especially politicians!), using a similar well-known ‘paradox’.

Like most people, I get annoyed when politicians refuse to give a straight answer to a straight question.

But I sometimes find myself siding with the interviewee when they’re asked something like: ‘Are you continuing to take bribes from this company? Yes or no.’

If the interviewee wants to deny having taken any bribes, the answer to the question is neither ‘yes’ nor ‘no’.