At 4/3/09 11:02 AM, Paranoia wrote:
Either Bill or Charles lying will make sense. Tom can't be telling the truth otherwise both Bill and Charles will by lying which means that there's a contradiction:
If Tom is telling the truth, then the two others have to be lying, or he wouldn't be telling the truth because he says they both lie. Therefore, Charles is telling the truth, so his statement that Tom is lying is true -> contradiction
If Bill is telling the truth, then Charles is lying, and therefore his statement that Tom is a liar is a lie. Therefore, Tom is telling the truth when he says both Charles and Bill are lying, and therefore Bill isn't telling the truth -> contradiction
If Charles is telling the truth, then Tom is a liar, therefore Tom is lying when he says Bill is a liar, and therefore Bill is telling the truth by saying Charles is a liar -> contradiction
This is a paradox if you say that none of them can be wrong in what they say. At least one of them has to be wrong - regardless of whether he's trying to lie or tell the truth.