CURIOUS LOGIC: on one side of a postcard are written the words “the sentence on the other side is true”. You turn over the card to see the words “the sentence on the other side is false”. Which of the two sentences, if either, is the true statement? – Head over to the Blog page to find out the answer.
Let’s call the first sentence ‘A’ and the second sentence ‘B’. If A is true then that means B is true, which implies that A is false – a logical contradiction. This means that A cannot be true.
What if A is false? That means that B is not true, so B is false, which implies that A is true – another logical contradiction!
Either way we have a problem, meaning that sentence A is neither true nor false. One possible conclusion is that we have a big problem and a logical paradox! A convenient way round this is simply to ban self-referential statements as being nonsense and refuse to even consider whether they are true or not.
MORE PUZZLES: how about if both sides read “the sentence on the other side is true” – then are they true, false or neither? And how about if both sides read ” the sentence on the other side is true” – what then? Thinking about funny puzzles like this was responsible for a revolution in maths in the 20th Century, with the ultimate result that some maths statements turn out to be “undecidable” – neither true nor false. Mind-blowing stuff!