Which line is true? Which line is false?

[wreckedit]

If "This line is false" is true, then it is false, which would in turn mean that it is actually true, but this would mean that it is false, and so on ad infinitum.

Similarly, if "This line is false" is false, then it is true, which would in turn mean that it is actually false, but this would mean that it is true, and so on ad infinitum.

Found this on Google since I didn't know how to explain the answer but I had a feeling it was one of those infinite circular things where one answer would contradict another and would go on for ever. If you could do this mechanically it would be perpetual motion.

 

[Space cat]

Here's how you solve it. You have to start somewhere so let's start with a hypothesis that the top line is true. It says:

"The bottom line is true." That's an absolute statement of fact so, based on our initial hypothesis, we must accept what the bottom line says, namely:

"The top line is false." This contradicts our initial hypothesis. We don't have to accept what the top line says after all.

Now for the clever bit. Most people will assume that, just because there is no requirement for the bottom line to be true, it must be false. Wrong. The bottom line can still be true. The false, top line doesn't say that it isn't.

Edit:

Here's another one I remember. A group of people want to cross a bridge but there's a problem. Anybody who crosses the bridge has to answer the question, "Why are you crossing this bridge?" Give the wrong answer and you get hanged.

A philosopher steps forward.

"Why are you crossing this bridge?"
"To be hanged."