An Amusing Conundrum

The commenting problems are proving harder to fix than I expected. The overlords have assured me that this is a high priority problem and that they are working on it. Apparently there is only one other blog around here that has been similarly affected. I don’t want to return to regular blogging until the commenting issues have been fixed, since without comments it feels like I’m just talking to myself.

But just to make it clear that I’m still around, here’s an amusing logic puzzle from Raymond Smullyan, from his book Forever Undecdied. Recall that on the island of knights and knaves, anything a knight says is true and anything a knave says is false. We also assume that everyone who lives on the island is either a knight or a knave.

Now suppose a native says to someone visiting the island, “You will never know that I am a knight.” What is the visitor to think? He might reason as follows:

If the speaker is a knave, then his statement is false. That means I will, indeed, know that he is a knight. But since you cannot know something that isn’t true, that implies that he is a knight. This is a contradiction, which means he can’t be a knave. So I now know that he is a knight.

But wait! If I now know that he is a knight then what he said is false. I have another contradiction!

Weird, no?

Strictly speaking this is not a paradox, since the difficulty is not purely logical. Our argument involves non-logical notions such as “knowing.” We have also assumed certain reasoning abilities on the part of the visitor. Still, it’s an amusing scenario to ponder.