A knight always tells the truth, and a knave always lies.

logic/smullyan/cannot.tell New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

A knight always tells the truth, and a knave always lies.  I asked a man
who is either a knight or a knave whether he is a knight or a knave.
Then he said, "Only from this statement you cannot tell what I am
without any logical contradiction."  What is he?

-- ps park (Seoul Univ.) <surd@apollo.hanyang.ac.kr>

Show solution

I cannot deduce that he's a knight (else his statement would be false).
If I cannot deduce anything, then his statement is true; therefore
(moving to metalogic as necessary) if I can deduce that I cannot deduce
anything, I've proven him to be a knight.  Therefore he must be a knave.

(Actually he's a knight who's smarter than I am and fooled me.)

-- Seth Breidbart <sethb@panix.com>

That's tougher than it looks.

If there is a real contradiction, the problem would have no solution,
so the only possibility is that his statement could be paradoxical.  But
if it is, then it is true, so it is not.

Now if we cannot tell who he is, then he must be a knight, which is a
contradiction.

So we _can_ tell who he is, and he must be a knave.

-- Dave Ring <dwr2560@tam2000.tamu.edu>

[ Editor: a variant posed in the same thread (December 1994), for which
no answer was collected: ]

I asked another man who is either a knight or a knave whether he is a
knight or a knave.  He answered,

        "From this statement you cannot tell that I am a knave."

What is he?

-- Dave Seaman <ags@seaman.cc.purdue.edu>