A man walks up to you and says:
"
Everything I say to you is a lie."
Is he telling you the truth or is he lying?
(In reply to
surely a paradox by maverick)
it's only a paradox if you take the statement on its own, i.e. "Everything I say to you is a lie." cannot be self-consistent, since it's truth implies that it is false. As he has only made one statement, you get "X implies not X", which is paradox.
Solving the problem breaks the paradox, because you have a different premise - either
"He is telling the truth when he says 'everything i say to you is a lie"
or
"He is lying when he says 'everything i say to you is a lie"
The first alternative is still a paradox, because it states "The assertion that 'X implies not X' is TRUE", which doesn't work (!); but the second statement gives "The assertion that 'X implies not X' is FALSE" is self-consistent, and the answer - the man is lying.
(Negating what the man says doesn't equate to "Nothing I say to you is a lie", just "Not everything I say to you is a lie" - this isn't one of those puzzles where everyone either tells the truth all the time, or lies all the time)
re: surely a paradox
