The absolutely honest judge has given the prisoner two contradicting statements: You will be surprised, and there is no day that you can be executed that you can, in fact, be surprised.
Similarly the absolutely honest husband who makes two condradicting statements to his wife, I'm giving you a gift tomorrow that will surprise you, and it will be that gold necklace we saw at the jewelry store.
In both cases this is a paradox only if the future is perfectly predictable, which it is not. There could be a prison riot and the prisoner could escape. The husband could develop amnesia and get the wrong present.
This operates on the same premise as another old thread here in the paradox section: The Minority Report Paradox. If the seers perfectly predict the future they will know that the crime they are supposedly seeing will be prevented because of their prediction, so there will be no crime for them to foresee. It is a paradox only if they can actually predict the future perfectly; however the physics tells us that it is intrinsically (by the very nature of the laws of physics) impossible for a perfect prediction of the future because, if nothing else, random locations and motions of sub-atomic particles do not have precise values, so cannot be perfectly observed.
Mathematics tries to cram a false absolutism upon an arbitrary, random world. Perfect logic is fundamentally flawed. Here we have the real paradox
Edited by seeksit, 20 May 2009 - 01:22 PM.