A and B met a genie and the genie grant each of them a wish.

A's wish: I wish that B's wish is not implemented

B's wish: I wish that A's wish is implemented.

• What have you tried yourself to answer this question, and where did you get stuck?
– user2953
Oct 18, 2016 at 6:16
• I have got that neither A's wish nor B's can happen. But is that enough to conclude that it is a paradox? Oct 18, 2016 at 6:22
– user2953
Oct 18, 2016 at 6:23
• A self-contradicting statement. Oct 18, 2016 at 6:25
• According to your definition, yes.
– user2953
Oct 18, 2016 at 6:33

This is a paradox (solvable, but rather undecidable at this stage), but not an aporia (logical impossibility).

I would consider your model as incomplete: there is no definition of the object "wish". In particular what is the scope of the effects it can have? May a wish (effect) influence back the source (genie) or not? If yes, what are the rules and limitations?

In mathematics, this comes under the heading of "feedback". In order to decide on an answer to this question, you would have to define the feedback function and see what happens to your system. It might stabilize to a definite answer (which is preferable), flip-flop to two or more answers, become wildly chaotic, go to infinity, etc..

The simplest way to solve the issue is, of course, to forbid feedback: a wish is invalid if it concerns the genie in any way, shape, or form, as well as someone else's wishes. But that would also remove the challenge in your question.

The answer of gnasher 729 is not that off the mark, even though it is formulated, as it were, as a reductio ad absurdum: his implicit assumption being that the genie is omnipotent: hence not only the wish cannot affect him, but he can break it (a value of humor is that is shows absurdity). His is an acceptable axiom, though perhaps not what you intended either.

But since you invented the problem, is up to you (not the genie) to give a more substance to your problem, so that it becomes decidable.

There's no paradox. The genie does whatever the genie wishes to do. When the genie "grants a wish" this doesn't invoke some law of physics where granting the wish becomes inevitable. The most likely outcome is that the genie does nothing, or if A and B agreed between them on their wishes, the most likely outcome is that the genie puts them both into a bottle and throws the bottle in the ocean.

Eliminating guesses about the free will of genies and other obviously irrelevant aspects, this is just a reiteration of the Lair's Paradox or the Cretan Paradox where some Cretan says all Cretans always lie. It does not add much, so why not stick to the original?