Pedant’s Paradox: Chrysppus’ Crocodile.

Pedant’s Paradox

About the series: Examining logic problems and paradoxes and dismantling them, because I am just that picky. Feel free to debate my answers. (Yes I am aware most of these have mathematical answers, but they’re dressed  in real-world examples so they can be looked at with real world logic). This month we are moving onto a traditional Egyptian puzzle.

The Problem: A woman is walking by a river with her child when her child is snatched from her by a crocodile. The crocodile tells her that it will return the child if she can correctly answer the question “What do you intend to do with the child?”

The Answer: The mother is traditionally supposed to reply “You intend to keep it.” to guarantee the return of her child.

 With this one it is not the problem that breaks, it is the solution. The crocodile could equally well answer false, and eat the child on the spot. Eating something is not the same as keeping it. It could also drop the child in the river so neither of them have it. The error is in that assuming the crocodile has only two options – to keep the child or hand it back. It also has options to destroy the child or dispose of it so no one has it.

Even “You intend to keep it” does not guarantee the return of the child or its condition when it is returned. Worse if the crocodile is, as many in myth were, a sage akin to an Eastern Dragon, the answer might actually be false. Its intent may be simply to test the mother’s intelligence.

So what could she say? The actual answer could be a negative. “You do not intend to return the child safely to me.” However there is no room in the question for a negative. Likewise the conditional, “You intend to return it if I can answer your riddle” may be disqualified although it is undoubtedly true.

Or as a mathematician friend put it: “You intend to use it to make me answer a stupid bloody question.”

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