Crocodile Dilemma

The Crocodile Dilemma is an unsolvable problem in logic.^{[1][dubious – discuss]} The premise states that a crocodile who has stolen a child promises the father that his son will be returned if and only if he can correctly predict whether or not the crocodile will return the child.

The transaction is logically smooth (but unpredictable) if the father guesses that the child will be returned, but a dilemma arises for the crocodile if he guesses that the child will not be returned.

If the Crocodile decides to	KEEP	the child, and the Father predicted the child would be	KEPT	then the outcome is	A PARADOX.
If the Crocodile decides to	KEEP	the child, and the Father predicted the child would be	RETURNED	then the outcome is	THE CHILD IS KEPT.
If the Crocodile decides to	RETURN	the child, and the Father predicted the child would be	RETURNED	then the outcome is	THE CHILD IS RETURNED.
If the Crocodile decides to	RETURN	the child, and the Father predicted the child would be	KEPT	then the outcome is	THE CHILD IS KEPT.

The question of what the crocodile should do is therefore paradoxical, and there is no justifiable solution.^[2][3][4]

The Crocodile Dilemma serves to expose some of the logical problems presented by metaknowledge. In this regard, it is similar in construction to the unexpected hanging paradox, which Richard Montague (1960) used to demonstrate that the following assumptions about knowledge are inconsistent when tested in combination:^[2]

(i) If ρ is known to be true, then ρ.

(ii) It is known that (i).

(iii) If ρ implies σ, and ρ is known to be true, then σ is also known to be true.

It also bears similarities to the Liar paradox. Ancient Greek sources were the first to discuss the Crocodile Dilemma.^[1]

It has been suggested that, realistically, the infinitely repeating dilemma would not occur because the father guessed correctly. In other words, the father was guessing at what the crocodile intended to do, not what the eventual result would be.

See also

• List of paradoxes

Notes

1. ^ ^{a b} Barile, Margherita. "Crococile Dilemma – MathWorld". http://mathworld.wolfram.com/CrocodilesDilemma.html. Retrieved 2009-09-05. 
2. ^ ^{a b} J. Siekmann, ed (1989). Lecture Notes in Artificial Intelligence. Springer-Verlag. p. 14. ISBN 3540530827. 
3. ^ Young, Ronald E (2005). Traveling East. iUniverse. pp. 8–9. ISBN 0595795846. 
4. ^ Murray, Richard (1847). Murray's Compendium of logic. p. 159.