The Crocodile Paradox is a paradox in logic in the same family of paradoxes as the liar paradox.  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. In the case that the crocodile decides to keep the child, he violates his terms: the father's prediction has been validated, and the child should be returned. However, in the case that the crocodile decides to give back the child, he still violates his terms, even if this decision is based on the previous result: the father's prediction has been falsified, and the child should not be returned. The question of what the crocodile should do is therefore paradoxical, and there is no justifiable solution.
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:
(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.
- Barile, Margherita. "Crococile Dilemma – MathWorld". Retrieved 2009-09-05.
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- Murray, Richard (1847). Murray's Compendium of logic. p. 159.