The crocodile paradox, also known as crocodile sophism, is a

paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

in the same family of paradoxes as the

liar paradox In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth ...

. The premise states that a crocodile, who has stolen a child, promises the parent that their child will be returned

if and only if In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is b ...

they correctly predict what the crocodile will do next. The transaction is logically smooth but unpredictable if the parent guesses that the child will be returned, but a dilemma arises for the crocodile if the parent guesses that the child will not be returned. In the case that the crocodile decides to keep the child, he violates his terms: the parent'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 parent's prediction has been falsified, and the child should not be returned. The question of what the crocodile should do is therefore

ical, and there is no justifiable solution. The crocodile dilemma serves to expose some of the logical problems presented by

metaknowledge Meta-knowledge or metaknowledge is knowledge about knowledge. Some authors divide meta-knowledge into orders: * ''zero order meta-knowledge'' is knowledge whose domain is not knowledge (and hence zero order meta-knowledge is not meta-knowledge ''p ...

. In this regard, it is similar in construction to the

unexpected hanging paradox The unexpected hanging paradox or surprise test paradox is a paradox about a person's expectations about the timing of a future event which they are told will occur at an unexpected time. The paradox is variously applied to a prisoner's hanging or ...

, which

Richard Montague Richard Merritt Montague (September 20, 1930 – March 7, 1971) was an American mathematician and philosopher who made contributions to mathematical logic and the philosophy of language. He is known for proposing Montague grammar to formalize ...

(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.

Ancient Greek sources were the first to discuss the crocodile dilemma.

Notes

{{Paradoxes Self-referential paradoxes Dilemmas

dilemma A dilemma ( grc-gre, δίλημμα "double proposition") is a problem offering two possibilities, neither of which is unambiguously acceptable or preferable. The possibilities are termed the ''horns'' of the dilemma, a clichéd usage, but dist ...

See also

Notes