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 or apparently true premises, leads to a seemingly self-contradictor ...
in
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
in the same family of paradoxes as the
liar paradox.
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" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either bo ...
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
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 or apparently true premises, leads to a seemingly self-contradictor ...
ical, 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
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 th ...
(1960) used to demonstrate that the following assumptions about knowledge are inconsistent when tested in combination:
Ancient Greek sources were the first to discuss the crocodile dilemma.
See also
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List of paradoxes
This list includes well known paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list collects only scenarios that have been called a paradox by at least one source and have their ...
*
Self-reference
Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields.
In natural or formal languages, self-reference ...
*
Halting problem
In computability theory (computer science), computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run for ...
– the usual proof of its
undecidability uses a similar contradiction
Notes
{{Paradoxes
Self-referential paradoxes
Dilemmas
dilemma
A dilemma () 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 distinguishing the dilemma from other kinds of p ...