Crocodile Dilemma
Encyclopedia
The Crocodile Dilemma is an unsolvable problem in logic
. 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.
The question of what the crocodile should do is therefore paradox
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
, which Richard Montague
(1960) used to demonstrate that the following assumptions about knowledge are inconsistent when tested in combination:
It also bears similarities to the Liar paradox
. Ancient Greek sources were the first to discuss the Crocodile Dilemma.
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.
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
. 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 paradox
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
ical, and there is no justifiable solution.
The Crocodile Dilemma serves to expose some of the logical problems presented by metaknowledge
Metaknowledge
Metaknowledge or meta-knowledge is knowledge about a preselected knowledge.For the reason of different definitions of knowledge in the subject matter literature, meta-information is or is not included in meta-knowledge. Detailed cognitive, systemic and epistemic study of human knowledge requires a...
. In this regard, it is similar in construction to the unexpected hanging paradox
Unexpected hanging paradox
The unexpected hanging paradox, hangman paradox, unexpected exam paradox, surprise test paradox or prediction paradox is a paradox about a person's expectations about the timing of a future event The unexpected hanging paradox, hangman paradox, unexpected exam paradox, surprise test paradox or...
, which Richard Montague
Richard Montague
Richard Merett Montague was an American mathematician and philosopher.-Career:At the University of California, Berkeley, Montague earned an B.A. in Philosophy in 1950, an M.A. in Mathematics in 1953, and a Ph.D. in Philosophy 1957, the latter under the direction of the mathematician and logician...
(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.
It also bears similarities to the Liar paradox
Liar paradox
In philosophy and logic, the liar paradox or liar's paradox , is the statement "this sentence is false"...
. Ancient Greek sources were the first to discuss the Crocodile Dilemma.
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.