Coercive logic

Coercive logic is a concept popularised by mathematician Raymond Smullyan, by which a person who has agreed to answer a question truthfully is forced to perform an undesired action, where not doing so would mean breaking their agreement.^[1] Smullyan presents the concept as a question:

Suppose I offer you a million dollars to answer a yes/no question truthfully, would you accept the offer? If so, you shouldn't, for I would then ask: Will you either answer no to this question or pay me two million dollars? The only way you can answer truthfully is by answering yes and then paying me two million dollars.^[2]

Smullyan's question is asking the reader whether at least one of the two options is true:^[3]

1. They will truthfully answer no to his question.
2. They will pay him two million dollars.

The reader is unable to truthfully give an answer of no, as doing so would be to assert that both of the statements were false: "no, my answer is not no" and "no, I will not pay you two million dollars". The first of these is a self-contradictory statement.

If the reader answers yes, they cannot be saying that "will truthfully answer no" is true (as they did not answer no), so must be asserting that "will pay two million dollars" is true. Therefore, they must give Smullyan two million dollars.^[3]

Smullyan credits the name of the process to his son-in-law Jack Kotik.^[2]

References

1. "The Bulletin of Symbolic Logic". Association for Symbolic Logic. 2009. Retrieved 3 March 2020. {{cite journal}}: Cite journal requires |journal= (help)
2. Smullyan, Raymond M. (2012). The Riddle of Scheherazade: And Other Amazing Puzzles, Ancient and Modern. Knopf Doubleday Publishing Group. ISBN 978-0-307-81983-3. Retrieved 3 March 2020.
3. Rosenhouse, J. "Coercive Logic". scienceblogs.com. Retrieved 3 March 2020.