Abstract
A teacher announced to his pupils that on exactly one of the days of the following school week (Monday through Friday) he would give them a test. But it would be a surprise test; on the evening before the test they would not know that the test would take place the next day. One of the brighter students in the class then argued that the teacher could never give them the test. “It can't be Friday,” she said, “since in that case we'll expect it on Thurday evening. But then it can't be Thursday, since having already eliminated Friday we'll know Wednesday evening that it has to be Thursday. And by similar reasoning we can also eliminate Wednesday, Tuesday, and Monday. So there can't be a test!”
The students were somewhat baffled by the situation. The teacher was well-known to be truthful, so if he said there would be a test, then it was safe to assume that there would be one. On the other hand, he also said that the test would be a surprise. But it seemed that whenever he gave the test, it wouldn't be a surprise.
Well, the teacher gave the test on Tuesday, and, sure enough, the students were surprised.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. R. Anderson and N. D. Belnap, Entailment, the Logic of Relevance and Necessity, Princeton University Press, 1975.
A. K.Austin, ‘On the unexpected examination’, Mind 78, 1969, p. 137.
R.Binkley, ‘The surprise test examination in modal logic’, Journal of Philosophy 65 (5), 1968, p. 127–136.
G.Boolos, ‘The logic of provability’, American Mathematical Monthly 91 (8), 1984, pp. 470–480.
M.Gardner, ‘A new paradox, and variations on it, about a man condemned to be hanged’, Scientific American 208, 1963, pp. 144–154.
D.Kaplan and R.Montague, ‘A paradox regained’, Notre Dame Journal of Formal Logic 1, 1960, pp. 79–90.
D.Kozen, ‘Results on the propositional μ-calculus’, Theoretical Computer Science 27, 1983, pp. 333–354.
I.Kvart, ‘The paradox of surprise examination’, Logique et Analyse 11, 1976, pp. 66–72.
D. J. Lehmann, talk given at IBM San Jose, May, 1985.
AMargalit and M.Bar-Hillel, ‘Expecting the unexpected’, Philosophia 13, 1984, pp. 263–288.
D. J.O'Connor, ‘Pragmatic paradoxes’, Mind 57, 1948, pp. 358–359.
D. M. R. Park, ‘Fixpoint induction and proof of program semantics’, Machine Intelligence 5 (ed. A. Meltzer and D. Michie), Edinburgh University Press, 1970, pp. 59–78.
V. R. Pratt, ‘A decidable μ-calculus’ (preliminary report), Proceedings of the 22nd Annual IEEE Conference on Foundations of Computer Science, 1981, pp. 421–477.
D.Scott and J. de Bakker, A Theory of Programs, unpublished, IBM, Vienna, 1969.
M.Scriven ‘Paradoxical announcements’, Mind 60, 1951, pp. 303–307.
R. Shaw, ‘The paradox of the unexpected examination’, Mind 67, pp. 382–384.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Halpern, J.Y., Moses, Y. Taken by surprise: The paradox of the surprise test revisited. J Philos Logic 15, 281–304 (1986). https://doi.org/10.1007/BF00248573
Issue Date:
DOI: https://doi.org/10.1007/BF00248573