Abstract
The teacher announces a surprise quiz next week, one whose particular date won’t be predictable in advance. It can’t be given on Friday, since then the students would know on Thursday night that it was coming the next day. But then it can’t be on Thursday, since then students would know on Wednesday night that it was coming the next day. And so on. So the quiz cannot be given on any day. The solution is to introduce intermediate degrees of belief. Each day that the quiz does not occur, the students increase their credence that it will occur the following day, up till Thursday night, when they should still be unsure whether the quiz will come on Friday or instead be cancelled.
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This chapter’s paradox goes back at least to O’Connor 1948. According to Rescher (2001, p. 112n19), the paradox was discussed by Quine in a paper circulated in the early 1940s and later published as Quine 1953, though the paradox’s inventor is unknown (Quine does not claim the credit). Quine’s version concerns a scheduled hanging, but I find the quiz version much nicer.
To forestall overly cute responses to the coming paradox, assume that the professor’s announcement includes the information that there will be one and only one quiz that week.
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Scriven (1951, p. 403) makes this point.
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Or perhaps they would both accept and reject it . . . and thereafter accept every proposition.
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Some authors interpret surprise in terms of lack of knowledge or justified belief (O’Connor 1948; Levy 2009, pp. 136–7), rather than merely insufficient credence. Pace Levy, the assumption that the students are self-aware, good reasoners renders mention of justification superfluous – the students will have a high credence in p if and only if they are justified in having a high credence in p. Mention of knowledge is similarly unnecessary for understanding the paradox.
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References
Cave, Peter. 2004. “Reeling and A-Reasoning: Surprise Examinations and Newcomb’s Tale”, Philosophy 79: 609–16.
Cohen, Laurence Jonathan. 1950. “Mr. O’Connor’s ‘Pragmatic Paradoxes’”, Mind 59: 85–7.
Janaway, Christopher. 1989. “Knowing About Surprises: A Supposed Antinomy Revisited”, Mind 98: 391–409.
Levy, Ken. 2009. “The Solution to the Surprise Exam Paradox”, Southern Journal of Philosophy 47: 131–58.
O’Connor, Daniel J. 1948. “Pragmatic Paradoxes”, Mind 57: 358–9.
Quine, Willard van Orman. 1953. “On a So-Called Paradox”, Mind 62: 65–7.
Rescher, Nicholas. 2001. Paradoxes: Their Roots, Range, and Resolution. Chicago, Ill.: Open Court.
Scriven, Michael. 1951. “Paradoxical Announcements”, Mind 60: 403–7.
Wright, Crispin and Aidan Sudbury. 1977. “The Paradox of the Unexpected Examination”, Australasian Journal of Philosophy 55: 41–58.
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Huemer, M. (2018). The Surprise Quiz. In: Paradox Lost. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-90490-0_6
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DOI: https://doi.org/10.1007/978-3-319-90490-0_6
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