ellauri096.html on line 90: W. V. Quine (1953) agrees with Weiss’ conclusion that the teacher’s announcement of a surprise test fails to give the student knowledge that there will be a surprise test. Yet Quine abominates Weiss’ reasoning. Weiss breeches the law of bivalence (which states that every proposition has a truth-value, true or false). Quine believes that the riddle of the surprise test should not be answered by surrendering classical logic. Me too. Right on Willard van Orman Quine! Thumbs up!
ellauri096.html on line 197: Critics of Lucas defend the parity between people and computers. They think we have our own Gödel sentences (Lewis 1999, 166–173). In this egalitarian spirit, G. C. Nerlich (1961) models the student’s beliefs in the surprise test example as a logical system. The teacher’s announcement is then a Gödel sentence about the student: There will be a test next week but you will not be able to prove which day it will occur on the basis of this announcement and memory of what has happened on previous exam days. When the number of exam days equals zero the announcement is equivalent to sentence K.
ellauri096.html on line 262: informed by the teacher’s announcement, so Binkley ought not to use a model in which the announcement is as absurd as the conjunction ‘I went to the pictures last Tuesday but I do not believe it’.
ellauri096.html on line 273: The teacher’s announcement that there will be a surprise test is equivalent to a disjunction of future mistakes: ‘Either there will be a test on Monday and the student will not believe it beforehand or there will be a test Wednesday and the student will not believe it beforehand or the test is on Friday and the student will not believe it beforehand.’
ellauri096.html on line 275: The points made so far suggest a solution to the surprise test paradox (Sorensen 1988, 328–343). As Binkley (1968) asserts, the test would be a surprise even if the teacher waited until the last day. Yet it can still be true that the teacher’s announcement is informative. At the beginning of the week, the students are justified in believing the teacher’s announcement that there will be a surprise test. This announcement is equivalent to:
ellauri096.html on line 283: Although (iii) is consistent and might be knowable by others, (iii) cannot be known by the student before Friday. (iii) is a blindspot for the students but not for, say, the teacher’s colleagues. Hence, the teacher can give a surprise test on Friday because that would force the students to lose their knowledge of the original announcement (A). Knowledge can be lost without forgetting anything.
ellauri096.html on line 289: Some people wear T-shirts with Question Authority! written on them. Questioning authority is generally regarded as a matter of individual discretion. The surprise test paradox shows that it is sometimes mandatory. The student is rationally required to doubt the teacher’s announcement even though the teacher has not given any evidence of being unreliable. Indeed, the student can foresee that their change of mind opens a new opportunity for surprise.
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