ellauri096.html on line 75: The teacher has free will. Therefore, predictions about what he will do are not true (prior to the examination). Accordingly, Paul Weiss (1952) concludes that the student’s argument falsely assumes he knows that the announcement is true. The student can know that the announcement is true after it becomes true – but not before. What a wimpy argument.
ellauri096.html on line 92: W. V. Quine insists that the student’s elimination argument is only a reductio ad absurdum of the supposition that the student knows that the announcement is true (rather than a reductio of the announcement itself). He accepts this epistemic reductio but rejects the metaphysical reductio. Given the student’s ignorance of the announcement, Quine concludes that a test on any day would be unforeseen.
ellauri096.html on line 157: The student’s overall conclusion, that the test is impossible, is also self-defeating. If the student believes his conclusion then he will not expect the test. So if he receives a test, it will be a surprise. The event will be all the more unexpected because the student has deluded himself into thinking the test is impossible.
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 257: Binkley illuminates this reasoning with doxastic logic. The inference rules for this logic of belief can be understood as idealizing the student into an ideal reasoner. In general terms, an ideal reasoner is someone who infers what he ought and refrains from inferring any more than he ought. Since there is no constraint on his premises, we may disagree with the ideal reasoner. But if we agree with the ideal reasoner’s premises, we appear bound to agree with his conclusion. Binkley specifies some requirements to give teeth to the student’s status as an ideal reasoner: the student is perfectly consistent, believes all the logical consequences of his beliefs, and does not forget. Binkley further assumes that the ideal reasoner is aware that he is an ideal reasoner. According to Binkley, this ensures that if the ideal reasoner believes p, then he believes that he will believe p thereafter.
ellauri096.html on line 259: Binkley’s account of the student’s hypothetical epistemic state on Thursday is compelling. But his argument for spreading the incredulity from the future to the past is open to three challenges.
ellauri096.html on line 279: Consider the student’s predicament on Thursday (given that the test has not been on Monday or Wednesday). If he knows that no test has been given, he cannot also know that (A) is true. Because that would imply
7