ellauri096.html on line 251: Robert Binkley (1968) anticipates van Fraassen by applying the reflection principle to the surprise test paradox. The student can foresee that he will not believe the announcement if no test is given by Thursday. The conjunction of the history of testless days and the announcement will imply the Moorean sentence:
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 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 264: Second, the future mental state envisaged by Binkley is only hypothetical: If
ellauri096.html on line 267: Third, the principle of reflection may need more qualifications than Binkley anticipates. Binkley realizes that an ordinary agent foresees that he will forget details. That is why we write reminders for our own benefit. An ordinary agent foresees periods of impaired judgment. That is why we limit how much money we bring to the bar.
ellauri096.html on line 269: Binkley stipulates that the students do not forget. He needs to add that the students know that they will not forget. For the mere threat of a memory lapse sometimes suffices to undermine knowledge. Consider Professor Anesthesiology’s scheme for surprise tests: “A surprise test will be given either Wednesday or Friday with the help of an amnesia drug. If the test occurs on Wednesday, then the drug will be administered five minutes after Wednesday’s class. The drug will instantly erase memory of the test and the students will fill in the gap by confabulation.” You have just completed Wednesday’s class and so temporarily know that the test will be on Friday. Ten minutes after the class, you lose this knowledge. No drug was administered and there is nothing wrong with your memory. You are correctly remembering that no test was given on Wednesday. However, you do not know your memory is accurate because you also know that if the test was given Wednesday then you would have a pseudo-memory indistinguishable from your present memory. Despite not gaining any new evidence, you change your mind about the test occurring on Wednesday and lose your knowledge that the test is on Friday. (The change of belief is not crucial; you would still lack foreknowledge of the test even if you dogmatically persisted in believing that the test will be on Friday.)
ellauri096.html on line 271: If the students know that they will not forget and know there will be no undermining by outside evidence, then we may be inclined to agree with Binkley’s summary that his idealized student never loses the knowledge he accumulates. As we shall see, however, this overlooks other ways in which rational agents may lose knowledge.
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:
9