If the class accepts the two-day announcement, then they must expect the exam to fall on the first day. For if the exam were to fall on the second, then, having accepted that there would be an exam, they’d know about this by the end of the first day, in violation of the teacher’s word!As mentioned, some people find this reasoning to be suspicious, and the following delicate criticism has often been levelled against it:But now that they expect it on the first day, this violates her word as well! So they cannot sensibly accept the two-day announcement.
If the exam were to fall on the second day, then, at the end of the first, the teacher’s words would promptly “reduce”This sort of critique has been suggested by a host of writers ranging from Doris Olin to Raymond Smullyan. Its upshot is that accepting the two-day announcement does not entitle the class to expect the exam on the second day if the first day were to pass without an exam. So the class cannot “rule out” the second day in the manner proposed above, and their reasoning flounders at the start.to the one-day announcement (“There’ll be an exam tomorrow but you don’t know this”), which we know to be a blindspot for the class.At this point, far from being entitled to expect the exam on the morrow (as the reasoning above would have us believe), the class would be forced to abandon the teacher’s announcement instead. After all, it has mutated into a blindspot!
Suppose that the n-day announcement is a blindspot for the class. Then they can embrace the (n+1)-day announcement only if they expect the exam to fall on the first day of the n+1-day period in question. For, as they may be presumed to see, were the first day to be exam-free, the teacher’s words would reduce to the blindspot that is the n-day announcement, and would then ring hollow.But now that they expect the exam on the first day, her words ring hollow anyway, and so the (n+1)-day announcement is a blindspot as well.