The Earliest Unexpected Class Inspection

Abstract

Now that you have settled into your new post, I am required to evaluate your teaching performance. The semester is well under way, so the sooner this is done, the better. If we were being scientific about sampling your teaching, the class observation would be a surprise inspection. Thus reason dictates that the visit should occur on the first day that you do not believe it will occur. But on reflection, this is an impossible demand. Could I give the inspection next Monday? No, because you would realize that Monday is the first available unexpected day. What about the next class on Tuesday? Well the previous elimination would make Tuesday the first available unexpected day. Hence, it falls prey to the previous reasoning. And indeed, parallel reasoning would eliminate all of the remaining days. Hence, the earliest unexpected inspection is impossible. Since we hired you in a buyer's market, you have obviously noted the resemblance to the surprise examination paradox. But you may have not noticed that the elimination proceeds in the reverse direction. It is odd that such a reversal could be effected by substituting a definite description ('The event will occur on the first unexpected day') for an existential generalization ('The event will occur on an unexpected day'). But that's logic for you. Thus I am compelled to take refuge in philosophy department's custom of asking you to propose a day for the class visit.