Can there really be a surprise quiz?

Somehow, in all my years in school, I never stumbled upon this classic bit of logic.

...can students really be "surprised" when the teacher tells them it will happen?

On Friday, a high school teacher announces to his class that there will be a surprise quiz some time during the next week. "By surprise," he states, "I mean that, the night before the quiz, you will not be able to deduce that the quiz will be the next day." A clever student raises his hand and says, "Well, the exam definitely cannot be on Friday because on Thursday night, we would be 100% certain that the exam would be the next day. But then, the exam cannot be on Thursday either because, knowing that it cannot be on Friday, on Wednesday night we could deduce that the exam must be on Thursday. By similar reasoning, it is impossible to give the exam on Wednesday, Tuesday, or Monday. Therefore, your claim that you will give a surprise quiz next week is clearly false."

This is clearly a silly paradox. If you add the possibility that there might not be a quiz, the logic breaks down. Still, can students really be "surprised" when the teacher tells them it will happen?

To truly surprise students, the teacher must never let on that there might be a quiz. Having no inkling of the quiz is the only way to make it a real surprise. Students beware!