It reminds me about the logic puzzle of the criminal sentenced to death, where the judge says "you will be executed on or before Sunday, and you won't know what day it will be until we come for you."

The criminal knows it can't be Sunday, because he would wake up on Sunday and know he was going to be executed that day. But if Sunday isn't possible, on Saturday he would know he was being executed that day; so Saturday wasn't possible either. The same reasoning can be repeatedly applied to every day between now and Sunday.

It's obviously flawed reasoning (Surprise! they execute you on Thursday), but the flaw is difficult to articulate.