I did understand the paradox. Those are the instructions he was given: he won’t know the date of his execution until he is told. He performs some reasoning, an

I did understand the paradox. Those are the instructions he was given: he won’t know the date of his execution until he is told. He performs some reasoning, and concludes that he can’t get executed any day that week: therefore he will go free. But if “he will go free” is a possibility, then his chain of reasoning falls apart. Previously he had argued “if I survive to the last day, I will be executed today. That won’t be a surprise. Therefore I can’t be executed on the last day.” But once he has “…or I won’t get executed at all” as an option, then his reasoning would begin “if I survive to the last day, then either I’ll get executed today, or I won’t get executed at all” … and that’s as far as he can go. He can’t use that to conclude he won’t get executed on the last day, and he can’t then use that to conclude he won’t be executed on the second last day, and so on. The entire argument breaks apart immediately.