A judge tells a prisoner: 'You will be hanged one day next week, but you will not be able to predict the day.' The prisoner reasons that he can't be hanged on Friday (he'd know by Thursday night), then can't be hanged Thursday (he'd know by Wednesday night), and so on, concluding he can't be hanged at all. But on Wednesday, he's hanged — and is genuinely surprised. What went wrong with his reasoning? Provide a rigorous logical analysis.