My intuitive solution to the paradox would simply be that although the prisoner can "deduce" that he won't be hanged on Friday, he can only make that statement if it gets past Thursday. In other words, the paradox relies on the statement (statement A), "If I am not hanged by Thursday, then I can conclude that I will be hanged on Friday".

We can decompose this statement to two statements 1) and 2):

1) I am not hanged on Thursday, and 2) I am hanged on Friday

Then statement A is of the form 1 $\rightarrow$ 2. From elementary logic, this statement is true if 1 & 2 are both true, 1 is false + 2 is true, and 1 is false + 2 is false. However as of the time the prisoner makes the statement, 1 hasn't happened yet, so the prisoner doesn't know if 1 is true or false. Therefore, 2 can also be true or false, and so the prisoner can't make conclusions at all. The prisoner can deduce that he will be hanged on Friday only if the hangman doesn't knock on his door by Thursday noon, but right until Thursday 11:59:59am, he can't make conclusions.

The problem with my solution is, of course, if it were correct I'd have expected someone else to have thought of it and resolved the paradox (since the solution is so elementary). But that hasn't happened, and the logicians working on the paradox focus on the word 'surprise' instead. What's the error in my solution?

• It's a surprisingly deep question. Many words have been expended on it. Here's a nice article about it that addresses your question and many others: jstor.org/stable/2024364 – dbx Dec 19 '17 at 1:20
• As you suspected, it's not that easy. And the prisoner can make deductions just fine, well before Thursday noon in fact. For one, the prisoner can dedue that if he will be hanged by Friday, then Thursday noon will come and pass, and so he will know he will be hanged, contrary to the assumption that he doesnt. So, before it is Thursday noon he can already deduce they cant wait until past Thursday noon to hang him. ... or so at least the reasoning goes. – Bram28 Dec 19 '17 at 2:12
• One interesting thing is that you can actually carry out the experiment if you change the problem to something more benign, like giving your friend 7 boxes numbered 1-7, only one of which contains a certain item, and tell them to open exactly one every day, in order. Before giving the boxes, flip a random coin to secretly place the item in either box 3 or 4 (but do not tell them that procedure). Tell them only "on the day you find the item, you will be surprised" and they actually will! – Michael Dec 19 '17 at 4:20