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?