I'm grading assignments for an introductory proof class, and the following exercise is in the book:
"Are the following propositions? If so, give their truth value."
"There are more than three false statements in this book, and this statement is one of them."
The answer key says that this is a paradox, so it is not a proposition.
Now, obviously we can't be expected to actually know the truth value, but why is this a paradox? Suppose that exactly one statement in the book other than this one is false. Then the problem statement is false and there seems to be no paradox. Thanks to the conjuction, this statement can be false without contradicting itself.
The statement cannot possibly be true, however, because then it must contradict itself and it is a paradox in that case. A "conditional" paradox?