Just a thread to discuss your favorite paradoxes. My two favorites are as followed: Liar Paradox: Let L be the Classical Liar Sentence. If L is true, then L is false. But we can also establish the converse, as follows. Assume L is false. Because the Liar Sentence is just the sentence "L is false," the Liar Sentence is therefore true, so L is true. We have now shown that L is true if, and only if, it is false. Since L must be one or the other, it is both. Ravens Paradox: (1) All ravens are black. Via contraposition, this statement is equivalent to: (2) If something is not black, then it is not a raven. In all circumstances where (2) is true, (1) is also true—and likewise, in all circumstances where (2) is false (i.e., if a world is imagined in which something that was not black, yet was a raven, existed), (1) is also false. Given a general statement such as all ravens are black, a form of the same statement that refers to a specific observable instance of the general class would typically be considered to constitute evidence for that general statement. For example, (3) Nevermore, my pet raven, is black. is evidence supporting the hypothesis that all ravens are black. The paradox arises when this same process is applied to statement (2). On sighting a green apple, one can observe: (4) This green apple is not black, and it is not a raven. By the same reasoning, this statement is evidence that (2) if something is not black then it is not a raven. But since (as above) this statement is logically equivalent to (1) all ravens are black, it follows that the sight of a green apple is evidence supporting the notion that all ravens are black. This conclusion seems paradoxical, because it implies that information has been gained about ravens by looking at an apple. Couldn't find a cleaner version of this one.
one of my favorites from a book frull of them that I read in HS, was... if a man is tasked with guarding a bridge, and the man can tell if you are lying, and his instructions are to kill anyone who tries to cross the bridge who lies about their reason for crossing it, and a 2nd man comes to the bridge and says, "I am here so that you can kill me", what does the first man do? If he kills him, he'd be violating the rule because the man was being honest. If he doesn't kill him, he makes him a liar and then would have to kill him, thereby making him honest, which means... ouch that hurts!
yeah that is the liar paradox. I believe in the story Socrates is crossing the bridge and Plato is guarding but in this version they say throw in the water. It is a very good one.