Paradoxes Prepared by L. Gilmore
What is it? • A paradox is an argument where the premises, if true, infers a conclusion that is a contradiction. • Paradoxes are self contradictory because they often contains statements that are both true, but cannot be true at the same time.
Let’s start with some basic examples: • A wise fool • Deep down, you’re really shallow. • If you didn’t get this message, call me. • Nobody goes to that restaurant because it’s too crowded. • Now we’re going to explore some more complex examples of paradoxes
Catch-22 This phrase originates from Joseph Heller’s novel of the same name. In this book, the main character experiences a paradox when he is fighting in war. He wants to get out of combat flight but the only way that will happen is if he is evaluated by the on-site doctor and found unfit to fly and “insane.” In order to be evaluated, he must first request an evaluation. However, the act of requesting an evaluation means he would be considered “sane.” The Catch-22 is that any person who wants to get out of combatflight isn’t really insane! (excerpt)
Buridan’s Ass • Picture this…a donkey is placed between a delicious pile of golden hay and a delectable pail of crystal clear water. Both items are the exact same distance away from the donkey. The donkey is equally hungry and thirsty. So, what happens to the donkey? • He dies. Because the donkey has no clear choice, he cannot make a decision, and therefore does not make a decision.
Morton’s Fork • A paradox in which contradictory statements lead someone to the same conclusion. • John Morton was the Archbishop of Canterbury in the late 15th Century and was responsible for collecting taxes. This was his taxation philosophy: Someone who lives extravagantly is obviously rich, and can therefore afford taxes. Someone who lives modestly must be saving money, and can therefore afford to pay taxes. So, everybody can and will pay taxes!
Zeno’s Arrow • In order for motion to occur, an object must change the position that it occupies. Picture an arrow being shot through the air, and we are taking snapshots of it as it flies through the air. In any one of our snapshots that preserves an instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there. It cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.
Pascal’s Wager • During the 17th century, Blaise Pascal proposed this argument in favor of believing in God: If you wrongly believe in God, you lose nothing (death is the absolute end). If you correctly believe in God, you gain everything (eternal bliss). On the other hand, if you do not believe in God and you are right, nothing happens (death is still the absolute end). However, if you do not believe in God and you are wrong…OOPS.
Achilles and the Tortoise • Achilles challenges a tortoise to a race and gives the tortoise a head start. Each runner runs at a constant speed (one fast and one slow), so after some finite time, Achilles will have run to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance to a second point. It will then take Achilles some further time to run the distance to the second point, by which time the tortoise will have advanced further. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.