PERA-DOXES

A paradox is a statement that on the surface makes no sense at all, yet cannot be disproven. They exist in many academic fields, including physics and mathematics. Here are a few logical paradoxes, with tips on how you could pass a lazy Friday afternoon by trying them out.

PARADOX OF THE COURT
A student of law tells his professor that should he win his first case, he will pay the professor $500. Before the student gets his first case, the professor sues him for that $500. If the student wins the case, he must give his professor the $500. If he loses, then the court will order him to pay $500. This is an interesting scenario: there does not seem to be a way for the student to avoid paying $500. The case is so flimsy that he is almost certain to win. And if he by a freak chance loses, he still has to pay. This is an interesting paradox to adopt in real life, and you could try it if the money is high enough. However, the legal costs and time invested into the case might well exceed the value of the amount disputed so you should be careful with this one.

SOCRATIC PARADOX
“I know that I know nothing.” A simple enough statement that has been quoted as an example of the deep wisdom and humility of Socrates. Yet, does it make sense? How can you know nothing if you do know that you know nothing? Knowing nothing is the still the act of knowing something. Black is after all a colour, zero a number, and Atheism a belief system. However, black is also the absence of light, zero the absence of value, Atheism the absence of anything to believe in. Can we classify absence as just being another sort of presence? Socrates didn’t know nothing, of course. He knew his own name, he knew how to speak Greek, he knew how to wear a toga; it doesn’t matter. Socrates may have been exaggerating, but the phrase remains powerful and irresolvable.

THE LIAR’S PARADOX
“I’m lying.” Is this true? Then I’m not lying. If it isn’t true, then I am lying, and it’s true. But if it’s true, then I’m not lying, and had been lying about lying, so it was true. Is the sentence a truth? Is the sentence a lie? This is the ultimate self-referential paradox; it contradicts itself, and you simply can’t beat it. However, you can be beaten quite easily so you’d best be careful about trying to baffle your friends with this one as a punch in the face hurts.

THE LIAR’S PARADOX
“I’m lying.” Is this true? Then I’m not lying. If it isn’t true, then I am lying, and it’s true. But if it’s true, then I’m not lying, and had been lying about lying, so it was true. Is the sentence a truth? Is the sentence a lie? This is the ultimate self-referential paradox; it contradicts itself, and you simply can’t beat it. However, you can be beaten quite easily so you’d best be careful about trying to baffle your friends with this one as a punch in the face hurts.

BURIDAN’S BRIDGE
Plato guards a bridge. Socrates is going to cross it but Plato stops him saying, “The first sentence you speak has to be true, else you cannot cross and will instead be thrown into the water.” Socrates, being Socrates, says, “You will throw me into the water.” This is quite like the Liar’s Paradox in how the scenario goes. Plato is stumped because he can only throw Socrates off the bridge if Socrates lied, i.e Socrates can only be thrown off the bridge if he can’t be thrown off the bridge. He can only cross the bridge if he can’t cross the bridge. You could re-enact this paradox with a simple puddle, a plank and a friend who has nothing better to do than to have you perplex him/her. However, don’t feel too smug about yourself because there is one easy way to beat this paradox.
Plato can let Socrates cross… and then run after him and throw him off the bridge.