What is a Paradox?

A paradox is a statement or situation that results from sound reasoning, but its conclusion is self-contradictory. Paradoxes can range in subjects from mathematics to science, but this article will focus on philosophical paradoxes.

The Ship of Theseus

The Ship of Theseus, also called Theseus’ Paradox, is perhaps the most well-known of the paradoxes on this list. The paradox originated in Ancient Greece and has been provoking interesting debates for centuries now. The Ship of Theseus comes from a Greek myth: the mythical king of Athens, King Theseus, rescued the children of Athens from King Minos, defeated the minotaur, and then left on a ship bound for Delos. To celebrate this, each year the people of Athens would go on the ship and set sail to Delos to honor Apollo. However, as time had passed, they would have to replace some of the boards, as they had started to rot. Thus, ancient philosophers proposed that, if there were no pieces of the original on the current ship, would it still be the Ship of Theseus? If it was not, then when had it stopped being the original ship? Essentially, this ancient paradox begs the question: Is an object the same after all of its original pieces have been replaced over time?

Achilles Paradox

Also named after a Greek hero, the Achilles Paradox is one in a series of philosophical arguments made by Zeno of Elea, an ancient Greek philosopher. These paradoxes question the notions of time, space, plurality, and motion, claiming that these lead to logical contradictions. The Achilles Paradox states that a fast runner such as Achilles cannot pass a slower-moving tortoise with a head start. The paradox claims that the distance between Achilles and the tortoise can be infinitely subdivided, so Achilles would need an infinite number of steps to catch up to the tortoise. These paradoxes have inspired many mathematical and philosophical discussions throughout the centuries.

The Paradox of Fiction

Also known as the paradox of emotional response to fiction, the paradox of fictional questions how people can become emotional over fiction: how are people emotionally affected by what does not exist? The paradox involves three statements: 

1. People are emotionally affected by things that they know are fictional.
2. For people to be emotionally moved, they need to believe that these things truly exist.
3. No one who thinks something to be fictional believes it to be true.

All three statements seem to be true individually, but if any two points are considered true, the third one must be false or contradictory.

Polanyi’s Paradox

In his book, The Tacit Dimension, British-Hungarian philosopher Michael Polanyi presents the theory that human understanding of how the world works and of our abilities is beyond our explicit comprehension. In other words, Polanyi proposes that there are many tasks which we intuitively know how to accomplish but could not put it in words for others to understand. He states that people rely on tacit knowledge, knowledge that is difficult to articulate, rather than explicit knowledge, knowledge that can be easily articulated. To put it simply, as said by Polanyi himself, “We can know more than we can tell.”

Buridan’s Bridge

Also known as Sophism 17, this self-referential paradox is proposed by Jean Buridan, a famous medieval philosopher, in his book Sophismata. In the paradox, Socrates wants to cross a river when he comes upon a bridge that Plato guards. Plato says to Socrates that if the first proposition Socrates makes he speaks the truth, then Plato will let him cross the bridge, but, if he does not speak the truth, then Plato will throw him into the water. Socrates replies that Plato will throw him into the water. Thus, Plato cannot throw Socrates in the water, because it would break his promise to allow Socrates to pass if he speaks the truth. However, he cannot let Socrates pass, because that would mean that Socrates did not speak the truth. This problem has been intriguing philosophers for ages and there have been many different proposed solutions to this problem. One answer is provided by the character of Sancho in Miguel de Cervantes’ Don Quixote. In the book, Sancho proclaims, “They should let him pass freely, as it is always more praiseworthy to do good than to do evil.”