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10 Mind-Boggling Logical Paradoxes

Humans generally like order and organization. After all, that’s how we historically made sense of the world. However, the real world works according to its own laws, much like nature does. This means that, in every sphere of human knowledge, we’re bound to run into inconsistencies sooner or later. That’s how fascinating paradoxes like the one we’ll discuss today are born. But be warned, these paradoxes have an unexpected side effect – they will make you scratch your head.

The Liar Paradox 

Famous Paradoxes Pinocchio

Let’s begin with one of the oldest and most famous paradoxes out there – the liar’s paradox. The premise is rather simple: the statement “This statement is a lie,” is a paradox. How come? Well, if the statement is a lie, then it would be stating the truth. And if the statement is true, then it would disagree with itself. In sum, the statement is self-contradictory because it’s both true and false at the same time.

There are many versions of this paradox. One of the oldest is the Epimenides paradox which dates back to 600 BC. Epimenides, a philosopher from the island of Crete, once said, “All Cretans are liars.” This included Epimenides, who was a Cretan himself. Therefore, if this statement is true, then Epimenides was lying when he stated it. At the same time, the statement would presuppose that at least one Cretan - Epimenides - was truthful when he said, “All Cretans are liars.” So then the statement would be false, which means that Epimenides was lying. This pattern of contradiction can go on until infinity.

Let’s look at one last fun version of the liar paradox. Called the Pinocchio Paradox, this version of the famous paradox poses the question: if Pinocchio said, “My nose grows now,” would his nose grow or not? Since Pinocchio’s nose only grows when he is lying, then it shouldn’t grow. But then, if the nose didn’t grow, it would mean that Pinocchio was lying… which means that his nose should grow, and so on.

The Fermi Paradox

Famous Paradoxes the Milky Way

We live on a planet surrounded by a vast universe, full of planets similar to Earth. In fact, researchers have already found several planets similar to ours in the observable universe, and there are likely millions and millions of other habitable planets in the universe. Logically, some percentage of those planets should also have developed life, and probably even advanced civilizations that have mastered interstellar travel. Why does it seem, then, that we are the only sentient beings in the universe?

The Fermi paradox is all about this dilemma. If Earth is merely one habitable planet in a universe full of them, why have no signs of extraterrestrial life discovered? This paradox was named after Enrico Fermi, a 20th-century Italian-American physicist. Since then, scientists have suggested many possible explanations for this paradox, but no firm conclusions can be made. The video below explains a few possible explanations for the Fermi paradox:

Sorites Paradox

Famous Paradoxes Hourglass

Let’s lighten the mood by shifting to a less depressing thought experiment. Called the Sorites Paradox, or the Paradox of the Heap, this dilemma points out how the language we use can be quite vague. The premise of the paradox is as follows: You have a heap of sand, a start gradually removing one grain of sand at a time.

If you remove one grain of sand from the heap, it’s logical to assume that it will still remain a heap of sand. The paradox becomes apparent when you’re left with just two grains of sand. If you remove one of the grains, can the last remaining grain still be called a heap? This paradox illustrates a philosophical and linguistic concept called vague predicates, or objects lacking sharp boundaries.

The Lottery Paradox

Famous Paradoxes Lottery Tickets

Do you like the lottery? If so, you’ll enjoy this one. In 1961, one Henry E. Kyburg Jr. posed the following scenario:

Say you bought a lottery ticket. If we assume that there are a million tickets and only one winning ticket, the likelihood of you winning is literally one in a million. 

You know that your chances of winning are quite low, so it’s reasonable to believe that you will lose. It’s also fair to assume that the following ticket will be a losing one, and so will the one after, and so on. In fact, calculations justify the assumption that every ticket you buy will be a losing one. Still, you know that one ticket will win.

So the paradox is: why is it reasonable to think that every ticket will be a losing one, even though you know that one ticket will win? This cool paradox has a lot to say about the psychology of choice, knowledge, and what it means to be rational.

Related article: These Optical Illusions Have the Internet Stumped - Can You Work Them Out?

The Dichotomy Paradox

Famous Paradoxes woman jumping over a hill

This paradox is one in a group of famous paradoxes conceived by the Greek philosopher Zeno of Elea in the 5th century BC. The name of the paradox comes from the Greek word dikhotomia, meaning "cutting in half," and it will show you the impossibility of motion.

To illustrate this famous paradox, let’s say that you are walking home. To reach home, you should first walk halfway to your destination. But even before that, you’d have to get a quarter of the way there. Moreover, to reach the quarter point, you’d have to move an eighth of the way, and a sixteenth of the way, and so on... Ultimately, Zeno concludes that one would have to complete an infinite number of tasks in order to arrive at a certain point, which is impossible. 

Since you can infinitely divide any distance into smaller and smaller parts, motion is just impossible - Zeno states. Yet, we see people and objects moving, and sometimes we even get there in time. So what’s going on? Discover the solution to this paradox in the fascinating video below:

The Irresistible Force Paradox

Famous Paradoxes Viking with a spear and shield

The unstoppable or irresistible force paradox can be framed in just one question: What happens when an unstoppable force meets an immovable object? 

Will we see the immovable object stop the unstoppable force, or will the force move the immovable object?

Two incompatible objects are forced together in this paradox, and the results are mind-boggling. In this example, we see that an immovable object and an unstoppable force cannot exist in the same world. In the event that one of these objects fails, then the defeated object can't truly be unstoppable or immovable.

A famous Chinese legend from the 3rd century BC illustrates the same paradox quite aptly. In the legend, a merchant was selling a shield and a spear. One customer asked him how durable the shield was, and he answered that it could block any spear. Another customer then inquired about the spear, and the merchant replied that it could pierce any shield. A third person then arrived and asked what would happen if the merchant took the spear and hit the shield. The merchant stayed silent, as he understood that the two statements were self-contradictory.

The Ship of Theseus Paradox

Famous Paradoxes Ship of Theseus

Let’s travel back to Ancient Greece, the origin of many famous paradoxes. This specific logical dilemma is about Theseus, a mythical hero from Athens famous for slaying the Minotaur and other heroic feats. 

During his lifetime, Theseus sailed a lot, and his ship became quite famous. The vessel was kept in an Athenian harbor as a reminder of the hero’s achievements. Over time, some parts of the ship started to decay. To preserve the famous vessel, the rotting wood planks were replaced one by one. This process of replacing old planks continued until the whole ship no longer had any original pieces of wood. The question is as follows: is this repaired vessel still the ship of Theseus? Take a look at the video below for some fascinating variations of this philosophical paradox.

This paradox raises the question of identity, and it has been the subject of philosophical debate for literal millennia. Some philosophers even expanded this idea to the identity of a person, which is exactly what the next paradox on this list is all about.

The Teletransportation Paradox

Famous Paradoxes Teletransportation

This fascinating paradox was first published in 1984 by the British philosopher Derek Parfit. In his book Reasons and Persons, Parfit asks readers to imagine a teletransporter machine. This machine makes you fall asleep, records data about the molecular composition of your entire body and divides it into atoms, and then sends all that information to another planet (let’s say, Mars).

On Mars, an identical machine rebuilds your body exactly as it was before. Scientists have also preserved all your memories, character traits, and all that makes you who you are. So let’s ask you this, “Is the person on Mars the same person that they were on Earth?” Will you still consider that person you, or did you stop existing when the teletransporter disassembled your body on Earth?

To complicate things even further, let’s assume that the teletransporter made a mistake. It didn’t destroy the original body, but still made a second copy of you on Mars. Remember, the replica shares your memories, and even claims to be you. Which of the two is the real you now?

Even though we’re not quite there yet technologically, this thought exercise questions personal identity and personal responsibility. If someone changes over time, can they still be considered the same person?

Related article: 8 International Health Paradoxes that Got Me Thinking...


The Grandfather Paradox

Famous Paradoxes Grandfather and grandson

Have you been waiting for this one? The Grandfather Paradox is one of the most iconic time travel conundrums. It’s been featured in media, including the world-famous 1985 sci-fi film Back to the Future, so it’s many people’s favorite paradox. This dilemma was first introduced in 1943 by the French journalist Rene Barjavel, who became obsessed with time travel. Barjavel asked the question: what would happen if someone went back in time to a year before their parents’ birth and killed their grandfather?

Logically, the grandad’s death would mean that one of their parents was never born, and neither did the person who murdered their grandfather. So, then, who killed the grandfather? Mind-boggling, we know! And it’s just one of many tricky time-travel paradoxes. The Bootstrap paradox, which we will discuss next, is another one in this series.

The Bootstrap Paradox

Famous Paradoxes Shakespeare

The Bootstrap Paradox questions the origins of an object transported from the future into the past. It’s another one of those ideas that’s heavily featured in science fiction plots. Let’s illustrate this idea like this: Imagine that Mary loves William Shakespeare’s Romeo and Juliet. After inventing time travel, Mary decides to travel back in time with a copy of the novel and get Shakespeare's autograph. 

When she finds Shakespeare and hands him the novel, she realizes that he had never heard of Romeo and Juliet. Baffled, Mary returns to her time, scratching her head. Meanwhile, Shakespeare copies the book and claims the authorship of the novel. Years pass, Romeo and Juliet becomes as popular as it is, and Mary’s copy lands in her hands just like before. But the question remains - who wrote the book?

Versions of the same idea appear in other philosophical conundrums. Watch this last video to see some fun twists on the Bootstrap paradox.

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