Paradoxes are really interesting but yet very frustrating. Paradox is when two things while still sounds logical, it contradicts each other. Here are 10 mind teasing paradox to torture your brain.

### 10. Liar Paradox

With variations of paradox, this is one of the most famous contradiction. One version is the Epimenides Paradox, where if a Cretan say “All Cretans are liar” he would be telling the truth and so not all Cretans are liar but if his statement is true, as he is a Cretan, he would be lying, implying not all Cretans are liars and so it repeats. You get the idea. Another very famous version is the Pinocchio paradox. As we all know Pinocchio is a children’s book character whose nose grows with every lie he tells. So in this paradox, if Pinocchio says “My nose will grow”, and it did not grow, he would be lying. Therefore, as he lied, his knew would grow but his nose grew, so he told the truth and his nose should know grow. This can go on and on. Frustrating isn’t it. Other variations include the Card paradox, Quine’s paradox and Yablo’s Paradox.

### 09. Barber Paradox

This paradox was used by Bertrand Russel, a British philosopher, though he heard it from someone else. Here’s how the paradox goes, In this town the Barber is the one who “Shaves all, and only all those who does not shave themselves”. So, what makes it a paradox? It is the question “Does the Barber shave himself”. This contradicts itself, as if the barber does shave himself, then the statement is not true as he would be shaving someone who shaves himself. If the Barber does not shave himself, then he is eligible according to the statement, thereafter, if he shave himself it goes against the statement again. This become a paradox when both situation is not possible. Or he could simply hire another barber to shave him.

### 08. The Omnipotence Paradox

This paradox was introduced by Averroës dating back as far as the 12th century. Also called the paradox of the stone, it questions “Could an omnipotent create a stone so heavy that even he could lift it?”. The Omnipotent on one hand has no limits to its ability while the stone on the other hand should be created such that it cannot be lifted by anything. If you have not figure out the paradox already, if the omnipotent has no limit to its capabilities, it is able to create a stone so heavy he could not lift, but at the same time as he ability is endless, he should be able to carry even the heaviest of stones. This two subjects contradicts itself. Others argue that an omnipotent despite having many abilities it still does have their limit. Nevertheless, based on the definition of omnipotent this paradox still contradicts itself. Previous version of paradox of the same includes “Can god deny himself’ and a more advance version, “Can god create a triangle with internal angles that does not make up 180 degrees”. Both this version is introduced by Christian theologian and philosopher, Pseudo-Dionysius the Areopagite in the 6th century.

### 07. Raven’s Paradox

Concept of this paradox is different from the few mentioned. This is known as a logical paradox. The paradox concludes that by looking at a green apple, we can tell that Raven’s are black. Proposed by a German logician Carl Gustav Hempel in the 1940s, the Raven paradox includes 4 different statements which relates to each other. The first statement “All ravens are black” which is the same as saying this second statement “If something is not black then it is not a raven”. This implies that if the first is true, the second is true, and if the first is false, the second is false. Third statement, “Nervermore, my pet raven, is black” this is evidence to the first statement. The paradox comes in the fourth statement, “This green (and not black) thing is an apple (and not a raven)” stating that because it is not black it is not a raven. From this we can come to a conclusion about a raven simply by looking at an apple. This paradox is to reason out that hypothesis cannot be made base on our sense of sight (Inductive reasoning). Much like how we can see the sun, stars and moons move across the sky, in early civilization believed this meant they revolve around the Earth.

### 06. The Unexpected Hanging Paradox

One of my all time favorite paradox, this paradox is another logical paradox originally to a prisoner hanging or in other variations, a surprise school test and fire drill. The story is a judge tells a prisoner he is to be hanged next week at noon on a weekday which would be a surprise, he would not know until the executioner knocks on his door at noon on the surprise day. Upon reflection the prisoner concluded that the hanging would not occur, firstly as it was on a weekday, Saturday & Sunday is out. Then, if the hanging has not occur by Thursday it would not be a surprise anymore as he would know it is happening on Friday. He applied the same logical reasoning for Thursday, when Friday is eliminated, if it has not happen by Wednesday, Thursday would not be a surprise anymore. With the same reasoning, he used it on Wednesday, Tuesday and Monday concluding that the execution cannot happen and it will not happen. However, he was still executed on Wednesday despite all that time wasted. However, logically while that is true he did use the word ‘If’ meaning it is only a presumption that it did not occur a day before.

### 05. Paradox of the Heap

Widely known as Sorites (Greek for heap) Paradox, was attributed to a philosopher, Eubulides of Miletus. This paradxox involves a heap of sand with each grain individually remove until only a single grain of sand is left. Is it still considered a heap? Maybe not but at which point did it stop being a heap of sand? Another way it can be observed is if we have 100 000 grain of sand it is a heap if we remove one grain, 99 999 grain of sand is still a heap, continuing until we have 1 grain of sand, it should still be considered a heap. What if we reverse the paradox, with a single grain we add a grain individually. Is it already considered a heap when there is two grain of sand? How many grains should there be until it is considered a heap of sand? Raising questions like this makes it a paradox. This type of paradox is termed vague paradox.

### 04. Unstoppable Force Paradox

Very much like the Omnipotence paradox, this physical paradox involves an unstoppable force as the name suggest and an immovable force. Originating from a 3rd century book, Han Feizi, this paradox written in Chinese tells a story of a man selling a spear and a shield. When asked how good the spear is, he said it can pierce through any shield and when asked the same about the shield, he replied it can stop any spear attacks. One then asked him, what would happen if the spear (Unstoppable force) hits the shield (Immovable object), he was unanswerable. This is then self-contradictory paradox. Another ancient paradox of the about the same idea involves a Teumessian Fox who can never be caught and a hound, Laelaps who never misses what it hunts. This then raise the question what if the hound hunts for the fox? Moving back to the unstoppable force against and immovable object, scientifically it is said that for a force to be unstoppable, it has to possess infinite amount of energy while for an object to be immovable, it has to have infinite mass. Realistically speaking both is impossible but theoretically it is said that it would cause a huge explosion. Some theorized the force would just bounce off which sounds illogical. It is still great to ponder on.

### 03. The Paradox of the Court

Introduced from ancient Greek, this paradox also known as Counterdilemma of Euathlus involve a sophist, Protagoras and his pupil, Euathlus. Protagoras took Euathlus as his student with the agreement that Euathlus would pay his teacher the full amount only after he has won his first. After the course was finished, the pupil decided not to continue a career in law. Protagoras then decided to sue Euathlus, the total amount owed for the teachings. This become paradoxical as either way the judge rules, winning or losing, it could benefit either of them.** Protagoras claims:** Based on the court ruling, in the case Euathlus won, he would have won his first which base on their original contract, he would have to pay Protagoras. If Protagoras won the case, he would still get back his money. **Euathlus claims:** In the case he won, he would not have to pay Protagarus by the court decision and if Protagoras won, he would not have won his first case and based on their original contract he is not obliged to pay. This is less of a paradox, more of a genius plot.

### 02. Grandfather Paradox

One of the many famous types of paradox is a time travel paradox. Time travel can be a very complicated subject, introducing all kind of questions and paradoxes however you go about it. If you have watched the 1985 film, ‘Back to the Future’ or DC comics television series, ‘The Flash’, you will notice many of the things does not make sense. One common time travelling paradox is the Temporal paradox, whereby a time traveler goes back to the past and does something that would prevent him to travel to the past in the first place. The grandfather paradox is one of the more well-known type of temporal paradox. Let’s say you are a time traveler and for whatever horrible your grandfather has done to you, you decided to travel back to the past, 45 years ago when he was still a teenager living his life, and kill him. As he did not exist, your mother or father would then cease to exist, therefore, making your existence impossible. The paradox here is that, as you no longer exist, you would not be able to travel back to the past and kill your grandfather, so he would still live and you would then exist. Not a good idea now huh? Well, there is still theories such as multiple timelines which could solve this paradox. But let’s not hurt our brain too much with it.

### 01. Monty Hall Problem

Popularized by a television game show ‘Let’s make a deal’, this mathematical paradox is named after its host, Monty Hall. May get a little complicated but bear with me. So you’re in a game show, the host offers you three doors, one of which has a car and the other two has a car behind it. Let say you pick door number one, and the host shows you behind door number three is a goat and asked you to make a switch. Should you make the switch? The answer is yes as it has a 2/3 chance of having a car behind it. The mathematics behind it is that originally you have a 1/3 chances of choosing the right door, after a door is eliminated the chances of the vacant door rose to 2/3. Why? To simply put, if you had pick the door with a goat, the chances of either door number 2 or 3 having a car is 2/3. If the door you pick has a car, the chance of you getting the car still remains 1/3. Don’t understand? The table below would maybe help explain it a little better.

Behind door 1 | Behind door 2 | Behind door 3 | Result if staying at door #1 | Result if switching to the door offered |
---|---|---|---|---|

Car |
Goat | Goat | Wins car |
Wins goat |

Goat | Car |
Goat | Wins goat | Wins car |

Goat | Goat | Car |
Wins goat | Wins car |

Here are there 10 mind teasing paradoxes. Although there are many more here are few of the more interesting ones. Hope you and your brain had fun processing it all, mine surely did not. Thank you for reading. Do check out my other Top 10s! Peace!