Did You Know

Philosophers have been dealing with paradoxes for centuries, and have given multiple interpretations for them. It is an incredibly interesting subject that will challenge our thought processes.

paradox is most commonly defined as a statement or a problem that contradicts itself. Even though such a statement or a problem often has valid reasoning, its conclusion defies all logic and is extremely self-contradictory. A paradox can often give us proof of something that goes against our intuition or expectations.

Philosophers have been dealing with paradoxes for centuries, and have given multiple interpretations for them. It is an incredibly interesting subject that will challenge our thought processes. Paradoxes are capable of turning everything we believed to be a fact on its head and make us doubt our common sense. That might sound confusing, but it will be clearer once we present you with our list of ten paradoxes that will bend your mind.

This is a paradox that starts with a statement that all ravens are black. We then make a counter-statement that everything that is not black is not a raven. This is also true, although it may seem unnecessary to point it out. This means that, whenever we see something that is not black, it actually proves that all ravens are black. It can be something completely unrelated, like an orange. It is not black; therefore, it proves that it is not a raven, and also that all ravens are black.

This is an example of a veridical paradox, meaning that its result is absurd but actually true and logical. This one starts with a sack of potatoes that weighs 100 pounds. The potatoes are composed of 1% solids and 99% water and are left outside in the sun. The heat reduces the amount of water in the potatoes to 98%; however, the sack now weighs only 50 pounds.

How is this possible? Wouldn’t the water weigh 99 pounds at the start, and the weight of the sack would drop to 99 pounds itself? Well, if the water content was lowered to 98%, the solid content is now 2%. This makes the ratio of solid to water 1:49, and since the solids weigh 1 pound, the water must weigh 49 pounds.

## 8. Galileo’s Paradox Of The Infinite

This paradox was proposed by the great mathematician Galileo, and it is incredibly confusing. It deals with the relationship between two different sets of numbers. We have square numbers on one side (1, 4, 9, 16, etc.) and non-square numbers on the other side (2, 3, 5, 6, 7, etc.). When these two groups are combined, it makes sense that the amount of numbers in total is higher than the amount of just square numbers.

After all, we put the two groups together, and it should make a larger group. However, this is not true because all positive numbers have a square, and all squares have positive numbers at their square roots, so it is impossible to be more or less of one than the other. Galileo wanted to show that concepts such as more or less can only be applied when dealing with finite amounts of numbers.

This paradox is another one that deals with time, so you know things will get weird. According to this paradox, if we fire an arrow, it is not actually moving. This is because, at each point in time, the arrow is considered stationary. Basically, the moving of an arrow is viewed through snapshots in time. If we look at it like that, the arrow has no time to move during the snapshot, so it can indeed be considered stationary. In a way, time is made up of an infinite number of instants, which would make this true. However, we know that it is not, and the arrow is moving.

This is a weird one, that is, in a way, tied to the Achilles and the Tortoise paradox. This paradox deals with the process of completing tasks, and the fact that each task can be divided into an infinite number of smaller tasks. For example, walking a specific distance - to reach your goal, you need to pass half of the distance first.

And to reach the halfway point, you’d need to walk a quarter of the way and to reach that an eighth of the way and so on. This means that something so simple as walking down the street actually contains an infinite number of smaller tasks, which should not be possible. Crazy, we know!

This paradox was used in the Middle Ages, and it is quite a tricky one. Time for a story! Imagine a crocodile that kidnaps a young child from its mother. The mother begs for the crocodile to return it, and finally, he replies that he will return the child if the mother can guess whether he will return it or not. If the mother says that he will indeed return it, there is no problem. If she is right, she gets the kid; if she is wrong, the crocodile keeps it.

However, if she says that he will not return it, we have a paradox. If she guesses right, the crocodile would need to return the kid, but that contradicts her answer and his word. But if the crocodile did intend to return the kid, she would be wrong, and he must keep the child. It is quite a predicament!

Another simple paradox that is confusing at the same time, the card paradox deals with a card that has something written on both sides. One side says, “The statement on the other side of this card is true,” and on the other side, it says, “The statement on the other side of this card is false.”

Try thinking about it, and you will see why this is a paradox. If both statements are true, the first statement cannot be true. However, if the first statement is false, that makes the second one false as well, but that makes the first one true. This one is confusing, and there is no solution to it, it is a really good example of a paradox.

## 3. The Boy Or Girl Paradox

This is a paradox that deals with the probability of the children in a family being of a particular sex. It is not a terribly complex formula, but we shall keep it even more simple. If a family has two children, and we know that one of them is a boy, what is the probability that the other child is a boy as well?

The most common answer is 1/2 since the child can either be a boy or a girl. However, since there are two children, there are actually four possible combinations - two boys, two girls, an older boy and a younger girl, and a younger girl and an older boy. We know that two girls are not an option in this case, but we are still left with three possible combinations, so the probability is actually 1/3.

The Bootstrap Paradox deals with time travel, so you know things can get weird. This paradox questions how an item from the future that is placed in the past through time travel could ever have been created in the first place. The item already exists in the past, so the process of its creation will not happen. Or is the time-traveling the process itself? This paradox is popular in many forms of media, including science fiction books and movies, and continues to boggle our minds.

## 1. Achilles And The Tortoise

This paradox has been one of the main topics of discussion in the theories of the Greek philosopher Zeno in the 5th century BC. This paradox deals with the race between Achilles and a tortoise. Achilles is faster, so he gives the tortoise an advantage of 500 meters before he starts to run.

Once he starts running, he is much faster, but somehow he is never able to catch up. The distance keeps getting smaller, but the process lasts infinitely. Naturally, we know he will be able to run past the tortoise eventually, but the goal of this paradox is to prove how all values (in this case, distance) can be divided infinitely.

Antonia is a sociologist and an anglicist by education, but a writer and a behavior enthusiast by inclination. If she's not writing, editing or reading, you can usually find her snuggling with her huge dog or being obsessed with a new true-crime podcast. She also has a (questionably) healthy appreciation for avocados and Seinfeld.