PARADOX

You may often hear the word "Paradox".Many of you even experienced it. The paradox is a statement or proposition that proves itself wrong with its conditions or you can say a self-contradictory statement. Sometimes, a paradox consists of two contradictory results which prove each other wrong but apparently, both are right and vice versa. Paradox will lead your mind to an endless loop. The paradox is slightly complex yet one of the most interesting thought-provoking problems. Paradoxes were firstly made by Greek philosophers. They believed that paradox was a great way for people to think differently. Some philosophers made paradoxes very difficult to think so they can establish themselves over other philosophers. In 1961, famous logician and philosopher named W. V. Quinne divided paradox into three categories in his book:

1. Veridical paradoxes (paradoxes of verification): In this category, the result of the proposition is absurd but logically it's true. As an example, we can choose the birthday paradox. Imagine someone born on 29th February in a leap year. After 40 years if he says that he is 10 years old he is not right actually but logically he is right because his birthday appeared only 10 times.
2. Falsidical paradoxes: In this category, the conclusion seems to be false and actually is false but the statement tries to prove the result to be true by some incorrect assumption. We can take the arrow paradox as an example. In order to hit a target first of all an arrow must travel the first half of the distance. Then for the other half, it must travel the first half of that half. In this way, it will take infinite times to hit the target. But we all know it is not true.
   
3. Antinomies: In this category, a statement ends up with two results which are both true or both false but the statement is presented in such a way that if one result is true the other can't be true. The same goes for false. Let's talk about the word "verb".Verbs are some words used to describe the action. But the word "verb" is a noun itself. These kinds of words are called heterological words.We have gone through the categories now we will observe some famous paradoxes

• Bertrand Russell's Paradox: According to the internet burtrendRussel's paradox is the most famous paradox also known as the Russell-Zermelo paradox. It is based on mathematical set theory.

Let R={x|x not belongs to x} then R belongs to R.

Let's understand with an example called The Barber Paradox. In a town, there is only one barber. He shaves only those people who don't shave and he must shave them. So who will shave the barber? If he doesn't shave then he is one of them who doesn't shave his own selves. Then he must shave but if he does so he becomes a man who shaves so it leads us to a contradiction.

• The Liar Paradox: The liar paradox is one of the easiest paradoxes to understand. Suppose there are 10 men and every one of them is a liar. Among them, one man tells you "Every one of us is a liar." It is true that every one of them is a liar but the man is telling the truth. So if he is telling the truth he is no more a liar but his statement then becomes a lie. So, he becomes a liar again. This goes on and on.
• Zeno's Paradoxes: Greek philosopher Zeno made many paradoxes. Those were falsidicial paradoxes. One of the paradoxes is The Achilles and the tortoise paradox. Achilles and a tortoise are running in a race where Achilles is much faster than the tortoise. Achilles was behind the tortoise when they started running. In order to surpass the tortoise Achilles must reach the starting point of the tortoise. By that time the tortoise will travel some distance. So Achilles has to reach there but the tortoise will move further. So Achilles won't be able to defeat the tortoise. But from the motion laws of Newton, we know if Achilles' speed is more than the tortoise's speed Achilles can easily defeat the tortoise.
  
  
  
  
• The Grandfather Paradox: This paradox is related to time travel.If time travel is possible what happens if u go to the past and kill your grandfather before your father's birth.If your grandfather dies then your father as well as you won't be born. So you will not be there for killing your grandfather. It creates an endless loop.
• Hope you understood the basics of paradox.Though paradoxes are very difficult to solve many logicians are trying to find out the conclusion.Some paradoxes are unsolvable.Though paradox creates a dilemma in our mind and provokes our thoughts, it is very entertaining and gives our brain a real challenge. You also should try to make and solve some paradoxes and share them with your friends to enrich your thinking capability.