Paradox a Brain messing thing Explained || Canteen Club

What is a Paradox?

So according to the Cambridge dictionary, a paradox is “a situation or statement that seems impossible or is difficult to understand because it contains two opposite facts or characteristics”. The first idea that pops into one's mind as soon as the word paradox is introduced is like, Quantum physics, breaking laws of nature, one object being at two places at once and etc. But considering the simplicity of its definition many ordinary-seeming sentences can be considered as paradoxes. Now to get an even more clear idea of our topic let's consider a few general characteristics.

According to definitions of paradoxes,

Paradoxes usually sound reasonable and simple initially.

Like “Nobody goes to Murphy’s bar, because it is too crowded”. The sentence has the properties to be a paradox, it contains two opposite fact that the bar is crowded and that nobody goes to the bar. It sounds absurd if nobody is in the bar how can it be crowded!

Paradox feels to be true and untrue at once

Now how can a sentence tend to be true and false at once let us consider the example of such a paradox? Here is the crocodile paradox, “A crocodile snatches a young boy from a riverbank. His mother pleads with the crocodile to return him, to which the crocodile replies that he will only return the boy safely if the mother can guess correctly whether or not he will indeed return the boy. There is no problem if the mother guesses that the crocodile will return him—if she is right, he is returned; if she is wrong, the crocodile keeps him. If she answers that the crocodile will not return him, however, we end up with a paradox: if she is right and the crocodile never intended to return her child, then the crocodile has to return him, but in doing so breaks his word and contradicts the mother’s answer. On the other hand, if she is wrong and the crocodile actually did intend to return the boy, the crocodile must then keep him even though he intended not to, thereby also breaking his word”.

The crocodile paradox is an ancient mind-boggling logical problem that even shaped the word "crocodility" which means you admit something that is used against you in the future.

Paradoxical are usually self-contradictory.

We can understand this fact by previous examples too when we consider a paradoxical sentence or condition, we always initially have a clear idea or result given by the statement or situation itself but after understanding underlying logic we have to admit that the result initially concluded by us contradicts the statement or situation.

Let’s consider another example, “The Liar Paradox” it has many versions of itself, let’s understand the simplest one ‘THIS STATEMENT IS A LIE’ it is a self-contradictory statement. Saying that it is a lie while saying a lie means it is indeed can be saying the truth. Liar paradox has been studied a lot from various perspectives to know more about it read Stanford encyclopedia of philosophy on liar paradox.

Now that we have built up enough understanding about what is a paradox? Let us proceed forward. This was just to give you a rough idea of about paradoxes. We have barely scratched the surface. The above-considered properties are not criteria for a situation or statement to be paradoxical.

Sources of paradoxes can be arbitrary, let us learn about a few of them.

Thought process can produce paradoxes like the Zeno’s Achilles and tortoise paradox. Here Achilles is competing with a tortoise and the tortoise is given a head start. Given that Achilles can run at any speed and the tortoise runs at a constant pace, Achilles can never catch up to the tortoise. Let us find the solution to this, how can a man with god-like powers be defeated by a mere tortoise. Zeno argued that Achilles must reach the point where the tortoise started first, but by then the tortoise has moved on to a new position. So then Achilles must run there – by which time the tortoise has moved on again. The process goes on indefinitely and Achilles or anyone can never catch up to the tortoise; hence a paradox is created. We know practically this isn’t possible.

 Let us look at one more thought process-based paradox namely the grandfather paradox, if you can travel back to the past and kill your own grandfather when he was young, you will stop yourself from being born since your dad will never be born and after all this if you are punched out of existence then who will kill your grandfather. Eventually the timeline will form a loop and it will keep correcting itself. For deeper understanding follow the citation in the link. 

Sometimes jumping to conclusions can form paradoxes. Consider this story of a father and son, both are going in a car down the road unfortunately they crashed into a tree and the father dies. The son is left in a critical condition, he is taken to the nearest hospital. Son needed an emergency surgery but when he is taken to the operation theatre surgeon says ‘I can’t perform surgery on him, he is my son’. Some people say the story is incorrect but they took a hasty decision that the only parent in the story is the father, the surgeon can be the child’s mother. 

Paradoxes also arise due to literature-based errors like the murphy's bar sentence.

Paradoxes are also called ‘Antinomy’. Since paradoxes are studied under many subjects such as mathematics, literature, and philosophy many mathematicians, philosopher and logician have tried to classify paradoxes. Willard Quine one of the many people who tried to make the classification according to logic and maths. 

According to his classification paradoxes can be divided into three parts 

1) Veridical paradoxes: These are paradoxes in which the result seems absurd, but presented in a way that makes it appear true. It is a situation seemingly impossible or contradictory but nevertheless true. There are various examples of veridical paradoxes like the Schrödinger's cat, the Monty Hall paradox, and most of the paradox related to infinity like Hilbert’s paradox of grand hotel. Monty hall paradox is based on mathematical probability whereas Schrödinger’s cat gives the classical idea of quantum physics. Hilbert's paradox of grand hotel also known as the infinity hotel is one of the best demonstrations of the properties of infinity. The infinity hotel has an infinite number of rooms and each room has one person in it, the hotel is completely full yet it can accommodate any number of people again. It plays with number theory and concept of infinity. To understand more about these paradoxes, follow the hyperlink attached to the respective words. 

2) Falsidical paradox: Falsidical paradoxes are based on the results that do not just seem untrue but really are false. The proof derived by seemingly correct reasoning that leads to an illogical and false conclusion. Achilles and tortoise paradox come under this category. Some of you may have seen this result of being 2 = 1 on a fun fact website.  

Let us look at the Augustus De Morgan version of the result 

Let x=1  

Multiply both sides by X now x2=x

Subtract one from both sides x2-1=x-1

Now factor out (x – 1) x-1x+1=(x-1)

Now we have x+1=1

Now using the fact that X = 1 we have 2 =1

 Obviously, the result is false and the result breaks some fundamental rule in mathematics.

3) Antinomies: paradoxes that do not belong to the two previous types. They are self-contradictory in the way they are presented or in reasoning, and the contradiction was caused by the adopted principles of reasoning. Seemingly correct reasoning proves that the reached conclusion is both true and false. Grelling nelson paradox is an example of the following type. Grelling nelson paradox considers the basic way how we conceive truth. Grelling’s paradox is also similar to the Russell’s paradox, it is more like the mathematical version of Grelling’s paradox.  

In conclusion this isn’t the best classification of paradoxes and I think there is no need to classify paradoxes since each paradox is unique in itself. Philosophers, logicians, and mathematicians have spent an immense amount of their life to create and explain these paradoxes. Think harder using your understanding from this article and create a paradox of your own.