A logically self contradicting statement is a paradox. Also known as antinomy. You can say it is a sentence that runs contrary to one’s expectations. Actually it’s just a smart mess. It does have valid reasoning but leads to a self contradictory or a logically unacceptable conclusion. It might seem absurd but is kind of the ultimate truth. That’s what makes it all the more interesting.

Let’s see some of the many interesting paradoxes that exist and try to understand them.

•Achilles and the tortoise 🐢🏃

One of the “greatest” there is. It was put forward by the Greek philosopher Zeno of Elea in the 5th century BC. It so happens that the great hero Achilles challenges a tortoise to a footrace. Being the hero that he is, he allows the tortoise a headstart of 500m. No doubt, when the race starts, Achilles is at a must faster speed than the tortoise such that by the time he has reached the 500m mark, the tortoise has only walked 50m further than him. When he has reached 555m mark, the tortoise has walked another 0.5m, then 0.25m, then 0.125 m and so on. It is a chain of such infinite small distances with the tortoise always moving forwards while Achilles always has to catch up. Now, logically, Achilles can never overtake the tortoise. Except, of course, intuitively he can overtake.

Don’t think of it in terms of distances and races but rather as an example of how finite value can always be divided an infinite number of times, no matter how small its divisions might become!

This is personal favourite. It is maths based by the way. Probability to be specific. You have already heard of this probably. It goes like this that in a group of 23 randomly selected people there is a 50% chance two of their birthdays match. Interesting? Wait. In a group of 367 random people there is a 100% possibility atleast two of their birthdays match. Sounds like such a small number. It counts as a paradox because we can’t handle such numbers.

A crocodile snatches a young boy from the riverbank. Pretty common situation right? Anyways, his mother pleads with the crocodile to return the boy. The crocodile being in a fun mood, wants the mother to guess if he will return the boy or not. Takes one guess to get the boy out safely. It looks simple – the mother guesses he will return the boy, if she is right she gets the boy, if she is wrong, the crocodile gets the boy. 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. And if she is indeed wrong and the crocodile did intended to return the boy, the crocodile must then keep him even though he intended not to, thereby also breaking his word. It’s a brain twisting dilemma.