Many of us would have come across Paradoxes, and would have passed through it without realizing that it is, indeed, a Paradox. Paradox is a statement, which appears to be true and false at the same time, and has something contradictory within itself, that defies logic and common sense. Some of them appear to be seemingly absurdities but are nevertheless true.
The most common example you can see nowadays is a page in most corporate documents stating "This page is intentionally left blank" - very simple, though drilling into it, you find that the page is not blank, because this one line is already printed on it. So, it is true and false at the same time. There are varieties of Paradoxes, and it is an extremely interesting topic to be dwelt upon.
I shall quote a few examples of Paradoxes, just to kick your interest up in the subject. Once you are bought into the beauty, you will start doing your own analysis and exploration :-)
a) "I always lie" is a paradox, because if you always lie, this statement is also a lie - which would mean that you never lie, and it goes back to a cycle - meaning the current statement is true, which links back to truth Vs lies.
b) "John, an American, said - All americans are liars" - again, a classical self-referential paradox. If John is an american, and he makes this statement, his statement is also a lie - which means all americans are not liars. Again, that would contradict the original stand and go on and on.
c) Curry's Paradox - "If this sentence is true, the world will end in a week"
d) Bandwagon Fallacy: Consider a situation in which a father and son are driving down the road. The car collides with a tree and the father is killed. The boy is rushed to the nearest hospital where he is prepared for emergency surgery. On entering the surgery suite, the surgeon says, "I can't operate on this boy. He's my son." The apparent paradox caused here is by the bandwagon fallacy. The reader, upon seeing the word surgeon, applies a poll of their knowledge of surgeons and reasons that since the majority of surgeons are male, the surgeon is a man, hence the contradiction: the father of the child, a man, was killed in the crash. The paradox is resolved if it is revealed that the surgeon is a woman, the boy's mother.
e) If your birthday is on February 29 you could state the paradox that you are thirteen years old although you have only had three birthdays.
f) Classical problem of Missing One Rupee:
Three guests check into a hotel. The Cashier says the bill is Rs 30 so each pays Rs 10. Later the cashier realizes the bill should only be Rs 25. To rectify he gives the bellboy Rs 5 back to return to the guests. On the way back to the room the bellboy realizes that he cannot divide the money evenly. As they didn’t know the total of the revised bill, he decides to give the guests Rs 1 each and keep Rs 2 for himself. Now that the guests have been given Rs 1 back, each has paid Rs 9. Three times nine is 27 and the bellboy has Rs 2 in his pocket. Two plus 27 is 29. If the guests originally handed over $30, what happened to the remaining one rupee?
Think of it, and try to find an answer for this yourself ;-)