Russell’s Paradox

There is an interesting scenario which seems to be both plausible and contradicted. We can describe it in the following story:

In the town, there is only one barber, who is male. And everyone in the town should be clean-shaven owing to the new mayor’s policy. Therefore, the barber is delighted because he earns lots of money after the mayor’s policy is implemented, and then said proudly,” I’m the man who shaves all men, and only those men, who do not shave themselves.” In the same time, a child near him ask a question of him,” Who shaves you, Mr. Barber?”

We actually get an amazing conclusion about this story. That is, if the barber shave himself, then he doesn’t shave himself. It is totally weird and unbelievable in the story that seems to be able to happen around us.

It is called Barber Paradox specifically, and is an example of a more widely known paradox named Russell’s Paradox. In reality, Russell’s paradox plays a vital role in the realm of mathematics as well. It is a paradox valued by both scholars and general public, and a paradox noted for both mathematicians and philosophers.

In 1902, Russell sent a message to the Canadian math professor Gottlob Frege and told the professor his discovering of Russell’s Paradox. At that time, Gottlob Frege was about to publish his new book about set theory. In fact, the books were already printed and was about to be sent to the bookstores. After knowing Russell’s Paradox, Gottlob Frege acknowledged that there were basically errors in the book. Nevertheless, there was no time for him to revise the errors or even appendix the revise to the book. Hence, the books had been sold for only one day before withdrawn.

In the next decades, mathematicians endeavored to find a solution to make the set theory more complete, therefore leading to Zermelo-Fraenkel axioms, which are used universally in the set theory nowadays. And all that reveals that Russell’s Paradox writes an indelible page in history.