## What is the barber shop paradox?

foundations of mathematics …to be known as the barber paradox: A barber states that he shaves all who do not shave themselves. Who shaves the barber? Any answer contradicts the barber’s statement.

**Who created Barber paradox?**

The barbershop paradox was proposed by Lewis Carroll in a three-page essay titled “A Logical Paradox”, which appeared in the July 1894 issue of Mind.

### How Russell’s paradox changed set theory?

In 1901 Russell discovered the paradox that the set of all sets that are not members of themselves cannot exist. Such a set would be a member of itself if and only if it were not a member of itself. This paradox is based on the fact that some sets are members of themselves and some are not.

**What is the barber paradox?**

The barber paradox is a puzzle derived from Russell’s paradox. It was used by Bertrand Russell as an illustration of the paradox, though he attributes it to an unnamed person who suggested it to him.

#### Which answer contradicts the Barber’s statement?

Any answer contradicts the barber’s statement. To avoid these contradictions Russell introduced the concept of types, a hierarchy (not necessarily linear) of elements and sets such that…

**Does the barber shave himself?**

Specifically, it describes a barber who is defined such that he both shaves himself and does not shave himself, which implies that no barber exists. The barber is the “one who shaves all those, and those only, who do not shave themselves”. The question is, does the barber shave himself? Answering this question results in a contradiction.

## How many barbers are there in the shop?

They explain that there are three barbers who live and work in the shop—Allen, Brown, and Carr—and some or all of them may be in. We are given two pieces of information from which to draw conclusions.