What is Bertrand Russel's Barber Paradox?

“Why Russell’s Shaving Man Can Never Exist”

Proposed by Bertrand Russell in the early 1900s, the Barber Paradox introduces a town where every single resident must be clean-shaven. There exists a barber in this town who only shaves residents who do not shave themselves.

These statements may seem simple at first, but a paradoxical proposition arises: Who shaves the barber?

The ground rules of the paradox are as follows:

1. The barber is one who shaves all those, and those only, who do not shave themselves.

2. Everyone in the town must be clean-shaven.

There are a few minor additional assumptions as well.

• One: that everyone’s face grows hair and thus needs to be shaven.

• Two: that the barber needs to be shaved.

• Three: that the townspeople can only shave themselves; no one else.

If the barber shaves his own face, then he shaves someone who also shaves themselves. This breaks the initial rule that the barber can only shave people who do not shave themselves. However, if the barber does not shave himself, then he breaks the second rule stating that everyone in the town must be clean-shaven. The question then remains: Who shaves the barber?

Despite the paradox’s popularity, it’s actually not even a paradox in the pure sense of the word. A man who shaves exactly those men that do not shave themselves by definition cannot exist, and consequently there’s no reason to expect otherwise.

Understanding this assumption provides an answer to this paradox and gives the source as to why it’s so infuriating. There is no answer; it’s impossible. The answer to the Barber Paradox is just that the statements themselves are equivocally false. Bertrand Russell created the paradox to examine our understanding of classes and groups in logical theory. In the end, he stated that in its original form the barger paradox is just noise without meaning. In this, his intention shines through: to create logical noise that appears paradoxical but is simply impossible.

That was all from my side. Do share your perspective regarding the said paradox. I am always ready to wrestle inside the comment box.

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