Who Shaves the Barber?

Is mathematics shakier than we realised?

In the second half of the nineteenth century, logic awoke from a sleep of two millennia: people realised that Aristotle, with his syllogisms, had yet to have the last word on the subject. Powerful and flexible systems were developed by the English mathematician George Boole as well as by the German logician Gottlob Frege. Soon, however, logic found itself entangled in self-reference (a statement which refers to itself or its own referent). Curiously, the self-reference debate was contemporary with the discovery of quantum theory, and Austrian logician Kurt Gödel's theorem of incompleteness was proved at about the same time as the uncertainty principle, with similar effects.

One of the first thinkers to point to self-reference, while Frege's work was in press, was the British philosopher Bertrand Russell. One form of his paradox refers to a village where the barber shaves precisely those people who do not shave themselves. Who shaves the barber? In particular, does the barber

Continue reading

Enjoy unlimited access to the world's leading thinkers.

Start by exploring our subscription options or joining our mailing list today.

Start Free Trial

Already a subscriber? Log in

Join the conversation