The Barber Paradox
Stimulating critical thinking - a loose series on paradoxes
Gödel's is a newsletter about interweaving ideas and making decisions under uncertain conditions. I discuss knowledge management, mental models, and supporting Tools for Thought.
Imagine a small town with a single barber. This barber has set a rule for whom he shaves: He shaves all and only those men in town who do not shave themselves. At first glance, this seems like a reasonable policy, but it leads to a paradox upon closer inspection.
The confusion arises when we consider the barber himself. Does the barber shave himself? If we say 'yes' to the barber shaving himself, we run into a contradiction. According to the rule, the barber only shaves those who do not shave themselves. So, if he shaves himself, he violates his own rule. On the other hand, if we say 'no' to the barber not shaving himself, we are still left with a contradiction. If he doesn't shave himself, according to his rule, he must shave himself because he shaves those who do not.
This circular logic creates an unsolvable loop. The barber cannot exist under the rules he has set.
This paradox highlights fundamental issues in logic and set theory. It shows us the problems that can arise when a set, or a rule in this case, tries to contain itself.
Source: Bertrand Russell: The Philosophy of Logical Atomism. In: The Collected Papers of Bertrand Russell. Band 8, 1918, S. 228.