The barber paradox
Suppose there’s a barber who shaves only those who do not shave themselves. The question is, does the barber shave himself?
That was the question I posed in a previous article. The hint to the answer was actually given in the article: “What if your original assumptions were wrong?”
So let’s begin, with two fictitious men, John and Ricky. John has this unfortunate streak of accidental cuts, so he doesn’t shave himself if he could help it. Ricky has this inexplicable fear of people wielding sharp objects around his face (ever watched Sweeney Todd?), so he shaves his own beard.
It’s actually a mathematical question on logic. So forming the statements, we have:
If John does not shave himself, the barber shaves John.
If Ricky shaves himself, the barber does not shave Ricky.
Here’s the interesting part. Let’s substitute “John” and “Ricky” with “the barber”.
If the barber does not shave himself, the barber shaves the barber.
If the barber shaves himself, the barber does not shave the barber.
Either way, the statements don’t make logical sense, each contradicting itself and creating a paradox. So what went wrong?
The statements were correctly formed. It’s our original assumption that’s wrong. What’s our original assumption? That
there’s a barber who shaves only those who do not shave themselves
So the correct answer is, there’s no such barber.
Comments
6 Responses to “The barber paradox”
Sign up now to get your free ebook of "How to self-publish an online magazine". Your email is kept confidential, and is used only to send information about the magazine.
Hi! I write about maths and programming and other topics of esoteric interest. I'm also the editor of the online magazine Singularity, and you can get the latest issue at the top (it's free!).
hehe, I like it. I like it a lot.
Hi Kevin, glad you liked it. And stop cutting yourself!
Damn it lol, at least I gave it a do.
I meant a go, don’t know what I was thinking there.
“gave it a do” reads fine. Besides, d and g are just an f key away
[...] Or being able to say, “That red dragon died because I missed with my Barber’s Paradox.” [...]