Who Shaves the Barber’s Beard: A Catch-22 and a Paradox too

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  • Post by  Jacob Smith Nov 24, 2014

 

Who Shaves the Barber’s Beard

 

 

A Catch-22 and a Paradox too

 

 

Well, what can we say, except, of course, that there’s sometimes just not enough sense to make sense of it all. But can we really ever expect to make sense of it all? Let’s set reasonable expectations for ourselves, okay? Okay. Here’s where office chit chat took us this past week, and we thought it might be worth sharing, if only to give you an opportunity to exercise your minds for a moment. So, here goes…

 

Looking today at two concepts that have become colloquial terms/anecdotes in modern usage, and two notions that are certainly linked (but just how we will have to explore together), we have catch-22, made famous by Joseph Heller’s iconic 1961 novel of the same name, as well as the infamous barber’s paradox, also known as Russell’s Paradox because of it’s use by philosopher Bertrand Russell to illustrate the logical basis for a paradox.

 

A catch-22 has come to mean any situation in which a problem requires a solution, but the solution is made impossible by the nature of the problem itself. For instance, having lost your glasses presents a catch-22, because, in order to search for them, you would need your glasses to see where you are looking. The original use, in Heller’s novel, appears in the form of a bureaucratic military rule, wherein if a soldier is deemed insane, that soldier may be discharged, however, said soldier must request a discharge, the act of which denotes sanity, which then precludes the requested discharge. Thus, there is no way out of the endless loop of military service.

 

Eerily similar is the barber’s paradox, in which a small village, where every man is clean-shaven, has but one sole barber (who is male), and this barber shaves all those, and only those, who do not shave themselves. The question, then, is: who shaves the barber? And here is where we encounter the paradox. If he shaves his own beard, as some of the other men in the village who do not have him shave their beards do, then he would, in turn, not shave his own beard. But if he does not shave his beard, then, like the men in the village who come to him for a shave, he would shave his own beard. An alternative explanation of the paradox is that either option – him shaving himself or going to the barber (who is himself) – causes him to shave his own beard, but the condition of the initial clause disqualifies this as a possibility, because he shaves only those men who do not shave themselves.

 

Either way, this creates a real headache, and, to be frank, what looks a lot like a catch-22 of sorts. So we have catch-22s and barber’s paradoxes, all of which amount to getting exactly nowhere fast, and scratching our heads raw in the meanwhile [and, therefore, forcing us to make an appointment with some barber (but perhaps not the really confusing one from the parable) to get our recently pulled-out hair evened up] just for, well, what exactly we were hoping you could help us out with. The biggest riddle we can see in the whole literary, logistical scramble is why exactly there is a town where every man in the whole godforsaken town remains clean-shaven! What the hell kind of town is that, and, more importantly, why would anyone want to live there? We’d prefer the town where there are several barbers who all encourage their clientele to grow their beards really long, but still take very good care of them, so that they look healthy and brilliant for all to appreciate. Yeah. That’s what we’re talking about. Thanks for listening.

 

 

- Jacob Smith