There are plenty of sarcastic ways to solve The Barber paradox depending on the wording. You could say the barber is a woman or that he does not live in that village or that he just grows a beard or can’t grow a beard (both of these still require him to shave though), but in the end you have to conclude that, strictly speaking, such a barber cannot exist.
So what the hell was the point Russell?!
Well actually it was just an interesting variation on Russell’s Paradox which exposed a problem in the foundations of Mathematics*. It states that any collection of something is a set. And there are some sets that do not contain themselves (the set of all Sci-ənce fans is not itself a Sci- ənce fan so it does not contain itself). But then there are the corollary sets that do contain themselves (the set of all things other than Sci-ənce fans is itself something other than a Sci-ənce fan and therefore contains itself).
Now pull back and consider the set of all sets that do not contain themselves.
Not containing itself in this set would mean that it itself was a set that does not contain itself and therefore it would belong in the set, which would make it not a set that does not contain itself. A paradox.
Are you still with me? Fuck it, it took me like ten minutes to try to simplify and phrase that correctly.
The point is when I hear something like this, I can’t let it go until I’ve digested it, and now that I’ve got it, I’ve got it. This, I think, lies at the heart of human ingenuity.
The fact that we can pass on a complex idea someone had 100 years ago through language and culture separates us from the clutches of natural selection and gives us educated decision making capabilities (that we were able to make these kinds of choices was probably selected for to begin with). We don’t have to invent ideas from scratch like evolution does through trial and error, instead we pass on and build off each other. Our inbuilt desire to learn more drives us to understand these things, and understanding such things drives us to want to learn more. A self-perpetuating system that once released, had no way of staying confined.
So I guess the question is, once we discovered that we had a choice to free ourselves from nature’s zombie-like process, did we really have a choice to do anything other than that?
Talk amongst yourselves.
Ah the barber’s paradox. This is the sort of stuff you use to kill robots. But as the comic above–and the various other solutions that have been smartassed over time–shows, its really hard to not find some sort of tricky solution outside of mathematics where you have the luxury of having no greek symbol for ZZ Top. But I imagine the math would look like this:
shaves(ZZ Top, Φ) :- male(X), not shaves(X,X),-female(λ).
Where Φ sort of looks like a pair of cheap sunglasses and we substitute λ for legs because it is the sexiest of the greek letters, and she knows how to use them.
Alright, I made that shit up. But my point is please be careful with paradoxes. They’re fun on paper, but should never be used in dire circumstances. The crazy bridge keeper is not going to let you pass while he tries to figure out the liar’s paradox. Similarly you should not try to be clever if a crocodile steals your baby. You’re not going to confuse the crocodile. He’ll probably just eat the kid anyway.
If you like logic, and you like comics, you really need to read Logicomix, an illustrated account of Russell’s life, his contemporaries, and his search for the Foundations of Mathematics.
This post was brought to you by Radium (Ra).
*The solution to Russell’s Paradox was proposed and known as Zermelo-Fraenkel set theory wherein they get rid of some of those pesky set problems.