101 Philosophy Problems Part 4: The Hairdresser of Hindu Kush

Or, more traditionally, Russel's Paradox, or the Barber's Paradox.

The paradox as presented by Cohen is horribly worded, and doesn't even manage to reach the status of contradiction, but that's not really anything new. In it's standard "barber" form, it goes:

Imagine a town with only one male barber, the Elders of the town are seriously committed to everyone having neat hair, so they require *by law* that the barber cuts the hair of everyone, and only those people, who does not cut their own hair. No-one else in the town is allowed to do any hair cutting. Everyone's hair must be cut.

So, does the barber cut his own hair? Obviously he can't, because then he wouldn't be allowed to cut it by law, but he must, because no-one else can cut it either. Blah, blah. The conclusion, one would think, is that this is a really silly law. Bertrand Russel certainly thought so (and never endorsed the "paradox" in this form).

However, it is supposed to be a version of Russel's real paradox - "The set of all sets which do not contain themselves". This set, it seems can neither contain itself or not contain itself, as either would lead to a contradiction. However, to simply declare that, like the barber, this set doesn't exist is rather rash - it undermines the axiomatic set theory that Russel spent a lot of his life developing. Luckily, it doesn't undermine Zermelo-Fraenkel Set Theory, so mathematics didn't entirely collapse in on itself.

101 Philosophy Problems Part 3 - Protagoras

Problem 3 is very similar in nature to problem 1 - it's just another classical, and mildly more complicated rewording of the Epimenides paradox (actually, I think it's probably Russel's paradox). Anyway, it was so uninteresting that it's taken me three month to write this, but here goes:

Protagoras was a lawyer, and a teacher. He was a teacher so confident in his own abilities that he used to agree very unorthodox remuneration packages with his students - with one, Euathlus, he agreed that he would receive *no* payment unless the student won his first case. Having completed his training, Euathlus decided that he didn't want the shame of losing a case, but he also didn't want the cost of paying Protagoras: his solution? Don't take on any cases.

Protagoras' was not happy with this turn of events, and decided to sue for his tuition fee. His argument was simple. If Eualthus won, he had won his first case, and must pay Protagoras. If he lost, then he had to pay Protagoras by order of the court. Either way, Protagoras must be paid.

Eualthus, however, had obviously been listening in his lessons. He argued that if he won, he did not have to pay Protagoras, by order of the court. However, if he lost, he clearly would not have to pay by virtue of their agreement.

To me this has never seemed either very interesting or very paradoxical - Eualthus should win, as he hasn't yet won a case. Then Protagoras can sue him *afterwards* for the tuition fee (as Eualthus will now have won his first case). However, if we are to take the paradox at face value, it is simply another liar paradox, which we will meet again, and discuss at greater length at that juncture.

101 Philosophy Problems Part 2 - Whaddya Know?

It's taken me a while to write this post because I wasn't sure if I really had anything interesting to say. Well, apparently I did have some stuff to say - I'm probably not a good judge of whether or not it's interesting.

This is the second problem in the book, and it is also available online here (same place as the last one). It's about knowledge, and I'm not sure how interesting it is - I think it's probably a real philosophical problem as opposed to one of those which doesn't even make sense to think about. It's about the nature of knowledge:

THE COW IN THE FlELD*

Farmer Field is concerned about his prize cow, Daisy. In fact, he is so concerned that when his dairyman tells him that Daisy is in the field, happily grazing, he says he needs to know for certain. He doesn't want~ just to have a 99 per cent idea that Daisy is safe, he wants to be able to say that he knows Daisy is okay.

Farmer Field goes out to the field and standing by the gate sees in the distance, behind some trees, a white and black shape that he recognises as his favourite cow. He goes back to the dairy and tells his friend that he knows Daisy is in the field.

At this point, does Farmer Field really know it?

The dairyman says he will check too, and goes to the field. There he finds Daisy, having a nap in a hollow, behind a bush, well out of sight of the gate. He also spots a large piece of black and white paper that has got caught in a tree.

Daisy is in the field, as Farmer Field thought.

But was he right to say that he knew she was?

Well, I think the answer is obviously no. He wasn't, was he? Imagine the dairyman had found out that Daisy wasn't in the field, then it couldn't possibly be true that he "knew" she was there when she wasn't? Could it?

One issue which Cohen fails to address in his discussion of this problem which I think is actually interesting is whether or not it is possible to know something that isn't true. Cardinal Ratzinger "knows" that Christopher Hitchens is going to Hell (I was going to say he knows I'm going to Hell, but I doubt he knows who I am, I guess he's heard of Hitchens). Hitchens "knows" that he isn't. Clearly one of them is wrong, but both would be very confident in their knowledge. Nor is this phenomenon restricted to untestable propositions like the existence of Hell - homeopaths "know" that their medicine works. I "know" that it doesn't. We both know that I'm right - but in what way does this affect our definition of knowledge?

Cohen proposes that knowledge be defined as that which is true, believed, and believed for a good reason. He then asks us what we need to add to this definition to explain why we don't think that Farmer Field knows that Daisy is in the field. He doesn't come to any conclusions. Nor can I - which leads me to wonder whether this is an interesting question after all. When we both know what knowledge is - "we know it when we see it" - does it really matter if we have a concrete definition? And if we did have a concrete definition, would "knowledge" necessarily be the same thing as "connaissance" - I think the problem of translation is one of the main reasons I can never get too interested in debates about the meanings of words.

101 Philosophy Problems Part 1

Problem One is Cohen's version of a classic. It is already available online here, so I don't feel at all bad about doing this one. Cohen has "Judge Dredd" doing the execution, but I'll pick a version I encountered many years ago:

I heard the story of a sailor stranded on a lost island.
Unfortunately (for the sailor), that island was inhabited by some very bad guys.
The bad guys said to the sailor:

"You are to be executed. As we're slightly insane bad guys, we will allow you to say one phrase.
If you speak a false sentence, you will be boiled in oil;
If you speak a true sentence, you will be hanged by the neck your until you die."

Cohen's answer to this problem is (essentially) you should say "I will be boiled in oil". Clearly, they now can't boil you in oil or hang you by the neck until you die (they could, of course, just feed you to the native fauna without breaking the rules of their game - Cohen's scenario attempts to get round this, but doesn't quite succeed).

Well - that's just boring. Firstly, there's an infinite list of statements which have the same self-negating truth properties as "I will be boiled in oil". Starting from the obvious "the statement is not true", and ranging to some more intriguing ones:

• "Quand precedé par sa traduction en francais entre guillemets n'est pas vrai" when preceeded by its translation into French in quotation marks is not true.
• This sentence claims to be an epimenides paradox but it is lying.
• If the meanings of "true" and "false" were switched then this sentence wouldn't be false.

To be fair, Cohen does have some more about Epimenides later on, so we'll let that part slide for a while, but there's still more to this problem. What about trying something where they just *couldn't know* if the statement was true or false? If I were ever captured by this insane band of epistemological hardliners I'd probalby say something like "the number I'm currently thinking of is larger than 78". Or what about "every even number can be written as the sum of two primes". As I've remarked before, if they did then execute you, at least you'd have the benefit of knowing something that no man in history has ever known before.


There is much more to Judge Dredd's tale than Cohen gives it credit for. The same, in my opinion, will be true of several of the other stories when we come to them.

101 Philosophy Problems Part 0

Just before Christmas I got a book by Martin Cohen called 101 Philosophy Problems. Martin Cohen is apparently the editor of The Philosopher and a "lecturer" - whatever that means, he doesn't actually work at a university, but then, since I'm not really sure if "philosophy" is a real discipline anyway I'm not sure what to think about that.

Anyway, so far as I'm aware none of the problems he addresses are original (although all of the little fables that introduce them probably are) so I'm going to go through the book and post my thoughts on the problems as I go along. I'm mostly doing this because I find some of Cohen's answers very unsatisfying - not just in the sense that they don't answer the questions, but in the sense that they don't even seem to notice why the question is interesting.

I'm not entirely sure it's legal for me to do this. I'm fairly sure it should be though. I'll discuss that in more detail if and when I come to problem 32... The next post will be Problem 1.