101 Philosophy Problems

Martin Cohen

• Publisher: Routledge
• Year: 2013
• ISBN:
  9781135088774
• Edition: 4
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

Does Farmer Field really know his prize cow, Daisy, is in the field? When is an unexpected exam not wholly unexpected? Are all bachelors (really) unmarried? Martin Cohen's 101 Philosophy Problems, Fourth Edition introduces philosophy in an entertaining but informative and stimulating way. Using philosophical puzzles, conundrums and paradoxes he skilfully unwraps some of the mysteries of the subject, from what we know - or think we know - to brainteasing thought experiments about ethics, science and the nature of the mind.

For the Fourth Edition there are many new problems, including Maxwell's Moving Magnets, Einstein Changes Train Times, and Zeno's Paradox of Place; as well as two brand new sections including puzzles such as Lorenz's Waterywheel, and the Battle for Fractal Farm, and perplexing ethical dilemmas. The book has been extensively revised to bring it up to date with new developments in philosophy and society.

With an updated glossary of helpful terms and possible solutions to the problems at the end of the book, 101 Philosophy Problems is essential reading for anyone coming to philosophy for the first time.

Discussions

Problem 1: The Cow in the Field

This is a good place to start our philosophy problems because philosophers, even more than farmers, are concerned about practical knowledge. And many people would say that, given human frailty, it is enough to say that we know something if:

• we believe it to be the case;
• we have a good, relevant reason for our belief;
• and it is so.

This is knowledge as ‘justified true belief’.

However, in Farmer Field’s case, he has satisfied all these conditions, and yet we still might feel he did not really know that Daisy was in the field.

This problem is also set out in Plato’s Theaetetus (201c–210d), and, in slightly more formal language, has perplexed many philosophers ever since, particularly since the twentieth-century interest in ‘analytic’ philosophy. In this example, Farmer Field:

• believed the cow was safe;
• had evidence that this was so (his belief was justified);
• and it was true that his cow was safe.

Despite this, we might still feel he didn’t really ‘know’ it. What this all suggests is that a different definition of ‘knowledge’ is needed. Yes, all knowledge may have to be ‘true, justified beliefs’, but not all true, justified beliefs seem to be knowledge. So many philosophers would say that what is needed is a more complicated (!) account – to get around this sort of counter-example.

This rejection of the three conditions as jointly still ‘insufficient’¹ has encouraged a few of them to simply add an extra rule: nothing inferred from a false belief counts as knowledge. But this is, of course, a bit tautological, tautology being the last refuge of the philosopher.

Other approaches have tried to dispense with the first requirement, allowing someone to know without necessarily believing, while others wished to make the criterion for ‘knowing’ to be something more than just belief, suggesting instead that what is required is ‘acceptance’, whatever that is ….

The problem of how to find rock-bottom certainty is the underlying theme of much Western philosophy, as practised by the ancient Greeks and epitomised by René Descartes (see Problem 3) in his questions to himself while meditating in his sixteenth-century oven room. He thought he’d found the answer in the certainty of his own existence as a thinking being, famously encapsulated in the words cogito ergo sum – I think therefore I am. This, René believed, was something that he definitely did know – not just believed to be the case.

Problem 2: The Raven

Or what even if the effect is more permanent and the raven stays green? For everything not black is not a raven ….

The problem could be posed as ‘all swans are white’, which was thought to be equally certain, until, of course, black swans were discovered alive and well in Australia. Which just goes to show that even a dire issue like this can have some bearing on reality. To avoid this sort of rude intrusion happening again, many philosophers prefer to discuss whether or not all bachelors are unmarried men, whether 2 + 2 = 4, or whether water needs to be composed of molecules of one oxygen and two hydrogen (see Problems 47–58). The discussion can then centre on whether the terms are analytic or synthetic, true a priori or a posteriori² and so on, and scientists can be left to their tentative, empirical study of the world. The court philosopher in this way may be trying to turn an ‘inductive’ question into a ‘conceptual’ one. But what about the green raven? It is probably – a posteriori – a synthetic raven.

Problem 3: Descartes’ Big Problem

The answer is, of course, you don’t. It seems unlikely that either you’re dreaming or suspended in a vat of chemicals (or both, as happens at some health clubs), but then computers of today are getting very sophisticated (and demons always have been). Anyway, we only know it’s unlikely by referring to other experiences that we’ve already had, all of which may have been made-up tricks too.

In fact, as René Descartes famously observed while curled up in an old French stone oven, there’s only one thing that anyone can be sure of, and that’s that there are thoughts. You can’t be ‘tricked’ into thinking you are thinking, because the trick still requires your thinking. Cogito ergo sum, as it goes in Latin – ‘I think therefore I am.’ Although, the ‘I’ in this can’t be taken too literally to refer to anyone in particular – only to a ‘thinking thing’.

This one certain truth, from which Descartes deduced the rest of the world, might better be translated as ‘There is a thinking thing thinking things.’Or then again, maybe not.

Anyway, who is the ‘thinking thing’? No one knows for sure. Perhaps it’s God.

Problem 4: The Hanging Judge

The ‘hanging judge’ is a slightly different case of the ‘All Cretans are liars’ type of paradox, which has kept philosophers from Aristotle to Zeno, and back again to Aquinas, busy for countless years. The riddle originated with the ancient Greek philosopher Epimenides, who is supposed to have claimed that people from Crete always told lies. This was not only somewhat racist, but somewhat inexplicable, as he himself was from Crete. If it was true, then what he himself was saying should have been a lie, but if it were a lie, then …. The truth of the claim affects the circumstances in which it is uttered which affects the truth of the claim, which … etc., an infinite twisting and turning of the truth. Effectively, the statements are neither true nor false, although they look like they ought to be. Unlike sentences such as, say, ‘Hello, vicar’, which do not need to be given a ‘truth value’.

And what did the prisoner say? ‘I will be hanged tomorrow’ (or something similar) will suffice to get him off. The Chief Executioner cannot execute him then because, clearly, the relatives could then sue her for wrongful execution arguing that the Philosopher had been telling the truth when he said ‘I will be hanged tomorrow.’ Likewise, if the Chief Executioner accepted this limitation and opted to send the Philosopher to prison, he might well be sent straight back, with the governor lacking the authority to admit him. For the governor would see that the Philosopher has clearly lied to the court again and so the punishment should have been execution after all.

Problem 5: The Hairdresser of Hindu Kush

The alarming thought that occurs to the hairdresser is, what is he to do about his own hair? Whatever he does, he seems to break one or other of the rules.

The ‘barber’ paradox, as this is more usually known, is a version of a very old concern that has come to the fore ever since the philosopher Bertrand Russell came across it in the early years of the twentieth century. Russell rather inelegantly summed it up as the problem of the ‘set of all sets that are not members of themselves – is it a member of itself?’ He was so appalled at the implications of the paradox, not only for logic, but for mathematics and even ordinary language, that he wrote in his autobiography that his life’s work seemed dashed to pieces, and that for weeks he could scarcely eat or sleep. He sent the paradox to his co-worker, the mathematical philosopher Gottlob Frege, who commented that ‘arithmetic trembles’.

A number of solutions have been suggested. One is that the hairdresser should try to outwit the guards with a bit of clever argument; another is that the hairdresser should arrange a nasty shock for himself with the aim of making all his hair fall out. However, neither of these devices really gets to grips with the fundamental problem.

In his magnum opus of a book, Principia Mathematica, Bertrand Russell undertook to find solutions to no less than seven incarnations of the paradox, and worked on his reformulation thus: Is the set of all sets that are not members of themselves a member of itself, or is it not, and if it is not, is it? Admirably precise though this specification of the problem is, it does not actually help resolve the contradiction, and so Russell took the drastic step of saying that all statements which refer to themselves should be ‘outlawed’, or at least treated as meaningless. Unfortunately, a great many meaningful statements are self-referential – arguably, that is what makes them meaningful.

Problem 6: The Tuck-Shop Dilemma

Jane will be thinking that if she does not confess, and nor does Janet, they will both have to be let off by Dr Gibb. However, if she does not confess and Janet does, then she will be expelled! Perhaps, then, the safest thing to do is to admit to stealing from the tuck-shop and be suspended for the rest of the term.

This, in fact, is the way guilty people do reason when put in similar situations. As long as they cannot communicate with their accomplices, and thus promise each other to keep ‘mum’, prisoners will mitigate their losses by confessing – even though the best solution requires them not to. (Of course, innocent people clinging to their principles may adopt a course of action which is totally irrational and causes them much more bother than confessing would have done.)

The first time this problem was set out was in 1951 by Merrill Flood in America, and since then ‘The prisoner’s dilemma’ has spawned wide discussion of the nature of ‘rationality’ and a new study, ‘Game theory’. This looks, for instance, at what is likely to happen in a situation like a global nuclear arms race, where both players are better off if neither upgrades their weapons, and the worst situation is if you don’t and the other side does. As in the problem, recent history shows the middle option prevails – both sides spend all their money on upgrading their weapons without getting any military advantage. At least, until the element of communication is introduced, at which point trust can blunt the horns of the dilemma.

Problem 7: Protagoras’ Problem

It is said that the court was so puzzled that it adjourned for 100 years. The paradox is that both ways of thinking seem to be correct, but they lead to two opposing conclusions.

This is a ‘classic’ problem – indeed, a classical problem – such as the ancient Greeks liked to discuss over a cup of wine. It’s not a ‘trick’ – or if there is one, no one has discovered it yet. Neither Euathlos nor Protagoras can be faulted on their logic – but both of them can’t be right. Which tends to undermine logic, and with it the basis for most of our reasoning. Which is why the Ancients considered these problems so interesting.

My learned friend adds:

Lawyers have also been very interested in the paradox, even if it never reached the celebrated Court of Areopagus, which was probably too busy trying animals and inanimate objects for murder. In part, this is because many bits of legal jargon refer to themselves, for example, saying things like ‘this law is no longer valid’, or even ‘this book is copyright’ (it is, but only by virtue of containing the announcement itself). Then again, there are many complicated legal ‘circles’ such as occur occasionally with insurance policies which attempt to exclude losses ‘covered by other policies’.

In the Ohio State v. Jones case in 1946, Protagoras’ problem was specifically cited in evidence. Dr Jones was being accused of carrying out an illegal operation on a Ms Harris. The case relied crucially on Ms Harris’ testimony that she had asked him to carry out the operation, and that he had then done so. The problem for the judge was that if Dr Jones had carried out an illegal operation, then Ms Harris was an accomplice, and her evidence was suspect and legally unsound. In this case, both the lower court judge and the Court of Appeals allowed the matter to be decided (illogically if necessary) by a jury. These non-philosophers simply ignored the cunning circularity and found the devious Dr Jones guilty.

Problem 8: The Unexpected Exam

Maybe a little bit like Zeno’s classic ‘Achilles and the tortoise’ paradox, there really is no flaw in Bob’s reasoning, but it still doesn’t work. Each step of the argument Patricia put is correct, and so is the conclusion – but (unfortunately for classes everywhere) it just doesn’t match reality!

Problem 9: Sorites

The question is, which of the three ships is the original Thunderprow? The material one on the trestles, the one being used or the mental one in the mind of the designer? Or is it another?

This is a similar problem to that facing someone trying to identify how many grains of sand make a ‘heap’, although it also raises questions about ‘identity’, whatever that is! As far as the sand heap goes, you might think this easy, at least to estimate, but try adding one grain to another and it is clear that the distinction is unreliable. (And imagine you get punished if you add unnecessary extra grains of sand to the heap!) Humans specialise in ‘fuzzy thinking’ whereby we put together inadequate information to come to a conclusion. But when it comes to reasoning, even humans rely on one iron distinction – that between what is and what is not. So, if it is impossible to say how many coins in a bowl would make a beggar rich, or how many grains of sand make a sandpit, it is also impossible to say when blue is not green, when an inch is really an inch, and so on. It’s worse than saying all our reasoning relies on approximations – because what are the approximations being compared to?

Problem 10: A Problem Arranging Ship Battles

At first sight, the philosopher’s best line is that Cassandra’s claims are indeed true – or false – but that as no one, on Earth at least, can know which one it is, so they may as well suit themselves. Yet clearly the gullible people have decided that she is the better judge of which it is, so this option is shut off.

The problem is, if the warnings are ‘true’ when Cassandra makes them, the events have then...