The surprise test

Who doesn’t know it, the so-called “surprise test”? Here is a version that I found on the website of the Encyclopaedia Britannica (https://www.britannica.com/list/8-philosophical-puzzles-and-paradoxes): A teacher announces to her class that there will be a surprise test sometime during the following week. The students begin to speculate about when it might occur, until one of them announces that there is no reason to worry, because a surprise test is impossible. The test cannot be given on Friday, she says, because by the end of the day on Thursday we would know that the test must be given the next day. Nor can the test be given on Thursday, she continues, because, given that we know that the test cannot be given on Friday, by the end of the day on Wednesday we would know that the test must be given the next day. And likewise for Wednesday, Tuesday, and Monday. The students spend a restful weekend not studying for the test, and they are all surprised when it is given on Wednesday. How could this happen?

There are various versions of this paradox, like the unexpected hanging paradox, and the versions are also known under different names (like “the surprise examination paradox” in my case). Until now there hasn’t been found a solution to this paradox. Here I’ll ignore the proposed solutions but life is full of surprises, and often our reasoning that certain things cannot happen hold no water. The reasoning of the student that a surprise test is impossible can simply be made invalid by drawing lots. And if the teacher draws a lot that the test will be on Wednesday, it’s a surprise despite any rational argumentation, if he doesn’t tell it the students.

One of the problematical aspects of this paradox is the time perspective involved – in two ways:

1) When the student argues that a surprise test is impossible, she reasons from the past to the present: She starts her reasoning as if it is already Friday and argues back to the moment that she talks with her fellow students. From this backward perspective what happens is fixed. The teacher, however, looks from the now to the future. From this forward perspective the date of the test is yet open and can yet be changed, even if the teacher has already decided to take the test on Wednesday. Surprises exist for what hasn’t yet happened.

2) Let’s assume now that the teacher said that the test will be either tomorrow or the day after tomorrow. Would we call it a surprise test, because we don’t know the exact date? Hardly, I think, and it is to be expected that the students will study hard for the test. Now assume that the test will be taken within three days. Would we call it a surprise test? Maybe. Now let’s say that the test will be taken within two weeks. Even if we can theoretically argue that this surprise test will not be possible according to the same reasoning as in the original one-week-case, I think that most of us will think that the argument cannot be correct. And I guess that everybody will think so if the teacher had said that the surprise test will be within one month let alone if he had said in January that the surprise test will be sometime before the end of the term in June. Seen this way, everybody feels that it cannot be right that a surprise test is impossible.

So, as I see it, something is wrong with the time perspective in the surprise paradox. Be rational, just when rationality fails.

Spinoza's ass

After I had written my blog on Buridan’s ass, I discovered by chance that soon his important comments on Aristotle’s Physics, in which he discusses the case, will be reissued by the Dutch publishing house Brill (see link below). It’s remarkable, however, that Jean Buridan himself didn’t talk about an ass or donkey but that his case is about a dog:

“Suppose that a dog is very hungry and very thirsty. He is placed between a bowl with food and a bowl with water, which are at exactly the same distance left and right of him and everything else is also the same. Then the dog will die of hunger and thirst, for he will look to the one and to the other and has no reason to choose the one or the other. And since the dog cannot go to both sides at the same time, he will stay where he is and he will die of inertia.”

This example is a comment on Aristotle’s reasoning that the earth doesn’t move but is in balance among the celestial bodies, since the earth has no reason to move into one direction or another. But Buridan doesn’t agree with this reasoning at all! For he adds: “This reasoning [in the dog’s case] seems to be false and the same so for what people say about the earth.” (source: see below).

As we see, the contents Buridan’s example is basically the same as the example of the alleged “Buridan’s ass”, but it’s not about a hungry donkey but about a dog. Why then this donkey? Nobody knows who talked first about a donkey. Anyway, many philosophers have commented on the case of “Buridan’s ass”. One of them was Baruch Spinoza. I don’t know whether Spinoza thought that the example had been thought up by Buridan and whether he had read Buridan, but actually his comment is about the same as Buridan’s. Spinoza mentioned the example of “Buridan’s” ass twice in his works: In his Cogitata Metaphysica and in his Ethics. This is what he said about it in his Ethics:

“... I readily grant that a man placed in such a state of equilibrium (namely, where he feels nothing else but hunger and thirst and perceives nothing but such-and-such food and drink at equal distances from him) will die of hunger and thirst. If they ask me whether such a man is not to be reckoned an ass rather than a man, I reply that I do not know, just as I do not know how one should reckon a man who hangs himself, or how one should reckon babies, fools, and madmen.” (Ethics, Proposition 49)

In other words, Spinoza scoffed at “Buridan’s” ass, but didn’t also Buridan scoff at “his” dog, as we just have seen? Man is not an ass. That’s what Spinoza and Buridan agree about.

Sources

- Link to the web page of the publishing house Brill on Buridan: http://www.brill.com/products/book/john-buridan-quaestiones-super-octo-libros-physicorum-aristotelis-secundum-ultimam-lecturam

- Buridan’s text can be found on https://books.google.nl/books?id=hACoP3x0yPQC&pg=PA26&lpg=PA26&dq=Mais+si+cet+endroit+n%E2%80%99est+pas.+La+quatri%C3%A8me+raison+est+celle-ci:+car+dire+que+la+terre+demeure+ainsi+au&source=bl&ots=3eZHERZNYx&sig=-JPY1vYr2bwYNrrUlmxG0Filr-U&hl=en&sa=X&ei=Ih80Vd7LO82AaaDUgagC&redir_esc=y#v=onepage&q=Mais%20si%20cet%20endroit%20n%E2%80%99est%20pas.%20La%20quatri%C3%A8me%20raison%20est%20celle-ci%3A%20car%20dire%20que%20la%20terre%20demeure%20ainsi%20au&f=false

Buridan's ass

Paradoxes have always fascinated me, not only since I have become interested in philosophy but already when I was a child. I remember that once I got a book titled To Measure Is to Know. Somewhere it discussed Zeno’s paradox about Achilles and the tortoise, which I treated already shortly in my blog dated 12 December 2016. I found the paradox very intriguing and I asked my mathematics teacher about it. He said that it was nonsense and that he had never heard about it. I was surprised and I still am, for how could a teacher that had studied at the university and taught at a Dutch gymnasium not have heard about it?

I also remember that even before I had read about Zeno’s paradox I came across the problem of Buridan’s ass. Here is a description of this paradox:

“A rational hungry donkey is placed between two equidistant and identical haystacks. The surrounding environments on both sides are also identical. The donkey cannot choose between the two haystacks and so dies of hunger, which is simply irrational.”

Actually, it’s not correct to name this paradox after the French philosopher Jean Buridan (1295-1363), for philosophers before him – including Aristotle – had already examined it, although often in another version. Also after Buridan, the paradox has been discussed again and again, for instance by Leibniz.

What would you do, if you were in the same situation as the ass? So, if you were in a situation that you inescapably had to choose between A and B without having criteria to choose between A and B? Will you do like the ass, so you’ll do nothing even if it leads to your destruction?

On the face of it it looks like a perfect case of free will: You can exactly do what you like, for there is nothing that forces you to perform one action or another; to choose the left hay stack or the right haystack or to abstain from choosing. Which choice you’ll make, it will be your choice, anyhow. However, I think that the case shows that free will cannot involve that you can make any choice you like. If there are no criteria you cannot choose, with the consequence that you’ll do nothing, and you’ll die like the ass between two haystacks. The case of Buridan’s ass illustrates that freedom is only possible within limits and these limits determine your criteria.

Happily, we are not asses. Even more, according to Michael Hauskeller also Buridan’s ass will survive, as he explains on https://philosophynow.org/issues/81/Why_Buridans_Ass_Doesnt_Starve . If you have no criteria, you’ll simply choose, with a reason (even if you don’t know it) or without a reason. Doesn’t this happen so often to us, for example in a restaurant? “Imagine”, so Hauskeller, “you go to a restaurant. Looking at the menu, you discover that they serve your two favourite meals – say asparagus and spinach tart. What will you do? You may hesitate for a while, but then you will make your choice. You have to make a choice, don’t you? Even if you’re hungry or greedy enough to order both, you have to decide which to eat first.” Has it ever happened to you that you don’t choose and that they chuck you out, because the restaurant closes and you have still to make your choice? Of course not. You ask your partner for advice; you wonder what you have eaten last week; you follow your gut feelings... And when the waiter comes to note down your choice, you say “I take the asparagus” or “I take the spinach tart”. And so it happens always in life. There is always a reason, even if there’s none. That’s the way we are constituted and be happy that we are.

All things have their season. Or don’t they?

My power machine (Tacx bike trainer and Batavus race bike)

I should write yet a bit about Piketty’s Capital in the Twenty-First Century. However, I would deviate then too much from philosophy and the leading themes of these blogs: Who am I and what do I do? Even if I should interpret theses themes very broad, as I often do. So, I dropped the idea.

But who am I and what do I do? And how does this develop in the course of life? One doesn’t remain always the same. For most people it is so that – to say it shortly – first they grow and after having reached the summit decay sets gradually in and actually there is no return from that. True?

Once I was asked to write an essay on “graceful ageing” (and much of what follows now is from that essay). Then someone said to me “Becoming older is not for sissies. You fall apart physically and mentally and you get lots of wrinkles. I don’t see any grace in that.” Now I am the last to deny that becoming old is often difficult, but has it only negative aspects?

In this blog I want to talk about the physical side of ageing and indeed, when you grow older, often this side of life becomes problematical or even unbearable. For many people the defects of the body become so dominant that there seems to remain only decay. It cannot and must not be denied, but is it the only thing there is? One can say: such a decay is ungraceful, anyhow. But even then, in Orwellian words: All decay is ungraceful, but some decay is less ungraceful than other decay. Often we are left some elbow room. For some people it is wide, for others it is limited, but I think that just this elbow room is the space where ageing can be less unpleasant despite its difficulties.

Although I am a philosopher and a sociologist, being active with my body has always been important for me. I started to do sports when I was a student, and since then sport has stayed a significant part of what I do. I know that sooner or later I’ll be forced to give it up, for it seldom happens that people stay sporty till a high age. Only some keep practising it even then, as my readers know from my blogs on Robert Marchand, who even succeeded to set up a world record in one-hour track cycling in the over-105 age group that was especially created for him. But Marchand is exceptional in view of the human fate. Anyway, I hope that I can postpone the date that I have to stop cycling and running till late in life, for I think that sport has two aspects that help making life pleasant. It is enabling in the sense that it contributes to feeling better and fitter and in this way it makes that other activities can be done better. Moreover, doing sport till an advanced age is also a way of good living as such. Sport enhances the quality of life. But in the end there is only a way down in life, or so people think, and that was why I was asked to write an essay on how to go the way down gracefully, if possible. However, must I accept the decay as a natural process, and that’s all that can be done?

In a certain sense it is and by and large the physical decay is predictable, although there are big individual differences. When earlier this year a cycling club was established in my town, I had the courage at my age of 67 to join this club, even though it was only for cyclists with a race bike – which I have, though – and even though the other boys and girls are younger, if not much younger. Moreover, in a reckless mood, I joined the group of the fastest riders (for happily so many enthusiasts had joined the club that several groups of riders could be formed). Well, I should have known better, but with some effort I always succeeded to follow the shadows of my fellow riders, although when it goes hill up some see my back, for I have always been a good climber. All this is very nice, of course, and wouldn’t be worth to write a blog about, but last week I had a fitness test and although I knew that my physical condition was already very good for my age, the unexpected happened: the result was better than three years ago, despite the fact that I had become older and despite the fact that it is more or less a natural law at my age that people go physically down.

Somewhere in his Essays Montaigne writes that all things have their seasons, also good ones. He devoted even an essay to the theme. In other words, if you become older if not old, you must stop doing things that were normal when you were younger, even if you are still able to do them. It has no sense to learn a new language after a certain age; it has no sense to try to acquire new knowledge. “When will you be wise, if you are yet learning?”, to paraphrase a quote from the Greek philosopher Xenocrates (396-314 BC) cited by Montaigne. I think that he would say the same of me and others who do like me and continue doing physical exercise till a later age. But, I think that my case illustrates that Montaigne is wrong. Human decay cannot be stopped but it is not a straight line. Not all things have their seasons.  Profit by it. Even well on in years you can become better, for in many respects you are what you do, even if it doesn’t look the natural way.