The Debtor’s Paradox

Πάντα ῥεῖ (Panta rei), everything is in flux, so Heraclitus. Therefore, you can’t step into the same river twice, he said. But is really everything in flux? Also your body? According to Epicharmus of Kos “Yes, indeed”. Epicharmus was a Greek dramatist and philosopher who lived about 500 B.C. He is said to have been the first to apply Heraclitus’s idea to the human body, which he did in one of his comedies. However, most of his work has been lost. Only fragments remain. So we know his “bodily version” of Heraclitus’s idea only from how others have reproduced it. It has become known as the Debtor’s Paradox.

Before telling how it runs, I must say a few words about the Growing Argument, which has also been introduced by the Old Greek. Say you show me a heap of pebbles and you take one pebble away. You ask me: “Has the heap remained the same?” “No, of course not”, I reply. Then you put back the pebble and add yet another one. You ask me: “Has the heap remained the same this time?” And again I reply “No, of course not”. Then you say: “One man grows and another shrinks, and so we change all the time. Never we are the same as we were just before and never we’ll be the same again”.

One year later I urgently need money and I call you up and ask you whether you can lend me thousand euros. “Of course, I can”, you say, “I am always prepared to help a friend. However, there is one condition: You must pay it back to me before the end of the year.” “All right”, I say “I’ll certainly do.” The next day I go to your home, sign a contract and receive thousand euros from you.

Next January I meet you on a New Year’s Party. “You still haven’t paid back the money!”, you reproach me.” “Why should I pay you money?” I return, “I don’t owe you any money.” After some quarrelling I say: “Oh, now I understand what you mean. You lent the money to a kind of lookalike of me. But don’t you remember the Growing Argument that you explained to my lookalike? And that you ended the explanation with the statement: We change all the time. Never we are the same as we were just before and never we’ll be the same again? That lookalike has changed into me, but it isn’t me. So I owe you nothing.”

Thus runs the Debtor’s Paradox (in my version). How did the story continue? I didn’t pay and it came to a court case. The judge asked me to show my identity card, she saw that the same card number was also written in the contract and concluded that it was I who had signed the contract, so that it was I who had to pay.

The upshot is that I am not my body, if we see a body as a fixed lump of matter. However, we are our body if we realize that it is a clustered lump of material characteristics. The composition of the lump may change but the cluster of material characteristics remains relatively stable, not counting the fact that we have also mental characteristics (and according to some identity philosophers it’s only the mental characteristics that are essential). So you can step into the same river twice, for the river is the flow and not the molecules.

P.S. Any agreement with the so-called “Ship of Theseus Paradox” is not a coincidence

Writing this blog I have been inspired by:

- Vincent Descombes, Puzzling Identities. Cambridge, Mass.: Harvard University Press, 2016; pp. 43 ff.

- “The Debtor’s Paradox”, on website http://metaphysicist.com/puzzles/debtor/

Philosophers at War

Monument for Ernest Psichari in Rossignol, Belgium

One week ago the end of the First World War (WW1) was commemorated in several countries; especially in France, Britain and Belgium. In 1914, this war was welcomed by many persons with great enthusiasm but this changed soon, when after a month it turned from a war of manoeuvre into a long lasting war of attrition. Finally after four years fighting ended on 11 November 1918. The political outcome was actually not more than a truce and twenty years later a new war started. The human outcome of WW1 was 17 million dead, both soldiers and civilians. For my blog the interesting question is: What did philosophers do in those days? In order to get a small impression I browsed the Internet. Here is the result. Note that the choice of the names is completely arbitrary and not representative. It reflects only my personal interest and what I happened to find during my search. The question would really be worth a thorough investigation.

- Ludwig Wittgenstein. On the outbreak of the war, Wittgenstein volunteered in the Austro-Hungarian Army. He served with the artillery but he has also been involved in some of the heaviest fighting at the front with Russia. Wittgenstein received several decorations for his courage. Later he fought at the Italian front with his Tractatus in his knapsack. There he was taken prisoner on 3 November 1918. It is clear that he run a serious risk to be killed, so how would philosophy have developed if Wittgenstein had died then or had lost his Tractatus?

- Bertrand Russell. Russell was a determined pacifist. He openly opposed WW1 and was, among other anti-war activities, active in an organisation that supported conscientious objectors. In 1916 he was fined for writing a leaflet supporting conscientious objection and in 1918 he was given a prison sentence of six months for “insulting an ally” (the American army). In 1916 he was dismissed from Trinity College (Cambridge University) because of his anti-war activities.

- Alfred North Whitehead. Whitehead had written with Russell the Principia Mathematica on the foundation of mathematics. Different from Russell, he supported the war and sent off his two sons at war. One didn’t come back. Their different opinions about WW1 drew both philosophers apart, although they always stayed on relatively good terms. Later Russell wrote about this that Whitehead “was more tolerant than I was, and it was much more my fault than his that these differences caused a diminution in the closeness of our friendship.”

- Max Scheler. Scheler voluntarily joined the German army, but was declared unfit, so he remained working as a philosopher. In 1917-1918, the German State Department sent him to Switzerland, Austria and the Netherlands to influence Catholic circles. He gave also lectures to sick and wounded German soldiers interned in the Netherlands. At the beginning of WW1 Scheler believed in the creative force of war. Later he changed his view and saw it as a moral disaster.

- Henri Bergson. Bergson supported in several philosophical writings the case of war. He was an important French advocate of the USA joining the war. In January 1917 he became a special envoy of the French government to meet the US president Wilson and he participated also in the negotiations that led to the American entry in the war.

- Edmund Husserl. Husserl lost one of his three children during WW1. Another son became wounded but survived. He saw WW1 as the collapse of the old European world. This meant for philosophy that it had to look for a new orientation.

- Ernst Troeltsch. Like most of his colleagues Troeltsch supported Germany’s war against France in 1914. “Yesterday we took up arms. Listen to the ethos that resounds in the splendour of heroism: To your weapons, To your weapons!”, he said. He considered the German soldiers as morally superior to their adversaries. Moreover, the French were decadent and arrogant, according to him. Later he changed his views. Already in 1916 his tone became moderate and after WW1 he supported the Weimar Republic.

- Mohandas K Gandhi. Of course, Gandhi, the advocate of non-violence and opponent of violence, did not support war. Nevertheless, he supported Britain actively in some sense. He happened to arrive in England on 6 August 1914 and one of the first things he did was helping to raise an ambulance unit. However, he became ill and didn’t serve in the unit himself, and soon after his arrival in England, he returned to India again. His motivation for this support of the British was, as he explained later: “I knew the difference of status between an Indian and an Englishman, but I did not believe that we had been quite reduced to slavery. I felt then that it was more the fault of individual officials than of the British system, and that we could convert them by love. If we would improve our status through the help and cooperation of the British, it was our duty to win their help by standing by them in their hour of need.”

The philosophers just mentioned survived WW1, mainly because they didn’t go to war themselves. Others were not so lucky and were killed in action. The names of most of them (as philosophers) will never be known or they have been forgotten by most of us. Take, for instance, Ernest Psichari. Some French readers may know his name, but I think that most readers hear of him here for the first time. I heard of him for the first time on one of my many trips along the battle fields of WW1. This French writer and philosopher died near Rossignol in Belgium on 22 August 1914, 31 years old. It was there on a stele that I read his name. Let him stand for all those fallen philosophers we never have heard of. This blog is dedicated to them.

The stag hunt

Once I was a deer hunter ... with my photo camera

There are several types of “games” like the Prisoner’s Dilemma. I discussed already the Prisoner’s Dilemma itself, the Tragedy of the Commons and the Chicken Game. To finish this mini-series about games I want to treat the Stag Hunt Game. Game theory is a rather new branch of mathematics. It was developed during the Second World War. However, its roots are older and the idea of the stag hunt game was already mentioned by Jean-Jacques Rousseau (1712-1778). In his A Discourse on Inequality he describes it this way (quoted from Bovens, p. 160; see Sources below]:

“If it was a matter of hunting a deer, everyone well realized that he must remain faithful to his post; but if a hare happened to pass within reach of one of them, we cannot doubt that he would have gone off in pursuit of it without scruple ...”

A group of hunters decides to hunt deer together, since a good way to do this is with a group: They drive the deer to a corner of the wood, and if they see one, they shoot it. However, if one of the drivers leaves his post, there will be a gap in the chain of drivers and the animals will have room to escape. So if you want to hunt deer in a drive, it is best for each hunter to cooperate and to assume that the others will do as well. But, as Bovens says “if I cannot be assured that others will cooperate then it is better to defect”, and so take my chance to shoot a hare that rushes by, for maybe others will take their chances as well, if they see one, even though cooperating would be better, provided that everybody does. Anyway, this is so if you value a deer more than a hare and if enough deer will be shot for all. Although cooperation is what normally should be expected, the uncertainty what others will do (“take your chance”) plus the wavering character of many people (“shall I abide by my decision to cooperate?”) makes that cooperation is often so difficult.

This time I’ll leave it to you to make a payoff matrix, but the case made me think of the fable of the fox in the hen run. A farmer makes a net fall to catch a fox that each night steals one of his chickens. The next night the fox is caught and the noise awakens the chickens in the coop. “Help me”, the fox cries, “for the farmer will kill me”. The chickens don’t want to do it, glad that the fox has been caught. However, the fox promises “I’ll do anything you say, if you free me.” The chickens don’t trust him, for might the fox not kill one of them, once released? Who says that he’ll keep his promise? Then one of the hens gets an idea and says: “If we set you free from this trap, will you remain here in this coop and protect us from any other foxes that try to get in?” Since his life is at stake, the fox agrees and promises to stay with them for the rest of his life. At first the chicken don’t trust him, but after careful consideration, they decide to set him free. For will it not also be advantageous if the fox stays with them? If the farmer kills the fox, soon another fox will come and steal chickens and the whole story will start anew. Maybe that fox will be smarter and will not let himself be caught. And so it happened that the chickens freed the fox, the fox kept his promise, and chickens and fox lived peacefully together and the latter chased away all foxes that tried to catch one of the birds.

Maybe the case of the fox in the chicken coop is not a pure stag hunt game, but the moral is the same: Often you are better off to cooperate. This is so if you do, because you are in trouble and have no choice, but also even if you know that the other cooperates because s/he has no choice.

Postscript: These things can happen in real:

https://www.express.co.uk/news/nature/466710/A-fox-keeps-chicken-eggs-warm-by-curling-up-on-them

Sources

- Bovens, Luc, “The Tragedy of the Commons as a Voting Game”, in Martin Peterson (ed.), The Prisoner’s Dilemma. Cambridge: Cambridge University Press, 2015; pp. 156-176 (especially p. 160).

- “The Fox in the Chicken Coop”, on website http://internetstoryclub.org/fables/20_the_fox_in_the_chicken_coop.html

The chicken game

You are driving on a narrow road. You are driving fast, for you are late. Then you see a car coming from the other direction, also driving fast. What will you do? Of course, you don’t need to think about it. You slow down and you swerve. Probably the other driver does the same. If you hadn’t swerved, you could have died in the accident that would follow, or at least the car would have big damage. And the same so for the other driver. Why take the risk that the other will not swerve? Nevertheless it sometimes happens that both drivers continue to drive straight on expecting that the other will give way, for why should it be you who must be the chicken? If both drivers think so, and no one swerves, even not at the last moment,  the consequences are fatal.

The case just described is an example of the so-called Game of Chicken. Sometimes it is really played as a game, often it is played in real with possibly fatal consequences, indeed. The Dutch Wikipedia (https://nl.wikipedia.org/wiki/Chicken_game ) mentions a game popular in New York in which youngsters throw knives to each other. Who ducks is a chicken. It also happens that the game is “played” in a real life situation in which the destiny of the world is at stake. A war of attrition is a chicken game of a sort. After mid September 1914, a month after the outbreak of the First World War, the front in Northern France had stabilized, with the Germans troops on the northern side of the frontline and the French and its allies on the southern side, it appeared to be impossible to force a breakthrough. It became a matter of waiting which party would be exhausted first and would ask for negotiations or would surrender. Finally it was Germany that gave way and lost. However, when we think of a political chicken game, the first that comes to mind is the Cuban Missile Crisis in October 1962.

My description of this crisis must be very simplified. What I must leave out, for instance, is that there was contact during the crisis, unlike what is supposed in the standard chicken game. It was not simply a matter of “you do this and I do that”, for there was room for negotiations; the “game” was not one-dimensional; etc. There wasn’t simply a good guy and a bad guy. But basically it was this that happened: The Soviet Union wanted to install missiles on Cuba that could reach US territory and so destroy it with nuclear bombs. Soviet ships with the equipment were under way to Cuba (in fact, some missiles had already been installed). When the USA discovered what was happening, it threatened to stop the ships. If no party would give in, so if the USSR didn’t withdraw the ships and the USA would stop them, the consequence could be a nuclear war. If one party would give in, while the other didn’t (the USA wouldn’t stop the ships and the USSR wouldn’t withdraw the ships; or the USA would stop the ships and the USSR would withdraw them instead of trying to sail them to Cuba with force), the chicken would suffer a defeat in front of the whole world. Here is a payoff matrix for this chicken game (the figures for the USA are first):

The figures are a bit arbitrary but I think that you see the point. Cell (a) describes a compromise and (d) a nuclear war. (c) involves that the USA wins, the threat has been removed and its political prestige in the world has risen a lot, while in (b) it’s just the USSR that wins and gains enormous in political prestige while the threat for the USA still exists. What really happened in 1962 was (a), but not exactly. The outcome of the crisis was a compromise of a sort for no party wanted to risk a nuclear war, but in fact the USA won: The Soviet Union withdrew its missiles, and the USA promised not to invade Cuba (as it had tried in 1961); the demand of the Soviets that the NATO missiles in Turkey should be withdrawn as well was ignored. Therefore (4,1) is a better description of cell (a) in this case. One result was positive for both parties and has been followed by other countries as well: It was decided to install a hotline between Washington and Moscow for direct communication between the political leaders in case of crisis. Unlike what many people think, the hotline is not a telephone connection but originally it used a Teletype equipment and nowadays it is a fax. Even if you play the game of brinkmanship, in the end it is better to connect.