Search blog.co.uk

  • Do you know if that's true?

    Suppose somebody asks the above question to you. Suppose that the reference of "that" has already been clarified, so perhaps they say something like "I heard that Muse's new album is rubbish. Do you know if that's true?"

    I think we can re-phrase the sentence as so:

    If that's true, do you know that that's true?

    Now let us use the material definition of "if". We can answer in the following 4 ways:

    Yes. It is true and I know it's true.
    Yes. It is false and I know it is true.
    Yes. It is false and I do not know that it is true.
    No. It is true and I do not know that it's true.

    Two of these answers entail Moore's paradox. The only consistent answers are:

    Yes. It is true and I know it's true.
    Yes. It is false and I do not know that it is true.

    Only the first of these sounds like a reasonable answer to the question. If somebody asked us a question like "Do you know if that's true?" and we answered "Yes", it would be very queer if what we really meant was "It is false and I do not know that it is true." It's also impossible to answer the question except in the affirmative, which would suggest that the speaker asked a pointless question such that the most simple correct answer (Yes/No) could not inform them either way. But it isn't a pointless question and it can be answered in the negative quite sensibly.

    So what are they really asking? Here are some interpretations:

    1. Is that true?
    2. Do you know that that is true?
    3. Do you know the truth-value of that? And if so, what is its truth-value?

    It's a tough one. If you answered "No", they might reasonably ask you "Is it false, or do you just not know?" If they asked this they would have to admit to having asked an ambiguous question in the first place, one that could be interpreted as either 1 or 2. "Yes" doesn't have the same problem because your assertion that it is true entails that you would assert your knowledge of its truth and your assertion that you know its truth entails that you would assert it is true. 3 is more often than not what they really intend, but we can't give them the benefit of having expressed 3 because they clearly haven't put enough work in to get 3. It's two questions and they only asked one and so should receive only one answer. Grice might argue that we really should interpret them as meaning 3, if that is most likely, but I'm not convinced that somebody wouldn't ask the question meaning only either 1 or 2.

    As the only possible answer is "Yes", they should expect us to give that answer beforehand, thus rendering the question pointless. They could ask "Do you know if that's true? Is it true or do you not know?" but then they could have just asked the second of these questions on its own.

    This question also reminds me of a few other kinds which can be interpreted differently so regularly that the asker of the question can't really ascertain the real answer from the one give, although they are not quite as sever as the one above. They are of the form:

    Do you mind if X?
    Are you sure you don't want to X?

    For the first of these if you answer "Yes" to a question about whether you mind then you are giving your disapproval for the proposed event or fact. And if you answer "No" then you give your assent to it. But we equate "Yes" with assent and "No" with disapproval so readily that we (the questioner) might hesitate about the answer given wondering if our partner has understood us properly. If the conversation ended with their answer then I suspect both participants would leave unsure of what the other believed. The second example is similar. Because of the way the question is constructed, "Yes" indicates disapproval and "No" indicates assent (although it could mean indecision too). Given that none of us work on the assumption that anybody else is rational, and that they could interpret these questions several ways, we ought to just stop asking them.

  • The Slippery Slope Argument

    Some people argue that when a change in the law is being proposed, a slippery slope may result from the application of the new law. For example, in recent years one of the hottest publicly-contested debates in the UK has been about whether people suffering from painful terminal diseases should be allowed to end their life prematurely, or whether their friends and family can assist them in doing so if they are not physically capable of it. The Assisted Dying for the Terminally-Ill Bill was rejected in 2004. Its proposal was that a person, X, could be assisted by others to commit suicide if the following conditions were satisfied:

    1. X is above the age of majority.
    2. X is competent. (X needs to sign two declarations of competence, one in the presence of a solicitor.)
    3. X has a terminal illness. {Two doctors must both assess that X has less than six months to live).

    Now it might be that some people opposed the Bill, while simultaneously finding the applciation of the bill to be positive, ceteris paribus. However, they might also believe in a slippery slope conditional of the form "If this Bill is passed, it will lead to the passing of a more extreme and less desirable bill". Perhaps they only have a low credence in this conditional, but they evaluate the expected utility of the bill being passed and find that the stark probabilities for deeply undesirable outcomes out-weigh the benefits of the bill in the probably case where the slope isn't really as slippery as previously thought. Therefore, even though the bill, in a perfect world, should be implemented, because the world is not perfect its passing will have ill secondary causes or negative externalities.

    A slippery slope argument of this sort might contain the following premise:

    If the proponents pass their bill they will continue to want more extreme bills passed. Specifically, they don't really believe in this bill but they know it's more likely that they can get their more dangerous bill passed if they pass this first.

    So the slippery slope argument seems to me to be more political than ethical. In the case of the assisted suicide bill, the opponents might argue that if it's passed it won't be long before any one of the conditions becomes unnecessary for assisted suicide, or perhaps unassisted suicide will be legalised. So these slippery slopers should take their argument up against the political system. "No more slippery slopes!" Perhaps they think that the general voting population is very naive and can be unconsciously corralled into adopting an extreme view, or perhaps they think it is the MPs who are this naive.

    Sometimes we need slippery slopes to get quickly to the correct positions which are so far from the current law. For example, somebody may have argued that men should be allowed to wilfully engage in sex with each other, but only if they're over 25 and have the consent of their neighbours. A hundred years ago this would have been a progressive opinion and would probably have contributed to the situation we have today, which has only very recently given reasonably equal constraints on homosexual sex as to heterosexual sex. Had the person described above been able to view the future and seen what the first bill on extended rights for homosexuals would lead to, they might argue against the passing of that bill. We might still have those laws if everybody took the slippery slope argument too strongly.

  • Napoleon's Changing Personality

    I've just finished reading "To Befriend an Emperor" by Betsy Balcombe, and prior to that I read "Billy Ruffian" by David Cordingly. The very end of the latter book deals with Napoleon's surrender to the captain of HMS Bellerophon and the former book deals with his interactions with a teenage girl when he was escorted to St. Helena for his second exile. The transition of his personality is absolutely unbelievable. In just four months he went to commanding the French in one of the most significant battles in history up to that point, to playing Blind Man's Bluff with Betsy and her sister, to the bafflement of the generals who chose to share his exile.

    Napoleon has always struck me as somebody who chided excellence, because nobody was as excellent as him. Furthermore he conversed with private soldiers and other non-entities and showed interest in their dreams and accomplishments because they were so far beneath him that they couldn't possibly compete with him. In his time Napoleon brought the greatest generals and monarchs to their knees. In 1807 he humiliated Tsar Alexander and Emperor Frederick William III and forced them to sign his treaty of Tilsit commanding them to abide by his Continental System.

    His own marshals, who were the cream of an army comprised of a million soldiers, he rarely had complimentary words for. He knew that most of what they did he could have done better if only he could replicate himself. On Marshal Murat, the swash-buckling cavalry general he said, "In battle he was perhaps the bravest man in the world; left to himself, he was an imbecile without judgment." To Marshal Soult and his other generals before the battle of Waterloo he ironically uttered, "Just because you have all been beaten by Wellington, you think he's a good general. I tell you Wellington is a bad general, the English are bad troops, and this affair is nothing more than eating breakfast." When Marshal Massena refused to join him in the one hundred days, when next Napoleon saw him he challenged him on whether Massena would have dared obey the king and gone to war against Napoleon. Even Marshal Ney, veteran of 30 years of war, was destroyed by Napoleon's ire and was never the same again. He famously promised to bring Napoleon to Paris "in an iron cage", and when approaching Napoleon's army declared of his men "They shall fight; I will begin the action myself, and run my sword to the hilt in the breast of the first who hesitates to follow my example." The closer he came to his former commander, the more hesitant he himself became. He finally agreed to side with the Emperor, on the condition that Napoleon no longer seek war. But he had already betrayed too much weakness and Napoleon sent him away and assumed command of Ney's army. I believe this to be the moment that Ney was finally mentally defeated, and paved the way for his erratic performance at Waterloo, his careless attempts to escape capture afterwards and his imminent execution.

    There are many other quotes of Napoleon that suggest him to be extremely intolerant of incompetence, which he thought to affect the whole world, and suggest him to have been especially arrogant and horribly aggressive in everything he did:

    “An order that can be misunderstood, will be misunderstood.”

    “He who fears being conquered is sure of defeat.”

    “I have never found the limit of my capacity for work.”

    “We walk faster when we walk alone.”

    “If you want a thing done well, do it yourself.”

    “Impossible is a word to be found only in the dictionary of fools.”

    “Friendship is only a word, I care for nobody.”

    “Circumstances? I make circumstances!”

    “Never ascribe to malice that which is adequately explained by incompetence.”

    After the Battle of Waterloo he appears to have undergone a remarkable change. he marched with his generals and a few loyal soldiers through France, not knowing what to do next. His army was completely routed and the Prussians had captured many and were marching on Paris. His advisors begged him to try to escape at the port of Rochefort but he insisted he should wait a little longer. The Bellerophon, and two British sloops were guarding the harbour, but it is thought he could have easily evaded them. Then his brother, Joseph Bonaparte, and probably the next most wanted in the family, visited him at Rochefort and tried to persuade Napoleon to go with him to America. Napoleon refused, Joseph escaped and lived without incident in New York for the next 20 years. Napoleon decided to surrender to the British, and naively expected to be given political exile in Britain like his brother Lucien had been given years before. His interactions with the officers and crew of the Bellerophon, who were in awe of the most famous and previously most powerful person in the world, are quite comical. He watched them perform a play and was amused at the larger men wearing women's clothing. He must have wondered how these cross-dressing buffoons could comprise the best sailors in the world.

    Furthermore, there is a definite change in Napoleon's comments about Britain. Previously he had been known to call them "Perfidious Albion" and had mocked his generals in the Peninsular War for being so horrendous as to lose to the British. Now he said to the ship's crew, "You have the honour of belonging to the bravest and most fortunate nation in the world", and referring to Britain as "the most generous of my enemies." Possibly these compliments were merely designed to incite mercy in the British who he saw as his only hope for a peaceful retirement. Certainly this theory is consistent with his previous quote, “I would kiss a man's arse if I needed him.” When the Bellerophon docked at Torbay Napoleon would come out of his quarters every day and wave at the crowd who had encircled the ship in little boats just to see the former Emperor. He would look at the crowd through his telescope and proclaimed how beautiful the English women were. He didn't seem to view his defeat as a humiliation, but rather the beginning of a new stage in his life. A truly remorseful and bitter person would have shut themselves away from the baying crowds and simply refused to converse with those who had been his enemies. At the news that he was to be exiled on St. Helena he said:

    "I am come here voluntarily to throw myself on the hospitality of your nation, and to claim the rights of hospitality. I am not a prisoner of war. If I were a prisoner of war, you would be obliged to treat me according to the law of nations. But I am come to this country a passenger on board one of your ships of war, after a previous negotiation with the commander"

    "What danger could result from my living as a private person in the heart of England under surveillance, and restricted in any way the Government might imagine necessary?"

    I'm trying to make allowances for hindsight, but it just seems plain foolish that he would be allowed the same treatment as his harmless brother. Some of the British estimated that Napoleon had caused the death of a person for every minute he had reigned in France, which considering that he reigned for about 15 years is a lot of bloodshed he was responsible for. For a man who had proclaimed that "Death is nothing. But to live defeated and without glory, is to die every day", the prospect of living in a cottage on an intolerably hot island with nothing to do and nobody to see and little news of the outside world was his idea of Hell. Even if he could never be allowed any of his previous power he wanted to at least be some way involved in the world.

    When he arrived at St. Helena he commented that “It is not an attractive place. I should have done better to remain in Egypt. By now, I should be Emperor of all the East.” It seems that he was resigned to his fate, and intended to adapt to his new life. On his first day on the island he was introduced to the Balcombe family who he was to live with until his cottage had finished being constructed. He and Betsy, who was 13 when he first met her, began an unlikely friendship, playing childish games and pranks on each other. Before they met, Betsy had proclaimed that she deeply feared Napoleon, for all British children had been taught that Napoleon was a horrible monster who would rather eat them than greet them. On first meeting her he quizzed her on European capitals. When she answered "Petersberg, formerly Moscow" as the capital of Russia, Napoleon asked her, "Who burned Moscow?" It's generally accepted that Moscow was burned by Russians while Napoleon occupied it, in order to diminish any resources he might procure there, but when Betsy proffered the Russians as the arsonists, Napoleon replied, "You know very well that it was I who burnt it." Later she tells us that one day a much younger girl, Miss Legg, was visiting the Balcombe household and was sitting in the garden. Betsy came outside and told her that Napoleon was about to come down the garden path. Miss Legg began trembling and crying at the prospect of meeting the monster, and Betsy went inside to tell Napoleon of her fears. Napoleon then decided to come running out howling at her and making scary faces, which made the girl hysterical and left Napoleon in fits of laughter.

    Napoleon used to joke to her that she should marry the son of one of his generals, Les Cases, which infuriated her. One day she decided to get revenge on him, when she, her sister, young Les Cases, old Les Cases and Napoleon were walking in single file along a steep narrow path. She pushed her sister hard until Les Cases ingloriously pushed into Napoleon causing him to slip. At the disgust of such a dishonourable attack on the Emperor, Les Cases pushed Betsy against the wall hurting her.

    "`Oh sir! He has hurt me!' `Never mind', replied the Emperor, 'do not cry - I will hold him while you punish him.' And a good punishing he got; I boxed the little man's ears until he begged for mercy; but I would show him none; and at length Napoleon let him go, telling him to run, and that if he could not run faster than I, he deserved to be beaten again. He immediately started off as fast as he could, and I after him, Napoleon clapping his hands and laughing immoderately at our race round the lawn. Les Cases never liked me after this adventure, and used to call me a rude hoyden."

    Another time they were playing whist, and Betsy's younger brother took a card representing a Mogul emperor and said "This is you, Bony". Napoleon couldn't understand what was meant by "Bony", and one of his followers translated it as meaning "thin", to which Napoleon laughed and said "I am not at all bony".

    These anecdotes are all quite entertaining, but we mustn't distinguish the playful and friendly conversationalist with the violent oppressor of nations. They are the same person. Betsy once asked him about a famous story involving him. In Jaffa he was alleged to have killed hundreds of wounded French soldiers who were too ill to march. Napoleon replied that he had wanted to kill them with opiates, because they would not have lived a day and the Turks would have tortured them when they found them. His Surgeon-general refused to kill them so Napoleon ended up ordering a rearguard to defend them until they had died. But Napoleon clearly didn't feel like telling her about the surrendered inhabitants of Jaffa he had executed. Betsy says of this, and other cruel acts attributed to Napoleon:

    "It is true that this dreadful deed will always remain a deep stain upon Napoleon's character, but it would be uncharitable to view it as the indulgence of an innate love of cruelty, for nothing in Bonaparte's history shows the existence of such a vice. It was one of the numerous and sad results of boundless ambition, united to unlimited power. In aiming at gigantic undertakings, he forgot to calculate the waste of human life which the execution of his projects necessarily involved."

    This, I think, is a good assessment of Napoleon. In his own words, “War must be made as intense and awful as possible in order to make it short, and thus to diminish its horrors.”

    It's also worth mentioning that various authors have written about suspected plots to rescue Napoleon from St. Helena and place him on a South American throne. Some people even thought that he might establish a great South American empire, and Lord Cochrane thought the same, seeing as he attempted to spring the former Emperor from St. Helena but was too late as Napoleon was already dead. Reading these recent works I'm inclined to think that Napoleon never considered his escape possible, or even wanted to set up a new empire. He wanted a peaceful retirement and enjoyed small pleasures. He also suffered small annoyances very severely. The governor of the island infuriated him by having him escorted around the island by armed guards, and even refused permission to the only local piano-tuner to come and fix Napoleon's piano.

    In the end it is middle age that resulted in Napoleon's downfall. After the battle of Austerlitz in 1805 he proclaimed “We are granted only a limited time for making war; I give myself another six years, after which even I ought to come to a stop.” Had he heeded his own advice his name might very well still be associated with a modern French Empire, as his troubles really began in 1812 with his disastrous invasion of Russia. On St. Helena he used to re-enact his past battles with chess pieces to determine how they would have developed had he tried something else. I wouldn't say he was consumed with regret, but to some extent he knew that he could have shaped the world much differently.

    “What I did is immense. What I had decided to do, and what I had projected were still more so.”

  • Thinkos Volume #1: Regret

    I've heard this phrase used so many times now that I thought it was worth commenting on. The phrase always goes something like this:

    "I don't regret anything, but if I could go back in time and do it again I would do it differently."

    Isn't the second part of that sentence actually the very definition of "regret"? When people say this I wonder if there are any thoughts in their head which they are expressing. It's not just the case of reporting a false belief, but of reporting nothing. There is just no content of that sentence at all, at least not in any possible world.

  • Could Diomedes have killed Achilles?

    I've been thinking recently about how one could write a story that tied up the Iliad, Odyssey, Aeneid and the Epic Cycle. I would want to somehow include everything that doesn't contradict with something of higher value that has been written about the Trojan war, as well as contain some historical perspective. I think there is also a little bit of room for creativity, and was considering a storyline whereby Diomedes is responsible for the death of Achilles. Upon the death of Penthisilea it is said that Thersites, Diomedes' cousin, laughed at Achilles when he fell in love with the dead Amazon queen. Achilles killed him, and Diomedes was so enraged that he challenged Achilles to a duel but the other Greek heroes intervened and prevented their two best warriors fighting each other.

    Now let us bring in some Shakespeare. In Troilus and Cressida, Shakespeare tells us that Cressida, the daughter of Calchas who defected from the Trojans to the Greeks, betrayed Troilus with Diomedes. I think a good story (and one I would use with Helen as well) is that she loved both Troilus and Diomedes (for Helen I would say she loved both Menelaus and Paris), and just hoped that one would not know about the other (although in Shakespeare Troilus does fight Diomedes about the issue). We are told in one of the original texts (Sophocles) that Achilles ambushes Troilus and his sister Polyxena, kills Troilus and mutilates his corpse, an act which is punished by his imminent death where Paris shoots him in his vulnerable heel. I think a viable storyline could be one where Diomedes and Cressida, jointly seeking revenge on Achilles, organise an ambush against him when he goes to meet Polyxena. It is said that Paris and his brother Deiphobus were both involved, but it would be interesting to imply the existence of a mystery "third gunman".

    Plus this story would help reinforce the innocence of Polyxena. Perhaps her love for Achilles was genuine and she kept their relationship a secret. Somehow Cressida comes to learn of it and informs Diomedes, who organises the ambush with his former enemies. This would constitute a major twist on the original story because Diomedes is often portrayed as the most honourable and brave of the Greeks, but at the same time there is clearly a one-sided rivalry with Achilles. He could have felt resentment that Achilles was considered the better fighter and more crucial to the war effort than himself, who contributed considerably more leadership to the invasion than Achilles, who was a bit-part player who fought when he liked.

    Furthermore the Little Iliad states that Odysseus attempted to kill Diomedes on the night that they stole the Palladium from Troy. This is one of the more unbelievable stories about Odysseus that doesn't necessarily fit with what we know about the rest of his character. (Although you can certainly make it. Odysseus has been depicted by some as a man of no morals who would do anything to further his own cause. It's quite relevant to this position that of all the Ithicans who left for Troy, he was the only one that returned.) In my story it might be that Odysseus teased a confession out of Diomedes for his part in the death of Achilles, and a fight ensued. Perhaps Diomedes defeats him and makes him swear not to reveal it to anybody else. This could also be one of the causes of Odysseus' later guilt about his responsibility for Achilles, and why he decided to embark on a quest for penance after his return to Ithaca.

  • Swoopo and chasing winnings.

    I want to talk at some point about the game theory of investing a lot of resources into a lottery that effectively owes you nothing. Two examples of these are a) the Swoopo auctioneering site, where players can have already invested $100 in buying a product and yet have no claim on it yet, and b) endurance contests, such as those in the USA (recently discontinued) where players try to touch a car for the longest and the one who do so wins the car. In the former, if you've invested a $100 in a product should your strategy from then on differ from somebody who has invested nothing in it? In the latter it seems fairly obvious that the best strategy is to either leave early and minimise your losses, or intend to never leave. Any strategy whereby you invest a lot of resources into it and eventually get nothing is a terrible strategy. But clearly lots of people end up doing this. Maybe they were all wrong about something (i.e. they believed they had the ability to last 48 hours and they didn't), or perhaps they knew there was a gamble involved and that they lost the gamble. These are interesting cases, and I think there may be serious justification to ban this sort of event as it tricks players via the Sorites paradox into giving away their net worth, or risking everything. It's a lot like chasing losses, but instead more like chasing winnings. Very curious cases that I think are worthy of discussion. Perhaps the only solution is a Leviathan figure to ban such competitions.

    They can be taken to ridiculous extremes as well. Somebody on the 2+2 forum suggested an adaptation of a Swoopo auction. Suppose an item starts at $50, and everytime somebody bids (costing 60c), 10c is actually taken off the price. If the price reaches 0 then it just keeps going, so that the eventual winner could win the item and the cash. The longer these auctions go on the higher the prize actually is. It could theoretically get to the point where the entire world has invested all the world's money and the last person with any money left wins the whole lot. Very curious, and very dangerous.

  • Dear BDT from Scientology

    I just got this e-mail from the Church of Scientology:

    Dear BDT,
    We are surveying Scientologists to find out how bright they are. Make out the following.

    Thank you.

    Kate Clarke

    Consultant

    Dianetics and Scientology Information Center

    Clearwater, Florida

    (727) 214-5743

    QUESTIONNAIRE

    Fill this out and send it in.

    1. What is the most certain thing you can get about yourself?

    2. What is the most certain thing you can get about your ability to communicate?

    3. What is the most certain thing you can get about your ability to work?

    4. What is the most certain thing you can get about your ability to help others?

    5. What is the most certain thing you can get about children?

    6. What is the greatest certainty that you can get about groups in general?

    7. What is the greatest certainty that you have about mankind in general?

    8. What is the most certain thing that you can get about animals?

    9. What is your highest certainty about the physical universe?

    10. What is your greatest certainty on the subject of spirits?

    11. What is the greatest certainty that you can get about God?

    12. What is your greatest certainty about life?

    13. What is the greatest certainty that you have about Scientology?

    14. What is the greatest certainty that you have about L. Ron Hubbard?

    15. What is the most certain thing you can be certain of in present time?

    16. What is the greatest certainty that you have about the future?

    -------------------------------------------------------------

    I'm not entirely sure what these questions are actually asking. Some of them are so badly worded and the whole e-mail is terribly presented. Part of me wants to know what the Church Of Scientology think the correct answers to these questions are. I suspect if I answered them honestly they would regard me as not very bright. If there was a promise of feedback from this then I would fill it in but as there isn't it isn't worth responding. These people are notorious for hounding you until the end of the Earth, so it's not worth provoking them.

  • On Backward Induction

    Imagine a centipede game is being played by perfectly rational agents. As has been well-established, the first player reasons using backward induction, and also reasons that their opponent will use backward induction, and therefore to maximise their own utility they are forced to end the game immediately, taking 1 util for themselves and none for their opponent, even when it was possible that they receive (about) 100 utils each had they co-operated.

    Here's the question. If the first player didn't end the game immediately, the second player would have good evidence that the first player plans to co-operate for some time to come. If the first player made the co-operative decision on the first turn, then they will on most of the rest since they are identical scenarios. Therefore the second player ought also to co-operate. Even if the other player decides to end the game prematurely in the future for no discernible reason, you still make more than you would by playing an ultra-defensive strategy. However there still is some kind of paradox looming, as the end-game will still be in the minds of the players. I haven't worked this one out yet.

    Centipede could be one of those rare games that turns up in game theory where it pains the player to be rational, just as Lewis thought the Newcomb's game paid off those less rational 1-boxers. One problem with this game is about knowledge. In the centipede game, your opponent knows that you are "rational", therefore you cannot choose to play irrationally because it is a given fact already how you will play. Hence decision theory of this sort becomes ironically indecisive and determined. We need to use the concept of common belief rather than common knowledge. In Centipede, if you play the co-operative move you also falsify the other player's belief, which will cause them to play differently. Not irrationally. It just happens that their behaviour is identical to the behaviour of an irrational agent, but not their thought process. This is a phenomenon that is observed very frequently in the world of professional poker.

    Suppose CBR, common belief in rationality, and suppose that Backwards Induction is essential for rationality. My earliest instinct then is that, given both players have CBR, if the first chooses to play co-operatively, the second player no longer has CBR, i.e. he comes to believe that the first player cannot be using backwards-induction and is therefore irrational. However, this cannot be the case. There are players who do use backwards induction but who still co-operate because they expect or suspect their opponent of being able to sympathise with them. So when the first player co-operates, essentially the other player still cannot tell whether the first is using BI or not. Like in poker, when an opponent makes a play you can only tell that they are not an intermediate, they could still either be an expert or a beginner.

  • The Popcorn Problem

    I'm just reading about this supposed paradox that apparently results from Jeffrey's logic of decision. It's a lot like the Newcomb's Paradox in that it raises the issue of whether causal back-tracking is metaphysically supported.

    The problem is this. You are in the cinema and want some popcorn. What you prefer most is for you to go to the lobby, there to be popcorn, you buy some, return to your seat and enjoy it, even though you will miss some of the film. The next best option is if you decide not to get popcorn and there really wasn't any there, so at least you didn't miss the film. The next best alternative is if you go down to the lobby and there is no popcorn so you miss some of the film. The worst option is to miss out on popcorn by deciding not to leave the cinema, and find on the way out that there was popcorn there all along.

    At the same time, you are fairly sure that there is no popcorn out there, because there very rarely is. Also, you're certain that if there was popcorn out there, the owners of the cinema would project onto the screen a subliminal message, reading "POPCORN!!!" every few seconds. You consider yourself to be suggestible, so if this were occurring you would definitely choose to go and look in the lobby for popcorn.

    Sobel argues that of all the alternatives, the probability that popcorn being in the lobby given that you look for it, and the probability that there will be no popcorn given that you don't look for it, are both close to 1. As the first of these alternatives has the highest expected utility, using Jeffrey's conditional decision theory we ought to go and look for the popcorn, which would otherwise seem irrational given that we already think the probability of popcorn being there is suitably low.

    This is similar to the Newcomb's problem because in both cases we suppose that our future actions could causally determine a past action to come to pass or be reversed. We know that the popcorn is either already out there or not. Our deciding to go and look for it should not affect it's being there. This is my conclusion and that of the 2-boxers, a group I am proud to share with the great David Lewis. I reject Sobel's argument for the following reason:

    We are told simply that if they had popcorn then they would be displaying the subliminal message, and we would decide to look for popcorn. But presumably we could decide to look for popcorn independently of the subliminal message, which it seems is a lot like what's happening now to the 1-boxers. Can we be sure that we are in an identical mental state now to how we would have been had the subliminal message been aired, i.e. that it would cause us to invoke decision theory and make the reasoning we are currently using? Let's just say yes for the purpose of the problem. Now, if it were also established that these thoughts of decision theory would not have entered my head unless the subliminal message was displayed, then I would be certain (or at least highly suspect) that there is popcorn outside and go looking for it. If it isn't impossible, i.e. if I could independently think of that reasoning without the message, then I would need to know the frequency with which my thought is caused by the message and the frequency with which my thought is caused by my own curiosity or urge for popcorn. If I don't know the frequencies then I probably end up making a principle of indifference between them, assigning them equally 1/2. I therefore only go outside to get the popcorn if my utility for "leave and get popcorn" is more than double my utility for "stay and miss out on popcorn".

    That is my current conclusion. I'll red what Sobel has to say about it and possibly edit this post later to account for belief revision.

  • A Perfect Iliad

    I think my favourite story during my childhood was that depicted in the Iliad, of the Greek invasion of Troy, focusing on Odysseus, Agamemmnon, Menelaus, Achilles and Diomedes, and Hector and Paris. When I was young we used to listen to a story in the car when we were driving on holiday. There were two audiobooks, "Odysseus: The Hero Of Them All" and "Odysseus: The Journey Through Hell", co-written and narrated by Tony Robinson. For about 5 years I tried to find these on the internet as we had had them from the library, and I finally managed to track them down and buy two copies of them, although I haven't re-listened to them yet because I'm waiting until I can convert them to a digital format.

    But these stories were one of the best parts of my childhood, the story of how Odysseus was called away from Ithica to fight in a war he didn't want to fight in, and the events of that war and his unbelievable journey to get home after the war. Tony Robinson managed to express comedy and tragedy perfectly, expressing deep sorrow for the deaths of Odysseus' comrades, the predicament of Penelope and the suitors, and Odysseus' unceasing fury when he returns.

    Since then I've read or watched at least three other depictions of the Trojan war. Firstly, there is the Iliad, wrriten by Homer, which the others are mostly based on. It's a tough read, mostly about constant warfare, talking about one hero killing another and very hard to follow given the number of names involved. There's one section close to the start that simply lists all the names of the Greek heroes and contingents sailing for Troy which lasts several pages. Secondly, there's Shakespeare's play "Troilus and Cressida", which puts forward some strange differences to the original. For example, Pandarus is not an archer but a merchant, and Troilus is considered to be a good fighter who at one point fights off both Diomedes and Menelaus (I think).

    Thirdly, there is the quite new film called Troy, starring Brad Pitt and Eric Bana. I've actually seen several film and TV adaptations of the Trojan war, but that one is by far the best. I now cannot even imagine the character of Achilles without thinking of Brad Pitt. Achilles was thought of as being the most beautiful man alive, and so is Brad Pitt. What I particularly like about the film is how you are never sure which side you prefer to win. The Iliad is extremely pro-Greek (and "Hellenocentric"?). You only ever see Hector dressed for full battle. Quite often you only hear about him on some other side of the battlefield cutting swathes through the Greeks. But the worse thing about the Iliad depiction, I believe, is that when Achilles challenges Hector to fight, Hector runs away from him leading to a humiliating chase around the walls of the city before he finally gets caught. And then he's killed with one stroke of Achilles' sword. I much prefer the depiction of the fight from the film Troy, where Hector is shown to know that he will die fighting Achilles but goes anyway as a matter of duty. Troy is one of the few Hollywood films with a fight where the audience honestly does not know who to root for. As far as the audience is concerned both Hector and Achilles are virtuous and good. That's extremely rare for Hollywood as it's almost always "Goodie vs. Baddie". In Troy there is a baddie, the despotic king, Agamemmnon, but the general attitude is that both the Greeks and Trojans are good (or they're all equally bad?), and that this war is an inevitable and tragic result of politics.

    The film does have some ridiculous alterations to the plot which ruins it though, for example Agammemmnon being killed by Briseis, and also Hector killing Menelaus during his duel with Paris. There's also a suggestion that Hector kills Ajax, and there's a complete lack of the other important characters like Diomedes, Antilochus, Idomeneus, Aeneas, Sarpedon, "little Ajax", Cassandra and a few others.

    When I read the Iliad a few years ago, I was quite disappointed about the ending, Hector's burial. I quickly began reading the Odyssey and was saddened to see a huge gap in the events that I had learned about growing up. Where was Achilles' death? Where was Ajax's suicide? Where was Paris' death, killed by an arrow shot by the bow of Hercules? (tipped presumably with the blood of the hydra) And of course, the famous wooden horse, the murders of Priam and Little Ajax's rape of Cassandra? (I think he's referred to as Oilean Ajax but I prefer "little Ajax"). In the film, Troy, I believe they had Briseis kill Agammemmnon to introduce some feminine influence, but they could have included the Amazonian Queen Penthesilea, who Achilles killed. They could have had the Ethiopian king, Memnon, who killed Antilochus and was in turn slain by Achilles. So much happens between the Iliad and the Odyssey which Homer only vaguely refers to during the Odyssey. Where did all this stuff even come from? Who wrote about those other stories?

    What I'd quite like to do is collect all the sources, all of the stories, and collect them into one good novel, probably about as long as The Lord Of The Rings. Absolutely every part of the story could be included, even Shakespeare's version, everything that doesn't contradict with some other bit anyway. Plus, like the film, Troy, the metaphysic of the novel would be atheistic, it would even resemble our best current scientifically influenced metaphysical theories as best as possible. For instance, Achilles would not be immortal, but purely an excellent fighter. Many others might believe him to be immortal, although he probably doesn't believe it himself. The novel could be written based on the notion that the Iliad represents an exaggerated and mystical history of the original event. Everybody believed Achilles was immortal, then he was shot in the heel with a poison-tipped arrow, and suddenly the story would become "He was dipped in the River Styx as a child and was immortal everywhere except his heel." There would be no gods fighting on the battlefield, guiding arrows to their targets, or arguing on Mount Olympus between scenes, although the characters might reasonably believe it.

    The toughest part of writing such a novel would be how to treat the Odyssey. How do you explain a cyclops or Scylla, a journey through Hell or sirens with a naturalistic explanation? It's possible that there would actually be a good opportunity for creativity to re-write the Iliad, explaining that most of the widely-known story is simply story, and that what really happened was actually completely different but somehow still related closely enough to make the plot intriguing. There's even the possibility you could develop the character of Odysseus to make him more sinister and cowardly than he was thought to be. If you think about it, if all that's left of an army is its general, who's washed up on the Ithican beach, you'd think there's more likely than not some foul play going on there. We already know that he was very quick-thinking and a good problem-solver, so the story could include his fabricating the whole story of the Odyssey. There is definitely a great potential for a brilliant story here. Possibly the story could be developed to include the stories of Aeneas, Diomedes, Menelaus and Agamemmnon after the Trojan War to make it a true epic tale that ties up every loose end.

Footer:

The content of this website belongs to a private person, blog.co.uk is not responsible for the content of this website.