What we should like, I suspect, is for Thug to repent, to be genuinely sorry for what he did - and to make some amends. This is secular penance. We may even countenance the thought that his recognition and repentance could be so heartfelt that he himself ends his life. Those who baulk at inflicting pain on the guilty should note that, in wanting Thug sincerely to repent and undergo remorse, we want him to inflict pain on himself. Remorse is not enjoyable.

Suppose Thug will not repent. Imprison him, torture him, execute him - whatever we do, suppose we cannot get him to see his ways as evil. Then, we are impotent. Then, for always, Thug claims a mysterious power over us, a power that unsettles us, that shakes our humanity or our belief in humans as made in G.o.d's image. We want to nullify, cancel, neutralize that power. If only we could break down the barrier that protects him from all moral concern, from all sense of humanity. If only we could get him to be human, to say sorry and mean it. If only*

Is that why we care about Thug?

Rationality/Probability

26.

BEAUTY AWAKE.

There is more to this puzzle than meets the eye, but let us meet the eye - and then touch the more. Sleeping Beauty has a walk-on part, or, more accurately, a sleep-on part, for her role is merely to be put to sleep and then awoken in the following little game.

It is Sunday. Beauty is truthfully informed that she will shortly be popped to sleep. What then happens - and she knows this - depends on a coin's random spin. The coin is fair. If it lands heads, she will be woken, just once, at 6.00am for ten minutes, on only one of the next five days, randomly chosen; and then returned to sleep until the end of the game. If it lands tails, she will be woken at 6.00am for ten minutes, every day of the game, then popped back to sleep, each time her memory wiped each day of any previous awakenings. The game ends on Sat.u.r.day, when she is woken, her memory fully restored. Before that Sat.u.r.day waking, whenever she is woken, she remembers everything about the game's set-up; but she is not told how the coin landed. Furthermore, as said, she fails to remember any previous awakenings.

So, if the coin has landed heads, then she wakes up once - obviously not remembering any prior waking. If the coin has landed tails, she wakes up five times, once each morning, but not remembering any other awakenings during the game. Speaking roughly, tails for total total possible awakenings; possible awakenings; heads heads for hardly any. for hardly any.

The puzzle is: when she wakes up during the game, what a.s.sessment should she make that the coin landed heads - or that it landed tails? This is a question of what is it rational for her to believe, given the evidence.

What should Beauty believe when she wakes up?

A few argue that it is obviously a fifty-fifty matter. When she wakes up, she has no new information, just the information given at the game's start. At the game's start, she knew that heads and tails were equally likely. She also knew that she was bound to wake up, whether heads or tails. So, now she is awake, how can she possibly conclude that tails must have been more likely? She has nothing new to go on.

Others argue that she should believe it more likely that the coin landed tails. If she bets on tails, then, over a series of such games, she is more likely to win overall than not. Suppose the game runs twelve times, one game per week: she is likely to lose the tails bet six times because there would, on average, be six awakenings resulting from heads coming up six times out of the twelve weeks. However, it is reasonable to expect her tails bet to win thirty times: on average, tails should come up for six games, and there are five awakenings for each of those six - hence thirty bets on tails when in fact it is tails.This type of consideration leads some to the conclusion that, whenever she is awake during the game, it is rational to believe it is more likely a tails awakening.

Here is a route into the puzzle. I am walking along a long bendy road, with a thousand turnings, a tree at each, but I can see only one tree at a time - mind you, I am not paying attention to them. I know that I have taken either a road (Max route) with a thousand goats, one tethered to each tree, or a similar road (Min route), but with only one goat tethered to a tree, independently of anything to do with me. The Min route is certain to have a goat at a tree, but it is a one in a thousand chance to which tree it would be tethered. In other words, Min is guaranteed to have an unlikely feature - just as a lottery may be guaranteed a winner, but it is a one in a million chance against any particular player being the winner.

My chosen road has been randomly chosen, perhaps by a fair coin's spin. I am on the road and just happen to pay attention to a tree. A goat is tethered to it. I think: although it is certain that Min has some tree with a goat, it is highly unlikely that the one I just happen by chance to look at should be that tree. With Max, it is certain that I see a goat whenever I look at a tree. Hence, I should judge that it is highly likely that I am on Max rather than Min.

Suppose, though, that my goat love is so great that whenever I pa.s.s a tree, I am bound to pay attention to it if, but only if, it has a goat tethered. Perhaps the goatish scent attracts me. Then, whichever route I walk, the first experience of tethered goat points equally to Min as to Max. Of course, if I have a second goat sighting, then that makes Max certain. If, however, I am always utterly forgetful whether I have seen a goat tethered, then I have no idea whether a sighting is a later one or a first; so, I am back to being unable rationally to judge one route as more likely.

In this traveller's tale, we have mentioned two features that may coincide: my paying attention to a tree and its having a goat. When it is just by chance that I attend, then, for all I know, I may see a goat or no goat: it could go either way. That it goes one way rather than the other is relevant evidence for me, when judging which route I probably travel. But when my attention is determined by goatish scent, then, whichever route I am on, there is no surprise in my finding a goat, when I pay attention. And so I cannot use the goatish sighting as evidence either way regarding which route.

With Beauty, when she awakes, there is no surprise at two features happening to be conjoined, such as attending to a tree and seeing a goat. It is not as if there is a coincidence between Beauty's being awake and noticing that she is awake. Whichever way the coin came down, she is guaranteed to have the experience of waking; and, with the memory loss, all awakenings seem a first awakening. So, on any game's awakening, she has no good reason to change her initial a.s.sessment; she should continue to believe that her being in the tails game is no more likely than her being in the heads game.

What of arguments that it is rational for Beauty, whenever awake in the game, to believe tails is the more likely outcome? Some present detailed probability considerations, but perhaps - note the hesitation - the puzzle shows how rational betting can separate from what it is rational to believe. Whenever Beauty is awake, she has no more reason to believe that tails came up than that heads came up. However, if she is awake because tails came up, then she has five opportunities to bet on tails and be right; but if she is awake because of heads, she has only one opportunity to bet on heads and be right. If she bets whenever awake, she should therefore bet tails. This is not because tails is more likely than heads, but because the tails outcome offers more betting opportunities than the heads outcome.

We may now reflect that if, whenever awake, she believes it is a tails game, she would have more correct beliefs over a run of games than if she believed heads. But that does not justify the claim that what is believed is more likely to be true. The evidence justifies neither the belief that it is a tails game nor the belief that it is more likely a tails game. If Beauty wanted to increase the number of times it is likely that she believes something true, and if she could, per impossibile per impossibile, switch on beliefs at will, then she should believe she is in the tails game, but that does not mean it is rational to believe the game is more likely to be tails than heads.

Sleeping Beauty has its source in work by Arnold Zuboff, leading him - all of us, apparently - into a marvellous metaphysics, one whereby all experiences are my my experiences, where we are all one and the same person. Before you turn to another chapter, nodding your head sadly at some philosophers' craziness, reflect on the following. experiences, where we are all one and the same person. Before you turn to another chapter, nodding your head sadly at some philosophers' craziness, reflect on the following.

My existence, according to the usual view, required a certain spermatozoon and ovum; and their existence depended upon a sequence of a vast number of highly specific events stretching back over generations and into evolutionary mists and mysteries. A sneeze, a delayed coach, a wrong foot, so to speak, centuries ago - and my great-great-great grandparents, for example, would not have been conceived; hence existence, according to the usual view, required a certain spermatozoon and ovum; and their existence depended upon a sequence of a vast number of highly specific events stretching back over generations and into evolutionary mists and mysteries. A sneeze, a delayed coach, a wrong foot, so to speak, centuries ago - and my great-great-great grandparents, for example, would not have been conceived; hence I should not have been conceived. Is it not an amazing coincidence, on the usual view, that the very specific requirements for my existence should have come about?

Of course - though paradoxically sounding - it is often highly likely that unlikely things will happen: witness the lottery example above. But, on the usual view, we have no reason to think it highly likely that the unlikely event of my my existing would have happened. That I exist, if I am a person distinct from others, is akin to the unlikeliness, when on the Min route, of my randomly looking up and seeing a tree with a tethered goat - but where there are trillions of trees yet still only one goat. A far more reasonable hypothesis, according to Zuboff, is that my existence occurs in a Max version of a consciousness creation. Whenever any experiences come about, they are mine. Indeed, the only factor that makes an experience mine is its first-person character; and every experience has that. If this is right, then that is what we all think, being all one individual consciousness - and yet do not think, because, in some way, consciousness is segmented. existing would have happened. That I exist, if I am a person distinct from others, is akin to the unlikeliness, when on the Min route, of my randomly looking up and seeing a tree with a tethered goat - but where there are trillions of trees yet still only one goat. A far more reasonable hypothesis, according to Zuboff, is that my existence occurs in a Max version of a consciousness creation. Whenever any experiences come about, they are mine. Indeed, the only factor that makes an experience mine is its first-person character; and every experience has that. If this is right, then that is what we all think, being all one individual consciousness - and yet do not think, because, in some way, consciousness is segmented.

Philosophical reflections can set minds reeling. Our reeling here requires thought on unlikeliness. The one-person view is struck by the seemingly highly unlikely coincidence of the conditions required for my existence being the conditions that arose. But we may then comment on the highly unlikely coincidence of the conditions required for this book's existence being the ones that arose. Does that show that there really is only one book? The response is: of course not, unless the book were conscious. Were it conscious, then its existence would be a coincidence Jorthebook Jorthebook. So, the one- person view hangs a lot on my existence involving a coincidence Jorme Jorme; but what is so special about the 'for me' concerning unlikeliness? Consider a lottery where it is certain that someone would win: it is still highly unlikely that the individual who won would be the winner, even if she, the winner, is unaware of having won. We may also wonder how the one- person view accommodates the fact, seemingly unlikely, that, for example, these these experiences, when writing these words, appear to be only within the experience of Cave and not Zuboff. And so we return to the baffling question: What is this 'me? experiences, when writing these words, appear to be only within the experience of Cave and not Zuboff. And so we return to the baffling question: What is this 'me?

Yes, philosophical reflections can set minds reeling. While our existence on the usual view is vastly, vastly unlikely, it may still be more likely than the truth, or even sense, of the one-person view. We may be tempted to sigh, 'Who knows?' And here we have as much perplexity with the nature of 'who' as with that of 'knows'.

Religion

27.

THE GREATEST MIRACLE?.

Water has been turned into wine - well, so some believe. The dead have been brought back to life here on Earth; someone has walked on water. Miracles, it is said, occur at Lourdes - to date, sixty-seven, according to the Catholic Church.

Many, many people have believed in miracles. Many, many people do believe. But what is a miracle? Sometimes people speak of miraculous happenings merely when very surprising and fortunate events occur. A mother who finds her child alive in an earthquake's wreckage, when hundreds are dead, may perceive the life as a miracle. She thanks G.o.d, or G.o.ds, for her child's lucky outcome, yet, were she to reflect, she should also temper her thanks with blame for the deaths of the others. Such 'miracles' though - as when difficult surgery goes well or weak candidates pa.s.s examinations - are normally accepted as in accord with the usual and natural ways of the world.

Let us focus, for the moment, on miracles as divinely caused events. That is one feature; but some believe that everything that happens is divinely caused. So, to avoid everything being miraculous, we need to add the condition that the events differ from what usually or naturally happens. In some way, miracles interfere with the laws of nature. Water is not the sort of stuff that turns to wine; corpses, according to known natural laws, do not suddenly sit up, alive again.

Often people believe miracles occur because they already hold a religious faith which accepts miracles; and then, certain events, which would otherwise be explained naturally, are taken to be miracles, sustaining that faith. This is, to say the least, a little self-serving. The reasoning loops round.

Some people reject miracles, even the possibility of miracles, on the grounds that any events that violate what we take to be the natural laws simply show that we have failed properly to grasp what the natural laws are. The laws are more complicated than we first thought. This rejection too is self- serving, serving those sceptical of miracles, ruling miracles out virtually 'by definition', as some may seek to rule out black swans by defining swans as white.

Is it ever rational to believe in miracles?

The question is puzzling because some people are so certain that it can be rational so to believe, whereas others flatly deny miracles. The philosopher most famously a.s.sociated with a 'no' to the question is the eighteenth-century philosopher David Hume - though a certain Thomas Woolston, writing a little earlier than Hume, outspokenly attacked biblical accounts of miracles as containing absurdities and improba- bilities.Woolston ended up in prison, where he died. Hume, despite being labelled 'The Great Infidel', was much luckier -and, it would seem, less inflammatory.

Let us now shelve the 'divine intervention' feature of miracles and focus on whether it is ever rational to believe that some remarkably unusual events, going against the natural laws, have occurred. For ease, hereafter we refer to such events as 'miracles', adding 'divine', when the feature of G.o.dly intervention in particular is being addressed.

Hume's position is often seen - probably mistakenly seen -as the following: while miracles are possible, it is always always irrational to accept as reliable any reports that they have occurred.We seem to have a paradox here. Although it is recognized that a type of event is possible and can be witnessed, it is argued that it is bound to be irrational to believe any events of that type ever happened. That sounds paradoxical. After all, it is not as if we are discussing events that can only occur when human beings did not exist. There are observers of the alleged miracles. irrational to accept as reliable any reports that they have occurred.We seem to have a paradox here. Although it is recognized that a type of event is possible and can be witnessed, it is argued that it is bound to be irrational to believe any events of that type ever happened. That sounds paradoxical. After all, it is not as if we are discussing events that can only occur when human beings did not exist. There are observers of the alleged miracles.

Why may it always be irrational to believe in miracles? Well, we have considerable evidence for our beliefs that laws of nature hold. For example, none of us, despite wishes, has ever seen water turned to wine. True, many things happen to water - freezing, steaming - and theories have been developed explaining such changes. We have, though, no evidence at all to think that water can have the intoxicating transforming possibilities reported as having occurred. Indeed, it may be partly because water has not, in the experience of billions of people, ever turned to wine that we are confident that water naturally lacks such possibility. Now, what could lead us to think that a few times, centuries ago, some water was turned into wine?

Well, a few eyewitnesses reported such a change. Could their testimony, testimony pa.s.sed down, make it rational for us to believe that water underwent such change? Let us a.s.sess the different evidences in play.

On the one hand we have considerable evidence in favour of water not turning to wine - from centuries of everyday uniform experience and experimentation. On the other hand, we have considerable evidence that reports of events can be misleading, either wilfully or by accident. We should, of course, apportion our belief to the evidence. Further, very high standards must be set for reports of exceptionally unusual events. Evidence against water turning to wine: exceptionally strong. Reliability of reports of events, of testimony: sometimes low. Hence, without other factors, it would appear irrational to believe in the so-called miracle - and all other so-called miracles, for similar reasons - at least when based on what people say. It is more likely that the reports are mistaken than that the exceptional events occurred.

Are things essentially different if we personally have experiences of the seeming miracle? Again, it may be more likely that we could offer a better explanation for what we experienced than its being a miracle. The exceptional nature of the experience, if a miracle, needs to be contrasted with the well-known fact that we make mistakes, can be misled, tricked, are tempted by the extraordinary - or are just plain tired.

The overall conclusion is not that we should be absolutely certain that any 'miracle' reports are false, but simply that it is irrational to believe that the reported miracles happened. However, even this conclusion is too sweeping.

Hume supposes people, of different nations, reported a darkness over the planet during the first eight days of the seventeenth century. It could then be rational to believe that that highly unusual occurrence took place, given the number of reports, different sources, and so on. This shows that Hume does not argue that it is always always irrational to believe reported unusual events have happened - 'miracles'. irrational to believe reported unusual events have happened - 'miracles'.

Maybe Hume's position is that it is always irrational to take the further step and believe the events were divinely caused, were divine miracles. Even here, we may wonder. Suppose that the reports of the eight days of darkness also spoke of a booming voice from the skies, speaking in all languages, telling of the creation of the world, of eternal life, of its being the voice of the one true G.o.d to be worshipped*

Well, such an extraordinary event may lead us to think that there is some conscious power present, but it would still be a big leap to conclude that therefore the power must be an eternal all-powerful deity who is all good. After all, there is still all the suffering in the world, which at least suggests that the power in question is not thereby all good - the problem of the existence of evil in the world, a problem for those who believe in G.o.d as a being who is all good and all powerful.

It is wise to be cautious of people's reports of miracles, of apparently highly exceptional events. Such caution, though, does not guarantee avoidance of error. In the eighteenth century, the King of Siam had not seen ice. He refused to believe the Dutch amba.s.sador's reports that, during Holland's winters, water became so hard it could support the weight of elephants. Depending on what other evidence was available to him, the King, even though mistaken, may well have been rational in believing the reports false.

As well as an event's likelihood, we need to take into account reporters' motives, their position to judge, and whether similar events would be expected to occur that could be checked. In principle, more and more evidence could be given to the King, showing that, in certain circ.u.mstances, water regularly turns to ice.

Hume nicely quipped that religious believers must be conscious of a continual miracle in their person in holding their religious belief. Perhaps that is the greatest miracle. But, of course, religious faith and belief in miracles are very common - so, really, their existence is no miracle at all. Despite the belief's irrationality, it is far from a miracle that people believe in miracles. Indeed, it may be the very irrationality that explains why it is that so many people do believe. And irrationality is no miracle at all. After all, many believers accept that rationality alone cannot lead them to G.o.d; rather, they commit themselves to leaps of faith, or, as quipped before, hops, skips or jumps of faith.

Metaphysics

28.

c.o.c.kTAILS, RIVERS, AND SIR JOHN CUTLER'S STOCKINGS.

A c.o.c.ktail unshaken or unstirred can quickly cease to be a c.o.c.ktail, for the ingredients separate. When wanting a gin and tonic, your want may not be divisible, such that you want a gin, whatever the outcome regarding the tonic, or vice versa. A gin and tonic needs to be mixed - and it is the mixture you want. These simple examples remind us that some items are what they are and remain the same only if they have parts with some swirl, some mixing of ingredients. Even if the parts remain constant, the items may not - and that can be simply because of absence of swirl, absence of mixing.

The c.o.c.ktail ceased to be; yet the ingredients remained. Rivers remain; yet the ingredients change. An oft-cited remark in connection with this is from the early fifth-century bc ancient Greek philosopher, Herac.l.i.tus: You cannot step into the same river twice.

Quick-fired responses have been that you cannot even step into the same river once. They may depend on a logical point that stepping into the same the same implies stepping more than once. They may, though, be relying on the fact that the waters are forever changing, whether you step once or twice. implies stepping more than once. They may, though, be relying on the fact that the waters are forever changing, whether you step once or twice.

What may have intrigued Herac.l.i.tus - and what has intrigued later philosophers - is that when Herac.l.i.tus first bathed in the river, he was indeed bathing in some water. The river consisted of just that water and nothing else. Yet the next time when he bathed in the same river, because the waters had flowed, he bathed in some different water, even though the river was the same river.

How can the river be the same, yet the water be different?

The river is, of course, extended in s.p.a.ce; so, at one and the same time, two different people may be bathing in the same river yet in different patches of water, just as two people may be seeing the same mountain, yet one sees its bare rock to the south and the other its forests to the north. Some would then urge that the river be thought of as stretched not merely in s.p.a.ce but also in time, as having not merely spatial but also temporal parts. We may then account for how bathing at the same location, in the same river, but at different times, may involve bathing in different waters.

Strictly speaking - a dangerous expression - Herac.l.i.tus bathed in one temporal slice of river, identical with a patch of water, at one moment on one day; he then bathed in a distinct temporal slice of the river, identical with a different patch of water, at a later time. The first temporal slice is not identical with the second, but both are slices of the one temporally extended river.

Thinking of items, such as rivers, pokers, and people, as collections of temporal slices, though, seems to lose the idea that one and the same thing endures yet changes - a problem outlined in Chapter 4, In no time at all In no time at all.

A more obvious response to the Herac.l.i.tean aphorism is to resist the ident.i.ty of the river with its waters, making instead the common-sense observation that a river is composed composed of water. One and the same river is composed of ever-changing waters - otherwise it would not be a river, but perhaps a long thin lake. What makes something one and the same river does not depend on its possessing the same composition, the same watery ingredients, over time - and, with c.o.c.ktails in mind, even when something has the same ingredients, it does not follow that it is the same item. Herac.l.i.tus, in his thinking, may have simply been making, albeit enigmatically, that common-sense point. Indeed, he offers a c.o.c.ktail example: 'The barley drink disintegrates if it is not stirred.' of water. One and the same river is composed of ever-changing waters - otherwise it would not be a river, but perhaps a long thin lake. What makes something one and the same river does not depend on its possessing the same composition, the same watery ingredients, over time - and, with c.o.c.ktails in mind, even when something has the same ingredients, it does not follow that it is the same item. Herac.l.i.tus, in his thinking, may have simply been making, albeit enigmatically, that common-sense point. Indeed, he offers a c.o.c.ktail example: 'The barley drink disintegrates if it is not stirred.'

Changes in composition can be essential to the ident.i.ty of a thing. That the river yesterday is the same river as the one today does not amount to its having the same composition.

But then, what does make it the same river?

Sir John Cutler, of the seventeenth century, was much attached to his black worsted stockings, so attached that, as holes developed, his maid would darn them, with silken thread. Eventually, his stockings no longer consisted of the original material, but of silk.The composition of his stockings was clearly different. Yet, it could reasonably be said, they remained the same stockings, in that they possessed a continuity through s.p.a.ce and time and were used by Sir John to cover his legs to fine effect. What made them the same stockings did not depend on material sameness, but on continuity, ownership, and function.

And what makes something the same river depends on location, usually a long geographical continuity, and changing waters flowing into a sea. A river may be the same river over time, even if during a period it runs dry, but is later replenished. And there will be times when we are unsure what to say, when rivers flow into each other. It may seem not to matter until, so to speak, it matters - as when there may be disputes about land or irrigation or fishing rights.

Here is a much discussed further example. As the parts of the Duke of Theseus's ship wore out, they were replaced, plank by plank, sail by sail, rope by rope, until - as with Sir John's stockings - not one of the original parts remained in the ship. The tale of Theseus's ship, though, has a twist. Suppose scavengers h.o.a.rded all the worn-out planks and other parts cast asunder, and then reconstructed the original ship, admittedly excessively shabby and unseaworthy. Which is really Theseus's ship - the one now composed of new parts, yet in Theseus's continual ownership, or the shabby one consisting of the original materials?

We may again be tempted by the thought that there is no 'really' about it, just a matter of decision. Here, though, it is a decision with consequences - especially if Theseus's new- looking ship is lost at sea, yet insurance companies refuse to pay out, claiming that the ship insured was the one composed of the same material, not the one now lost.

Metaphysics/Knowledge

29.

HOVE AND LATE: A GRUESOME AFFAIR.

Even the closest friends may possess little quirks. Although Miranda was a close friend, my girlfriend indeed, her little ways of calling blue things 'bleenly' coloured and green things 'gruely' irked me, though I tried to see them as sweet linguistic quirks rather than irks. I had no reason whatever to think things appeared differently to Miranda than to me; well, no more so than anyone else. After all, she called the sky 'bleen' and the gra.s.s 'grue'. And when she wore her aquamarine dress - was it really green or blue? - she wondered whether it was really grue or bleen.

What do I care, I mused, about her linguistic ways? Mind you, I thought it best not to discuss whether she considered this or that person was grue with envy; and, when we engaged in musical reflections, I resisted asking her whether she liked the bleens. My silence on such matters turned out to be sensible - for we were about to have enough troubles.

Ah, yes, there was one other little quirk. Whenever we were in romantic mood and I was declaring how much I loved her, she expressed her love too - save she said how much she hoved me. And curiously, when she expressed dislike of abstract art, football crowds, and champagne breakfasts, she would speak of lating them.

One sultry summer's day, having fallen asleep on the green gra.s.s, out in the sun, under clear blue skies, I awoke, with Miranda tugging me. She was astonished - even distressed. 'Why, what's wrong?' I asked. 'Don't you see?' she cried, 'The gra.s.s is now bleen and the sky grue - whatever am I to do?'

I was baffled. They looked the same to me. 'But, Miranda, do they look differently from how they used to appear to you?'

'Well, I suppose they must - I guess. I am not really sure what to say. The sky, though, certainly is no longer bleen; I can tell that. And I haven't suddenly changed what I mean by my words.'

I looked at the calendar: while we were asleep, there would have been a rare comet crossing the sky at the same time as a partial eclipse of the sun.