(1) All tortoises glory in champagne.

(2) Mr T is a tortoise.

(Conclusion) Mr T glories in champagne.

We know that the conclusion is false, but logic is making the point that the conclusion follows follows from the premisses (1) and (2); that is, were those premisses to be true then the conclusion would be true too.' from the premisses (1) and (2); that is, were those premisses to be true then the conclusion would be true too.'

'That Miss Logic is very rigorous and disciplined indeed, sir. And, of course, I bow to her wisdom; but may I just check things out? For the sake of the argument - isn't that what you say, sir? - I'll accept that all tortoises glory in champagne and that Mr T is a tortoise, but - and here I must scratch both my sh.e.l.l and my head - I am not all that sure. Do I have to accept the conclusion that therefore Mr T glories in champagne? You see, sir, I am not sure if I quite follow - despite the sternness of Miss Logic's gaze.'

Can we help Mr T to see that the conclusion must follow?

We may be tempted to reply, with the dialogue continuing: 'Look, Mr T, can you not see, through that thick sh.e.l.l of yours, that.'

'I am sorry, sir, but I have never seen through my sh.e.l.l.' 'It was just a manner of speech, Mr T.' 'It may be "just" to you, but not to me, brought up as I was with only a second-hand cracked sh.e.l.l and*'

'Let's get on, Mr T. Can you not see that, if all tortoises glory in champagne and Mr T is a tortoise, then it must follow that he glories in champagne?'

'Ah, you mean, if premisses (1) and (2) are true, then (C) must be true.?' 'Exactly.'

'So, that is an important step in my grasping the argument?'

'Er, yes, I guess so.'

'We had better write it down, in case I forget it. It is another premiss that seems essential to the argument.' 'Well, yes - er, yes, yes, so the full argument is: (1) All tortoises glory in champagne.

(2) Mr T is a tortoise.

(3) If (1) and (2) are true, then Mr T glories in champagne. (Conclusion) Mr T glories in champagne.'

'Ah, I see.'

'I hope very much that you do see, Mr T, for if you do not, Miss Logic will grab you by your throat, dance on your sh.e.l.l and*'

'Now, don't get carried away, sir. Let me check it through, to make sure I understand. I accept (1) and I accept (2) and I accept (3), but, I still wonder, does (C) have to follow?'

'Oh dear, Mr T, you are a dunce. Do you really not see that if (1) and (2) and (3) are true, then the conclusion must follow?'

'I feel another premiss coming along, sir. You have just explained why the conclusion follows by giving me a premiss (4), namely, (4) If (1) and (2) and (3), then Mr T glories in champagne.

You must pop that premiss into the argument too.'

At this, we all sigh, for, of course, now that Mr T has got us going, into offering additional premisses, there will be no end, well, no logical end, though there may be a weary end to the conversation. And Mr Lewis Carroll who first wrote, so splendidly, of a tortoise setting these challenges, had his Achilles writing down more and more premisses in his notebook, in his attempt to justify deduction. He would indeed need a notebook with an infinite number of s.p.a.ces for writing - which, of course, all notebooks have, but that is another story about the endless division of s.p.a.ce.

It is readily accepted that deduction cannot be justified by offering more premisses. As a result, some say that what justifies particular deductions is their conforming to certain rules or schemes of logic, for example: All S are P; a is an S; therefore a is a P. I doubt if this would silence our Mr T, for, once such a rule is offered, he can set off again, asking for a further rule concerning the application of the offered rule - and so on. Further, in explaining all this, we are already making use of such deductive arguments: if you accept this Mr T, then you should accept that.You do accept this; therefore you should accept that. * * *

'Er* er*'

'What is it, Mr T? About to cause more trouble for Miss Logic?'

'Certainly not. I wonder if I may help you all out.'

'Go on, Mr T.'

'Your mistake, if I may be so bold, sir, was to attempt to justify deductive practices. It was understandably kind of you to try to explain matters. Maybe making some of those comments that I forced you to write down as premisses could help in some cases. Drawing little diagrams also can help. These, although valuable tricks to open eyes to validity, do not make the arguments valid. That an argument is valid, if it is, is simply manifested in, for example: (1); (2); therefore (C). Rules and schema and additional premisses do not justify (C)'s following from (1) and (2). (C) just does follow. Indeed, sir, the rules and schema are derived from the particular cases - such as the champagne case just cited.

'This too should remind some that from the premiss that a figure is a square, it validly follows that the figure has four sides. There is no need painstakingly and wrongly to insist that it only validly follows if we have another premiss such as "All squares have four sides.'

And with that, Mr T set off, his head held high - well, not that high, given his tortoise's height - muttering something about the muddles that Humpty Dumpty and Ms Turkey were getting into, thinking that inductive reasoning too needed justification. Of course, how Mr T managed to move through s.p.a.ce and time, reaching a desired end at all, remained something of a mystery for him.

Meaning/Life/Arts

33.

FRAGILE CREATURES THAT WE ARE*.

McTaggart - John McTaggart Ellis McTaggart no less, though also no more, a philosopher at the turn of the twentieth century - kept a cat, a cat named 'Pushkin'. In winter, people who visited McTaggart in his Cambridge rooms were astonished to see Pushkin enjoying pride of position fireside front, while McTaggart shivered at his corner desk. 'Why ever do you give Pushkin the warmest slot?' 'Because,' replied McTaggart, 'that's the best it gets for a cat.'

Human beings often reflect on their lives - unlike cats.We reflect not only when in philosophy cla.s.ses and on therapists' couches, but in pubs and clubs, while trapped in airports, or lazing on seash.o.r.es, alone or with friends - and also in the night's stillness when sleep is elusive and only breathings and heartbeats sound. And while it is not uncommon, when the going gets tough, to wish to be feline - my mother's wish when ensnared by shrinking, twilight years - most of us value being a person much more than being a cat. Only we humans can chart the heavens, be compa.s.sionate and just, and laugh when the barmaid, having asked which drink - 'Bitter?' she says - receives the reply, 'No, just tired.'

There is far more to human life than to the feline; and we value the more.Yet, once reflecting, we meet trouble, for we may trouble ourselves about what gives meaning or sense.

How can we make sense of our lives?

Some think that lives can only make sense if they exist for purposes beyond themselves; then, looking for purpose beyond all human lives, they are either overwhelmed with despair at its absence or embrace the mystery of purpose divine, the divine apparently requiring no purpose outside. Yet we need not quest for purposes beyond all human purposes. Making sense may occur when we cast light on moments, relationships, and activities, seeing them as holding together in recognizable patterns, with values, histories, and developments. The arts - especially the narratives of drama, novels, and opera - help us to see sense by casting light on fictional lives, that is, by telling stories.

Stories open our eyes, proposing perspectives, revealing connections, and pinpointing clashes.We may come to understand the characters' lives and meaning, through seeing how the characters connect, how their pasts stand with their futures, and which values they grow to espouse. Stories appear as myths and sagas, tales and drama, poems and opera - and today's ever-playing operas of soap. Instead of ancient gossip, Grecian in mode, about Zeus, Apollo, and Dionysus, today's lager and wine speculations antic.i.p.ate the next s.e.x in the City s.e.x in the City, Curbyour Enthusiasm Curbyour Enthusiasm or or Housewives so Desperate. Housewives so Desperate.

Although the arts do not exist with the purpose purpose of helping us through life, in appreciating them we may relate them to ourselves. We see how lives hang on contingencies of birth, on flicks of the hair, on chance encounters. We meet with fragilities and tragedies, yet also resolutions and magical ways of seeing. Think how, centuries on, we still live lives through Greek myths, our understanding of ourselves being shaped by updated tales and psychological theories, invoking Oedipus, Narcissus, and Helen of Troy. of helping us through life, in appreciating them we may relate them to ourselves. We see how lives hang on contingencies of birth, on flicks of the hair, on chance encounters. We meet with fragilities and tragedies, yet also resolutions and magical ways of seeing. Think how, centuries on, we still live lives through Greek myths, our understanding of ourselves being shaped by updated tales and psychological theories, invoking Oedipus, Narcissus, and Helen of Troy.

A life may lack sense because experiences are fragmentary, no pattern discerned, emotions in turmoil. And, as sketched in Chapter 3's A pilljor everything A pilljor everything?, we may then anguish over what we truly are and want, rocked by seen and unseen conflicts. By way of example, here is a conflict, captured in Greek myth: the Apollonian versus Dionysian.

On the one hand, the image of Apollo signifies a rational world of limits, of distinct objects, of rules: a clenched fist in control. The image gives rise to aesthetic ideas of the simple, beautiful, and precise. We humans often aspire to such ideals. On the other hand, the Dionysian is intoxication, drunkenness, where boundaries become blurred, through ecstasy and frenzy: palms are open, welcoming, yielding; we melt and meld with others. Few of us think in terms of such explicit categories, itself an Apollonian enterprise; yet many of us recognize the conflict between control and succ.u.mbing - between straight lines and tangles. We need, though, the particularities of characters, details that novelists offer, that philosophy alone too easily lacks, to enlighten our struggles.

Thomas Mann's Death in Venice, Death in Venice, for example, brings to life a conflict - be it through the novella, Visconti film, or Britten opera. Gustav von Aschenbach, the Apollonian personification, the disciplined writer, admirer of aesthetics, is struck by the beauty of a mysterious youth. Aschenbach's Apollonian, aesthetic appreciation transforms into a Dionysian, obsessive, sensual desire - all from afar. Aschenbach becomes desperate and degraded, degraded by an elderly man's erotic love, a yearning for youth. Yet ambiguities persist. His death on the sh.o.r.e, his dying gaze towards the ocean - they may generate new ways of giving sense to his life, of feeling at one. for example, brings to life a conflict - be it through the novella, Visconti film, or Britten opera. Gustav von Aschenbach, the Apollonian personification, the disciplined writer, admirer of aesthetics, is struck by the beauty of a mysterious youth. Aschenbach's Apollonian, aesthetic appreciation transforms into a Dionysian, obsessive, sensual desire - all from afar. Aschenbach becomes desperate and degraded, degraded by an elderly man's erotic love, a yearning for youth. Yet ambiguities persist. His death on the sh.o.r.e, his dying gaze towards the ocean - they may generate new ways of giving sense to his life, of feeling at one.

The brief description does not captivate - but the novel, the film, the opera captivates many.We may lose ourselves in the work's beauty, while also relating to conflicts within ourselves and others. The arts, at their best, paradoxically both free us from self-absorption and shape how we see our lives and others, bringing new perspectives to bear. Religions do this too. Religious believers live lives in the light of stories, rituals, and music, derived from scriptures and tradition - though with the, arguably questionable, addition of looking beyond to an existent afterlife with G.o.d.

Let us not, by the way, foolishly and optimistically, think that good art leads to good deeds. Some tormenters - think of those responsible for the Shoah, the Holocaust - have marvelled at the splendour of, for example, Beethoven and Schubert. The arts do not make our choices for us.

'Life must be lived forwards, though can only be understood backwards,' wrote Soren Kierkegaard. Our life can never be grasped properly because we are never at rest to adopt the backwards-looking position. Even were we to rest, we should receive distorted pictures: how we should read the past depends in part on the future. Imagine a football game frozen ten minutes before the end: how the game is a.s.sessed up to then could differ radically from how that early period is a.s.sessed, once at end of play. What was viewed as dreadful formations, by the end is praised as inspired.

'In retrospect' has value, as does what is in prospect. Narrative art displays both: lives in prospect and retrospect. Jean-Paul Sartre saw that, prior to death, we are free to create our lives, to take them in new directions, leading to fresh 'in retrospect' views. The sting in death, according to Sartre, is awareness that, once dead, we are prey to the Other: we are impotent, as others try to interpret, fix, and cla.s.sify us. Narrative art, though, should remind us that such attempts may receive continual revision. Reflect on how people debate and review interpretations of characters' lives in a play.

Earthly life, as also paradoxes, offers both too much and too little. There lies tragedy. Perhaps we should like all our life to be that of an itinerant global traveller, yet we may also long for a life growing within one small, stable community. We may crave the life of the unworldly, yet also the worldly; of the loyal family man, yet also the Casanova - of the woman about town, a poetess, a courtesan, yet also someone down to earth. Lifestyles rule out others. We cannot try them all. Storms rule out calm. Greyness rules out rainbows.

Many of us give wry smiles at life's clashes, incongruities, and absurdities. Pity Pushkin the cat; he knows of no absurdities, of no smiles.Yet pity us too - for we cannot know for certain how our lives finally work out. 'Pity us', did I say?

Knowledge of our lives as ultimately viewed, if viewed at all, may be knowledge best not to have; but what is worth having is the mishmash, the muddles, the melee of life as we live it. There is a richness to the human life that eludes Pushkin's. Not only can we humans revel in reflections, ambiguities, and humour, flying close to the sun with loves and aspirations, but also we lose ourselves in art, in music, in wonder - in wonder at the land, the sea, the stars, at the vibrant jazz of city life, and the lingering look on a face.

With philosophy an a.n.a.lytical and reflective art, this book's perplexities have engaged reflection - reflection upon reflection, as does this sentence. It is, though, fitting to emphasize, here at the close, that not not reflecting also brings value, brings meaning. There can be paradoxical delight in losing the self, in simply surrendering, as perhaps Pushkin does, to dawn, to dusk, to desires - to mosaics of colours and sounds, from scuffling leaves and storms of snow to a skylark ascending over a heath. There is charm in saying nothing, in saying nothing at all. There is charm in - experiencing. reflecting also brings value, brings meaning. There can be paradoxical delight in losing the self, in simply surrendering, as perhaps Pushkin does, to dawn, to dusk, to desires - to mosaics of colours and sounds, from scuffling leaves and storms of snow to a skylark ascending over a heath. There is charm in saying nothing, in saying nothing at all. There is charm in - experiencing.

When the mountainjlowers are blooming, Their scent carries their meaning.

APPENDIX 1.

FURTHER READING.

My earlier book of philosophical perplexities, Can a Robot be Human? Can a Robot be Human? - hereafter - hereafter Robot Robot - recommended various good introductions. There are many more, so, resisting repet.i.tion, I mainly note some of the more. - recommended various good introductions. There are many more, so, resisting repet.i.tion, I mainly note some of the more.

For paradoxes and enjoyment, try Robert M. Martin, There are Two Errors in the the t.i.tle oj^this Book There are Two Errors in the the t.i.tle oj^this Book (Peterborough, Ontario: Broadview, 2002). Raymond M. Smullyan provides magnificent and enjoyable collections of logical puzzles: google for his many works. Serious recommendations for fun that raise philosophical questions are the excellent Lewis Carroll's 1865/1872 phantasies, (Peterborough, Ontario: Broadview, 2002). Raymond M. Smullyan provides magnificent and enjoyable collections of logical puzzles: google for his many works. Serious recommendations for fun that raise philosophical questions are the excellent Lewis Carroll's 1865/1872 phantasies, AliceinWonderland AliceinWonderland and and Through theLooking Gla.s.s Through theLooking Gla.s.s.Yes, this is the Lewis Carroll who gave us the tortoise in this book's Chapter 32. Martin Gardner's edition explains much in his TheAnnotatedAlice TheAnnotatedAlice (New York: Norton, 2000), with original texts and Tenniel's ill.u.s.trations. (New York: Norton, 2000), with original texts and Tenniel's ill.u.s.trations.

For seminal philosophical texts with editors' commentary: Samuel Guttenplan etal etal., eds, ReadingPhilosophy ReadingPhilosophy (Oxford: Blackwell, 2003). If commentary is undesired, then Nigel Warburton, (Oxford: Blackwell, 2003). If commentary is undesired, then Nigel Warburton, Philosophy: Basic Readings Philosophy: Basic Readings, 2nd edn (London: Routledge, 2005). For an encyclopaedic dictionary, seek out Ted Honderich, ed., TheOxfordCompanionto Philosophy, TheOxfordCompanionto Philosophy, 2nd edn (Oxford: OUP, 2005). For the small, try Thomas Mautner, 2nd edn (Oxford: OUP, 2005). For the small, try Thomas Mautner, The Penguin Dictionary of Philosophy The Penguin Dictionary of Philosophy (London: Penguin, 2005). (London: Penguin, 2005).

Returning to paradoxes themselves, a valuable reference work remains Michael Clark's Paradoxesfrom AtoZ Paradoxesfrom AtoZ, 2nd edn (London: Routledge, 2007). A light and introductory topic- based survey is my This Sentence Is Talse: An Introduction to PhilosophicalParadoxes This Sentence Is Talse: An Introduction to PhilosophicalParadoxes (London: Continuum, forthcoming). (London: Continuum, forthcoming).

Recent works on serious ethical perplexities include Saul Smilansky, Ten Moral Paradoxes Ten Moral Paradoxes (Oxford: Blackwell, 2007) and Kwame A. Appiah, (Oxford: Blackwell, 2007) and Kwame A. Appiah, Experiments in Ethics Experiments in Ethics (Cambridge, MA: Harvard Univ., 2008). A humanist perspective on ethics and religion, expanding on some of the thoughts here, is my (Cambridge, MA: Harvard Univ., 2008). A humanist perspective on ethics and religion, expanding on some of the thoughts here, is my Humanism Humanism (Oxford: Oneworld, forthcoming). (Oxford: Oneworld, forthcoming).

APPENDIX 2.

NOTES, SOURCES, AND REFERENCES.

Preface and acknowledgements

For exposure of some 'postmodernist' muddle, see Alan Sokal and Jean Bricmont, Intellectual Impostures Intellectual Impostures (London: Profile, 1998), and Sokal's subsequent works.The quip about time appears in Samuel Beckett's (London: Profile, 1998), and Sokal's subsequent works.The quip about time appears in Samuel Beckett's Waitingjor G.o.dot Waitingjor G.o.dot (London: Faber, 1956). (London: Faber, 1956).

Acknowledgements are positive and praising. Let me paradoxically acknowledge some negatives. I worked in the British Library partly to avoid everlasting (it seems) construction works' inconsiderate noise and Thames Water's clattering incompetences, despite some welcome friendliness from James Fisher and Russell Harvey. Yet, in the British Library inconsiderateness also manifests itself. The library is one of the world's major copyright libraries, yet some readers have found it impossible not to scrawl in books; and some, presumably unacquainted with tissues, are incapable of reading without loud and disagreeable sniffs, and unnecessary computer jingles. Surely, they they should know better. Sadly, perhaps they do. should know better. Sadly, perhaps they do.

Chapter 1 On thinking too much: how not to win a princess's hand

This tale deploys Gregory Kavka's Toxin Paradox. A related puzzle is Mutually a.s.sured Destruction (MAD): a country threatens a retaliation that it would be mad to carry out. Can it be truly threatened? See Kavka, Moral Paradoxes ofNuclear Deterrence Moral Paradoxes ofNuclear Deterrence (Cambridge: CUP, 1987). A deeper perplexity is in my casual allusion to spotting people's intentions via brain scans. What is the relationship between neurological causal transactions and logical reasoning (raised in Chapter 17)? (Cambridge: CUP, 1987). A deeper perplexity is in my casual allusion to spotting people's intentions via brain scans. What is the relationship between neurological causal transactions and logical reasoning (raised in Chapter 17)?

Chapter 2 On the run: all's fair with bears?.

Trolley/tram scenarios, trapped miners, violinists plugged into you, people falling on others with ever-ready ray guns - such tales abound. See Jeff McMahan, TheEthicsofKilling TheEthicsofKilling (New York: OUP, 2002). Some stimulating thoughts are in Helen Frowe's 'Threats, Bystanders, and Obstructors', (New York: OUP, 2002). Some stimulating thoughts are in Helen Frowe's 'Threats, Bystanders, and Obstructors', Proceedings of theAristotelian Society Proceedings of theAristotelian Society 108 (London: Aristotelian Soc., 2008). 108 (London: Aristotelian Soc., 2008).

Chapter 3 A pill for everything?.

'Forced to be free' is from Jean-Jacques Rousseau, The Social Contract etc., The Social Contract etc., ed.Victor Gourevitch (Cambridge: CUP 1997). Isaiah Berlin made famous the negative-positive distinction: see ed.Victor Gourevitch (Cambridge: CUP 1997). Isaiah Berlin made famous the negative-positive distinction: see Liberty, Liberty, ed. Henry Hardy (Oxford: OUP 2002). Many think Berlin invented the distinction, but it goes back arguably as far as the eighteenth-century Benjamin Constant, even earlier. For interweaving concerns, see Adam Swift, ed. Henry Hardy (Oxford: OUP 2002). Many think Berlin invented the distinction, but it goes back arguably as far as the eighteenth-century Benjamin Constant, even earlier. For interweaving concerns, see Adam Swift, PoliticalPhilosophy PoliticalPhilosophy (Cambridge: Polity, 2001). (Cambridge: Polity, 2001).