The Beginning of Infinity

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by David Deutsch


  Another short-lived enlightenment happened in the Italian city-state of Florence in the fourteenth century. This was the time of the early Renaissance, a cultural movement that revived the literature, art and science of ancient Greece and Rome after more than a millennium of intellectual stagnation in Europe. It became an enlightenment when the Florentines began to believe that they could improve upon that ancient knowledge. This era of dazzling innovation, known as the Golden Age of Florence, was deliberately fostered by the Medici family, who were in effect the city’s rulers – especially Lorenzo de’ Medici, known as ‘the Magnificent’, who was in charge from 1469 to 1492. Unlike Pericles, the Medici were not devotees of democracy: Florence’s enlightenment began not in politics but in art, and then philosophy, science and technology, and in those fields it involved the same openness to criticism and desire for innovation both in ideas and in action. Artists, instead of being restricted to traditional themes and styles, became free to depict what they considered beautiful, and to invent new styles. Encouraged by the Medici, the wealthy of Florence competed with each other in the innovativeness of the artists and scholars whom they sponsored – such as Leonardo da Vinci, Michelangelo and Botticelli. Another denizen of Florence at this time was Niccolò Machiavelli, the first secular political philosopher since antiquity.

  The Medici were soon promoting the new philosophy of ‘humanism’, which valued knowledge above dogma, and virtues such as intellectual independence, curiosity, good taste and friendship over piety and humility. They sent agents all over the known world to obtain copies of ancient books, many of which had not been seen in the West since the fall of the Western Roman Empire. The Medici library made copies which it supplied to scholars in Florence and elsewhere. Florence became a powerhouse of newly revived ideas, new interpretations of ideas, and brand-new ideas.

  But that rapid progress lasted for only a generation or so. A charismatic monk, Girolamo Savonarola, began to preach apocalyptic sermons against humanism and every other aspect of the Florentine enlightenment. Urging a return to medieval conformism and self-denial, he proclaimed prophecies of doom if Florence continued on its path. Many citizens were persuaded, and in 1494 Savonarola managed to seize power. He reimposed all the traditional restrictions on art, literature, thought and behaviour. Secular music was banned. Clothing had to be plain. Frequent fasting became effectively compulsory. Homosexuality and prostitution were violently suppressed. The Jews of Florence were expelled. Gangs of ruffians inspired by Savonarola roamed the city searching for taboo artefacts such as mirrors, cosmetics, musical instruments, secular books, and almost anything beautiful. A huge pile of such treasures was ceremonially burned in the so-called ‘Bonfire of the Vanities’ in the centre of the city. Botticelli is said to have thrown some of his own paintings into the fire. It was the bonfire of optimism.

  Eventually Savonarola was himself discarded and burned at the stake. But, although the Medici regained control of Florence, optimism did not. As in Athens, the tradition of art and science continued for a while, and, even a century later, Galileo was sponsored (and then abandoned) by the Medici. But by that time Florence had became just another Renaissance city-state lurching from one crisis to another under the rule of despots. Fortunately, somehow that mini-enlightenment was never quite extinguished. It continued to smoulder in Florence and several other Italian city-states, and finally ignited the Enlightenment itself in northern Europe.

  There may have been many enlightenments in history, shorter-lived and shining less brilliantly than those, perhaps in obscure subcultures, families or individuals. For example, the philosopher Roger Bacon (1214–94) is noted for rejecting dogma, advocating observation as a way of discovering the truth (albeit by ‘induction’), and making several scientific discoveries. He foresaw the invention of microscopes, telescopes, self-powered vehicles and flying machines – and that mathematics would be a key to future scientific discoveries. He was thus an optimist. But he was not part of any tradition of criticism, and so his optimism died with him.

  Bacon studied the works of ancient Greek scientists and of scholars of the ‘Islamic Golden Age’ – such as Alhazen (965–1039), who made several original discoveries in physics and mathematics. During the Islamic Golden Age (between approximately the eighth and thirteenth centuries), there was a strong tradition of scholarship that valued and drew upon the science and philosophy of European antiquity. Whether there was also a tradition of criticism in science and philosophy is currently controversial among historians. But, if there was, it was snuffed out like the others.

  It may be that the Enlightenment has ‘tried’ to happen countless times, perhaps even all the way back to prehistory. If so, those mini-enlightenments put our recent ‘lucky escapes’ into stark perspective. It may be that there was progress every time – a brief end to stagnation, a brief glimpse of infinity, always ending in tragedy, always snuffed out, usually without trace. Except this once.

  The inhabitants of Florence in 1494 or Athens in 404 BCE could be forgiven for concluding that optimism just isn’t factually true. For they knew nothing of such things as the reach of explanations or the power of science or even laws of nature as we understand them, let alone the moral and technological progress that was to follow when the Enlightenment got under way. At the moment of defeat, it must have seemed at least plausible to the formerly optimistic Athenians that the Spartans might be right, and to the formerly optimistic Florentines that Savonarola might be. Like every other destruction of optimism, whether in a whole civilization or in a single individual, these must have been unspeakable catastrophes for those who had dared to expect progress. But we should feel more than sympathy for those people. We should take it personally. For if any of those earlier experiments in optimism had succeeded, our species would be exploring the stars by now, and you and I would be immortal.

  TERMINOLOGY

  Blind optimism (recklessness, overconfidence) Proceeding as if one knew that bad outcomes will not happen.

  Blind pessimism (precautionary principle) Avoiding everything not known to be safe.

  The principle of optimism All evils are caused by insufficient knowledge.

  Wealth The repertoire of physical transformations that one is capable of causing.

  MEANINGS OF ‘THE BEGINNING OF INFINITY’ ENCOUNTERED IN THIS CHAPTER

  – Optimism. (And the end of pessimism.)

  – Learning how not to fool ourselves.

  – Mini-enlightenments like those of Athens and Florence were potential beginnings of infinity.

  SUMMARY

  Optimism (in the sense that I have advocated) is the theory that all failures – all evils – are due to insufficient knowledge. This is the key to the rational philosophy of the unknowable. It would be contentless if there were fundamental limitations to the creation of knowledge, but there are not. It would be false if there were fields – especially philosophical fields such as morality – in which there were no such thing as objective progress. But truth does exist in all those fields, and progress towards it is made by seeking good explanations. Problems are inevitable, because our knowledge will always be infinitely far from complete. Some problems are hard, but it is a mistake to confuse hard problems with problems unlikely to be solved. Problems are soluble, and each particular evil is a problem that can be solved. An optimistic civilization is open and not afraid to innovate, and is based on traditions of criticism. Its institutions keep improving, and the most important knowledge that they embody is knowledge of how to detect and eliminate errors. There may have been many short-lived enlightenments in history. Ours has been uniquely long-lived.

  10

  A Dream of Socrates

  SOCRATES is staying at an inn near the Temple of the Oracle at Delphi. Together with his friend CHAEREPHON, he has today asked the Oracle who the wisest man in the world is,* so that they might go and learn from him. But, to their annoyance, the priestess (who provides the Oracle’s voice on behalf of the god Apollo) merely
announced, ‘No one is wiser than Socrates.’ Sleeping now on an uncomfortable bed in a tiny and exorbitantly expensive room, SOCRATES hears a deep, melodious voice intoning his name.

  HERMES: Greetings, Socrates.

  SOCRATES: [Draws the blanket over his head.] Go away. I’ve already made too many offerings today and you’re not going to wring any more out of me. I am too ‘wise’ for that, hadn’t you heard?

  HERMES: I seek no offering.

  SOCRATES: Then what do you want? [He turns and sees HERMES, who is naked.] Well, I’m sure that some of my associates camped outside will be glad to –

  HERMES: It is not them I seek, but you, O Socrates.

  SOCRATES: Then you shall be disappointed, stranger. Now kindly leave me to my hard-earned rest.

  HERMES: Very well. [He makes towards the door.]

  SOCRATES: Wait.

  HERMES: [Turns and raises a quizzical eyebrow.]

  SOCRATES: [slowly and deliberately] I am asleep. Dreaming. And you are the god Apollo.

  HERMES: What makes you think so?

  SOCRATES: These precincts are sacred to you. It is night-time and there is no lamp, yet I see you clearly. This is not possible in real life. So you must be coming to me in a dream.

  HERMES: You reason coolly. Are you not afraid?

  SOCRATES: Bah! I ask you in return: are you a benevolent or a malevolent god? If benevolent, then what do I have to fear? If malevolent, then I disdain to fear you. We Athenians are a proud people – and protected by our goddess, as you surely know. Twice we defeated the Persian Empire against overwhelming odds,* and now we are defying Sparta. It is our custom to defy anyone who seeks our submission.

  HERMES: Even a god?

  SOCRATES: A benevolent god would not seek it. On the other hand, it is also our custom to give a hearing to anyone who offers us honest criticism, seeking to persuade us freely to change our minds. For we want to do what is right.

  HERMES: Those two customs are two sides of the same valuable coin, Socrates. I give you Athenians great credit for honouring them.

  SOCRATES: My city is surely deserving of your favour. But why would an immortal want to converse with such a confused and ignorant person as me? I think I can guess your reason: you have repented of your little joke via the Oracle, haven’t you? Indeed, it was rather cruel of you to send us only a mocking answer, considering the distance we have come and the offerings we have made. So please tell me the truth this time, O fount of wisdom: who is really the wisest man in the world?

  HERMES: I reveal no facts.

  SOCRATES: [Sighs.] Then I beg you – I have always wanted to know this: what is the nature of virtue?

  HERMES: I reveal no moral truths either.

  SOCRATES: Yet, as a benevolent god, you must have come here to impart some sort of knowledge. What sort will you deign to grant me?

  HERMES: Knowledge about knowledge, Socrates. Epistemology. I have already mentioned some.

  SOCRATES: You have? Oh – you said that you honour Athenians for our openness to persuasion. And for our defiance of bullies. But it is well known that those are virtues! Surely telling me what I already know doesn’t count as a ‘revelation’.

  HERMES: Most Athenians would indeed call those virtues. But how many really believe it? How many are willing to criticize a god by the standards of reason and justice?

  SOCRATES: [Ponders.] All who are just, I suppose. For how can anyone be just if he follows a god of whose moral rightness he is not persuaded? And how is it possible to be persuaded of someone’s moral rightness without first forming a view about which qualities are morally right?

  HERMES: Your associates out there on the lawn – are they unjust?

  SOCRATES: No.

  HERMES: And are they aware of the connections you have just described between reason, morality and the reluctance to defer to gods?

  SOCRATES: Perhaps not sufficiently aware – yet.

  HERMES: So it is not true that every just person knows these things.

  SOCRATES: Agreed. Perhaps it is only every wise person.

  HERMES: Everyone who is at least as wise as you, then. Who else is in that exalted category?

  SOCRATES: Is there some high purpose in your continuing to mock me, wise Apollo, by asking me the same question that we asked you today? It seems to me that your joke is wearing thin.

  HERMES: Have you, Socrates, never mocked anyone?

  SOCRATES: [with dignity] If, on occasion, I make fun of someone, it is because I hope he will help me to seek a truth that neither he nor I yet knows. I do not mock from on high, as you do. I want only to goad my fellow mortal into helping me look beyond that which is easy to see.

  HERMES: But what in the world is easy to see? What things are the easiest to see, Socrates?

  SOCRATES: [Shrugs.] Those that are before our eyes.

  HERMES: And what is before your eyes at this moment?

  SOCRATES: You are.

  HERMES: Are you sure?

  SOCRATES: Are you going to start asking me how I can be sure of whatever I say? And then, whatever reason I give, are you going to ask how I can be sure of that?

  HERMES: No. Do you think I have come here to play hackneyed debating tricks?

  SOCRATES: Very well: obviously I can’t be sure of anything. But I don’t want to be. I can think of nothing more boring – no offence meant, wise Apollo – than to attain the state of being perfectly secure in one’s beliefs, which some people seem to yearn for. I see no use for it – other than to provide a semblance of an argument when one doesn’t have a real one. Fortunately that mental state has nothing to do with what I do yearn for, which is to discover the truth of how the world is, and why – and, even more, of how it should be.

  HERMES: Congratulations, Socrates, on your epistemological wisdom. The knowledge that you seek – objective knowledge – is hard to come by, but attainable. That mental state that you do not seek – justified belief – is sought by many people, especially priests and philosophers. But, in truth, beliefs cannot be justified, except in relation to other beliefs, and even then only fallibly. So the quest for their justification can lead only to an infinite regress – each step of which would itself be subject to error.

  SOCRATES: Again, I know this.

  HERMES: Indeed. And, as you have rightly remarked, it doesn’t count as a ‘revelation’ if I tell you what you already know. Yet – notice that that remark is precisely what people who seek justified belief do not agree with.

  SOCRATES: What? I’m sorry, but that was too convoluted a comment for my allegedly wise mind to comprehend. Please explain what I am to notice about those people who seek ‘justified belief’.

  HERMES: Merely this. Suppose they just happen to be aware of the explanation of something. You and I would say that they know it. But to them, no matter how good an explanation it is, and no matter how true and important and useful it may be, they still do not consider it to be knowledge. It is only if a god then comes along and reassures them that it is true (or if they imagine such a god or other authority) that they count it as knowledge. So, to them it does count as a revelation if the authority tells them what they are already fully aware of.

  SOCRATES: I see that. And I see that they are foolish, because, for all they know, the ‘authority’ [gestures at HERMES] may be toying with them. Or trying to teach them some important lesson. Or they may be misunderstanding the authority. Or they may be mistaken in their belief that it is an authority –

  HERMES: Yes. So the thing they call ‘knowledge’, namely justified belief, is a chimera. It is unattainable to humans except in the form of self-deception; it is unnecessary for any good purpose; and it is undesired by the wisest among mortals.

  SOCRATES: I know.

  HERMES: Xenophanes knew it too; but he is no longer among the mortals –

  SOCRATES: Is that what you meant when you told the Oracle that no one is wiser than I?

  HERMES: [Ignores the question.] Hence, also, I wasn’t referring to justified
belief when I asked whether you are sure that I am before your eyes. I was only questioning how you can claim to be ‘seeing clearly’ what is before your eyes when you also claim to be asleep!

  SOCRATES: Oh! Yes, you have caught me in an error – but surely only a trivial one. Indeed, you may not be literally before my eyes. Perhaps you are at home on Olympus, sending me a mere likeness of yourself. But in that case you are controlling that likeness and I am seeing it, and referring to it as ‘you’, so I am seeing ‘you’.

  HERMES: But that is not what I asked. I asked what is here before your eyes. In reality.

  SOCRATES: All right. Before my eyes, in reality, there is – a small room. Or, if you want a literal reply, what is before my eyes is – eyelids, since I expect that they are shut. Yet I see from your expression that you want even more precision. Very well: before my eyes are the inside surfaces of my eyelids.

  HERMES: And can you see those? In other words, is it really ‘easy to see’ what is before your eyes?

  SOCRATES: Not at the moment. But that is only because I am dreaming.

  HERMES: Is it only because you are dreaming? Are you saying that if you were awake you would now be seeing the inside surfaces of your eyelids?

  SOCRATES: [carefully] If I were awake with my eyes still closed, then yes.

  HERMES: What colour do you see when you close your eyes?

  SOCRATES: In a room as dimly lit as this one – black.

  HERMES: Do you think that the inside surfaces of your eyelids are black?

  SOCRATES: I suppose not.

  HERMES: So would you really be seeing them?

  SOCRATES: Not exactly.

  HERMES: And if you were to open your eyes, would you be able to see the room?

 

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