LRB on Leibniz

Dispersed and Distracted

by Jonathan Rée
Leibniz: An Intellectual Biography by Maria Rosa Antognazza  Buy this book

When Queen Anne died in August 1714, the news was received with excitement in the medieval town of Hanover in Lower Saxony. Under the terms of the Act of Settlement of 1701, Anne’s death meant that Georg Ludwig, the stolid local duke, was about to become the next occupant of the English throne. A month later he was on his way to London with his German-speaking retinue, ready for his coronation in October and a new life as the first King George of Great Britain and Ireland.

But one of the most venerable members of his household had been left behind in Hanover, feeling rather sorry for himself. Geheimrat Gottfried Wilhelm Leibniz had joined the Hanoverian court under the last duke but one, and apart from occasional absences in Vienna and Berlin, had been supplying the family with legal and political advice for almost 40 years. On state occasions, he still liked to turn out in style; but he was now in his late sixties, and when he draped his arthritic frame in the sumptuous formal dress of an age long past, he was said to look more like a jester than a learned servant of the court. The rest of the time, he preferred to keep to his private quarters, cosseted in fur stockings, felt socks and fur-lined gown, and coiffed with a long dark wig. He would work day and night, surrounded by towers of books and manuscripts, taking meals on his own at irregular hours, and napping at his desk when he was tired. His masters might get exasperated with his serene self-absorption, but he continued to bring credit to the house through his reputation as a philosophical virtuoso, and they still valued his opinions and took pleasure in having him at their elbow as a personal ‘living dictionary’. He distinguished himself from other men of letters, moreover, by keeping himself clean and sweet-smelling and retaining a wistful sense of humour. ‘I have never,’ he reflected, ‘been so old as I am now.’

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Soon after his appointment as court counsellor in 1676 Leibniz had been asked to trace the pedigree of the Hanoverian clan through the house of Brunswick and back to the royal dynasty of Guelfs. But his archival investigations ran into a series of unlucky delays. In the first place, he had to apply himself to technical problems at the family’s silver mines in the Harz mountains, working on geological surveys and experimental designs for wind-powered lifts and water-pumps. In the end his efforts came to nothing – he blamed the intransigence of the miners – but seven years were lost to the project before he could return to his researches in family history. By that time his conception of the task had grown. He had persuaded himself that the Guelf line needed to be traced all the way back to the origins of the Holy Roman Empire, and that the story would be incomplete without two preliminary discourses, one on the history of the earth as a whole, the other on the origins of the nations of the world as evidenced by their languages. The more work he put in on his assignment, it seems, the more remained to be done.

Georg Ludwig eventually lost his patience. ‘Leibniz is nowhere to be found,’ he complained in 1703, ‘and if anyone wants to know why, he always claims to be working on his invisible book.’ The invisible book was more than thirty years overdue by the time the court decamped to London, but Leibniz excused himself on the grounds that he had recently completed three preparatory volumes, comprising medieval legal documents about the Guelfs and Lower Saxony, while making steady progress with his supplementary studies in geology and etymology. Indeed, he suggested that his newly crowned employer might wish to reward his diligence with a promotion: ‘the king would not misuse the honour and the salary,’ as he put it in a plaintive letter from Hanover, ‘if he were to appoint me to the post of Historiographer of Great Britain.’ George demurred: his elderly retainer should not at present entertain any thoughts of joining the British court, and had better not stir from Hanover till the Origines Guelficae was finished and printed and bound; afterwards, of course, he could ‘hope for everything’. In the event the king’s bluff was never called: Leibniz remained in Hanover, working on the family genealogy, till his lonely death two years later at the age of 70; and it turned out that when he laid down his pen for the last time, he had still only got as far as 1005.

Like many other deadline-dodgers, Leibniz was a stranger to anxiety and self-doubt. He had been accustomed to adulation for as long as he could remember: his father, a professor of moral philosophy at Leipzig, claimed to see in him signs of God’s especial grace, and even at his christening in the Lutheran Nikolaikirche he was commended for his exceptional spiritual powers. Afterwards he achieved renown as the child scholar who would browse for hours on end in his father’s library, while the teachers at his Latin school had difficulty curbing his ‘unseasonable and precipitate’ appetite for logic and secular history. When he enrolled in the philosophical faculty at Leipzig at the age of 14 he soon won the respect of his masters with his combination of verbal agility and perfect recollection of everything he read. He went on to excel in law as well, and then mathematics, and in his mid-twenties he was elected to the Royal Society in London after demonstrating an improved design for a calculating machine. He later became a corresponding member of the Académie Royale in Paris and first president of the Societät der Wissenschaften in Berlin, and when he obtained salaried work at the Hanoverian court at the age of 30, he took it for granted that he would continue to pursue his vocation as a universal intellectual and perpetual child prodigy, though by now the spread of his interests was beginning to seem exceedingly broad, even to him. ‘I often do not know where to begin,’ he admitted; ‘I am trying to find various things in the archives . . . I receive and answer a huge number of letters . . . I have so many new results in mathematics, so many philosophical plans, and so many other important literary investigations to pursue.’

Despite his scheduling problems, Leibniz managed to compose hundreds of scientific essays in his spare time. He preferred to keep them to himself, however, and on the rare occasions when he chose to offer something to the public, he withheld his name and omitted crucial details, while hinting that his results were only a few crumbs from his table – fragments of a universal science which, for the time being, the self-effacing author preferred to hold in reserve. In 1684, he published a tantalising account of a new mathematical technique – the infinitesimal calculus – in a Leipzig monthly review; ten years later he offered a suggestive ‘specimen’ of a new science of dynamics, based on conservation of ‘force’ (mv2) rather than ‘quantity of motion’ (mv); and afterwards he constructed a telling critique of the absolutist metaphysics of Isaac Newton, arguing that space and time had no reality of their own, but could be resolved into inherent properties of the objects that are said to occupy them. Newton took offence at these comments, and became incensed by the suggestion – probably correct, as it happens – that Leibniz had beaten him to the invention of the calculus: if the new king did not already have enough reasons for keeping Leibniz away from London, he might have done so in order to avoid a row with an irascible president of the Royal Society and master of the Mint.

As his life drew to an end, Leibniz began to fear that he had not left himself enough time to give a comprehensive account of his intellectual achievements, and asked his secretary to sort through his manuscripts after his death and prepare them for publication. But the archive turned out to comprise some 200,000 sheets of paper – nearly ten for every day of his life – so this last request proved stupendously unrealistic. An authorised version of the Origines Guelficae would eventually be printed in two magnificent folios in 1750, but the definitive Sämtliche Schriften did not start to appear till 1923, and only 50 volumes have been published so far out of a projected total of 120. Leibniz had indeed been interested in ‘too many things’, as he put it in a rare moment of pathos: ‘I cannot say,’ he wrote, ‘how extraordinarily dispersed and distracted I am.’

The life of such a chronic incompletist does not make a promising subject for biography. The novelist and raconteur Bernard de Fontenelle was the first to make the attempt, delivering a eulogy before the Académie Royale in 1717 to mark the first anniversary of Leibniz’s death. But he did not find it easy: his late colleague had gorged himself on books since infancy, and as Fontenelle put it, ‘he was what he read’ – hence his polymorphic productivity not only as a mathematician, philosopher and theologian, but also as poet and orator, diplomat and politician, inventor and engineer, geologist, archivist, historian, linguist and etymologist. But his reputation for brilliance was always shadowed by doubts about his probity. At the age of 20 he had set about insinuating himself into a secret alchemical society in Nuremberg, devoted to the quest for the philosopher’s stone. ‘He procured some books,’ Fontenelle wrote, ‘and picking out the darkest phrases, he sent off a letter that was altogether unintelligible, even to himself.’ The subterfuge was so successful that he was immediately admitted to the society and offered a salaried position as its secretary. We are not told if he took up the offer, but Fontenelle leaves us with a niggling suspicion that the art of constructing bogus arguments – ‘unintelligible, even to himself’ – came easily to the young Leibniz, and that it may later have become a settled habit.

On the other hand, Fontenelle found no evidence that Leibniz ever succumbed to greed or corruption, or even to compassion or the temptations of love. There was a credible rumour that when he reached his fifties his thoughts had turned towards marriage, but ‘the person he had in mind asked for time for reflection’, which gave him the chance to reconsider his options, the consequence being that he ‘never got married after all’. It was a life, it seems, without any unifying theme or development, either emotional or intellectual: a case, you might conclude, for lists and analytical catalogues rather than conventional discursive narratives.

But the enigma of Leibniz’s missing personality did not detract from his intellectual allure. In his lifetime, he published only one sustained work of philosophy: the Essais de Théodicée, which appeared anonymously in 1710. It was written, fashionably, in French, but despite its helpful numbered paragraphs and an affectation of ‘a rather informal manner’, it was criticised from the outset as wayward, prolix and extremely difficult to understand. Even the title proved a stumbling-block: Leibniz had coined the term ‘theodicy’ to convey a serene idea of divine justice, but one of his earliest readers missed the point and jumped to the conclusion that the essays were the work of an unknown author called Theodicaeus. Leibniz’s cover was soon blown, however, and in the coming decades the Theodicy was frequently reprinted over the name of the ‘Freiherr von Leibnitz’ (a dignity to which the author was not strictly entitled). Its fabled impenetrability, instead of alienating readers, won it a certain modish notoriety, and gave rise to what was then a novel literary derivative: the simplified introduction to an obscure contemporary philosopher, promising help and reassurance to the so-called ‘candid reader’.

The Theodicy was an elaborate attempt to justify the ways of God to man: having spent a lifetime practising the arts of spin on behalf of the Hanoverian court, you might say, Leibniz was now proposing to perform the same service in the cause of the Almighty. There were two grave challenges that needed to be faced down: first, if God is as benevolent and powerful as he is made out to be, how come we have to suffer so much injustice and grief? And second, how can we be expected to believe in an open future if God is omniscient, and therefore fully apprised of future events, including the actions we have yet to perform of our own free will?

Leibniz’s solution was based on the simple but wholly original notion that the world we inhabit is just one member of an infinite set of ‘possible worlds’. To imagine this world slightly different from what it is, Leibniz says, is in fact to imagine another world entirely. If I had chosen to stay at home today instead of going to the library, then we would all be living in a different ‘possible world’ – a world that contains not me, freely choosing a day in the library, but someone else, exactly like me except for deciding to spend the day at home. And if we accept that the actual world is the creation of a wise and benevolent God, then we have to recognise that it must contain the greatest achievable amount of goodness compatible with the smallest amount of evil, since otherwise God would not have chosen to actualise it in preference to other possible worlds. It follows both that we can be free in spite of divine foreknowledge, and that the world we actually inhabit must be ‘the best – the optimum – of all possible worlds’.

Leibniz invented the word ‘optimism’ to describe his theory of ‘the best of all possible worlds’, and the word has gone on to enjoy a remarkable international career. The doctrine itself, however, is extremely elusive, and – at least in Leibniz’s original conception – a fine example of the kind of philosophical difference that makes no difference at all. Leibniz’s optimism does not imply that evil is unreal, or that the world is better than we might otherwise think, or that it has any tendency to improve as time goes by; it merely suggests – as Leibniz made clear – that however rotten or unfair things are, and even if they are going from bad to worse, there is no point in wishing for anything better. Strictly speaking, Leibniz’s optimism is not so much a counsel of hope as a cry of despair – don’t blame the creator, he’s doing his best.

The Theodicy has the same sort of relation to mainstream philosophising as science fiction to mainstream science, and it is still hard to read it as anything but a deliberate exercise in metaphysical make-believe. Alexander Pope may have tried to take it seriously, but the vapid humanism of the Essay on Man, published in 1733, was a muddled travesty of Leibniz’s lofty and impassive stoicism. (‘Of Systems possible, if ’tis confest,/That Wisdom infinite must form the best . . . /Then in the scale of reas’ning life, ’tis plain,/There must be, somewhere, such a rank as Man.’) Voltaire, in a pamphlet written in 1738, tried to defend the sainted Newton from Leibniz’s diabolical ingenuity, and promised to rely on ‘ratiocination alone’, scorning the vulgar weapon of ‘ridicule’. But he could not quite restrain himself, and in 1759 his hilarity blossomed into the perfect satire of Candide, ou l’optimisme.

The hero of Voltaire’s tale is an ingenuous lad who does his best to follow the teachings of Pangloss, a know-it-all Westphalian philosopher whose doctrine of metaphysico-theologo-cosmolo-nigology supplies him with an optimistic ready answer to every possible question even before it is asked. Both Candide and Pangloss are obliged to leave Westphalia in a hurry, and we then follow their misadventures as they flee across Europe to South America and back, ending up in Constantinople, capital of infidelity. Candide has grown bored with philosophy by now, but Pangloss carries on chattering about Leibniz and the best of all possible worlds, till at last he meets his match in a celebrated Sufi sage – ‘the greatest philosopher in Turkey’ – who demonstrates that there is no point in discussing the reality of good and evil. For the first time in his life, Pangloss is perplexed: ‘But in that case,’ he asks, ‘what is to be done?’ ‘Te taire,’ says the dervish: ‘Just shut up and be quiet.’

Candide is not so much a philosophical commentary on Leibnizian theodicy as a lampoon at the expense of metaphysics as such, and it became the source of a complacent and sometimes philistine tradition that uses philosophical optimism as an example to prove the futility of the ‘conjectural method’ in general, if not of philosophical reflection as a whole. Leibniz’s name, like that of Einstein in the 20th century, had already become a byword for the kind of superhuman cleverness that leaves the rest of us not only open-mouthed in admiration, but also a little nervous, patting our purses to make sure we are not being swindled out of our hard-earned common sense. According to the standard 18th-century work on the history of philosophy, Leibniz was ‘one of those universal geniuses, who at once surprise and benefit the world’, but at the same time his ideas had to be judged ‘too hypothetical to afford entire satisfaction’. In 1821, Dugald Stewart gave a further twist to the tale by linking Leibniz with what he called ‘the continental philosophy’, suggesting that a habit of ‘deference to the authority of Leibniz’, combined with a short-sighted mistrust of honest John Locke, might be responsible for the ‘striking contrast between the characteristical features of the continental philosophy . . . and those of contemporary systems which have succeeded each other in our own island’.

By that time various posthumous collections of Leibniz’s logical, mathematical and philosophical papers had made their way into print, and readers who took the trouble to read the letters about space, time and Newton (first published in 1717), and the so-called Monadology (1721), together with the extended commentary on Locke (1766), were rewarded with much more than the famously inane optimism of the Theodicy. Leibniz came to be noted for, among other things, his ability to discover intellectual treasures in the most unpromising texts, especially the works of the much derided ‘pseudo-philosophers’ of the scholastic Middle Ages; and before long his own works were beginning to benefit from the same kind of creative and anachronistic rereading.

The notion of possible worlds may have originated in some theological delirium, but it has never ceased to suggest new interpretations of the logic of necessity and contingency (‘truth in all possible worlds’, ‘truth in none’ and ‘truth in some’). Moreover, it serves as a prelude to the even more exotic doctrine of ‘monads’, which states that everything that really exists belongs, in the last analysis, in a class of its own, or in other words, that two things cannot be distinct from each other unless they differ in some specific and describable way. This, as Leibniz was glad to acknowledge, was exactly what the scholastic theologians used to say about angels – that, lacking any physical body to individuate them, they must all be qualitatively distinct, or in other words that they are ‘monadic’ as opposed to ‘sporadic’. Once we have finished laughing at Leibniz’s daffy vision of the universe as a disembodied choir of angelic monads, we should remember that his descriptive account of identity has remained an inspiration to subsequent logicians, and was eventually taken up by Frege and Russell and turned into the basis of modern mathematical logic.

The afterlives of monadology and the theory of ‘possible worlds’ may seem specialised and abstruse, but the same cannot be said of the notion of ‘perspective’. Leibniz was the first thinker to pluck it from its original role in the theory of design in order to arrive at the general proposition that every object we encounter – a table or a city, for example – will present different aspects when viewed from different vantage points, and conversely that every act of knowledge or perception takes place within a particular projection or from a specific ‘point of view’. In the course of the 20th century this suggestion declined into a set of murky commonplaces about ‘relativism’, but Leibniz himself used it fastidiously and constructively, to open up the previously unexplored territory of what he called phaenomena bene fundata – the ‘well-established appearances’, confirmed from numerous points of view, that, he suggested, constitute a kind of borderland between the realm of fleeting subjective illusions, on the one hand, and that of immovable objective facts, on the other. Take rainbows: they are, as Leibniz pointed out, too substantial to be dismissed as mere appearances, but not substantial enough to count as enduring realities. They could perhaps be described as real appearances, or apparent realities, and Leibniz was convinced that the same applied to all the objects of everyday spatio-temporal experience: they were mirage-like manifestations of the non-spatio-temporal reality of the angelic monads. Few of his readers have been willing to follow him quite so far, but without his pioneering explorations of the realm of well-established appearances, Kant would never have developed his theory of the phenomenal world and the role of mental activity in it, nor Hegel his account of history as the process by which truth becomes a phenomenon, nor Marx his critique of fetishism and the delusive phenomenal forms of capital.

The trouble for the biographer is that practically all the interpretive possibilities that make Leibniz interesting were unavailable during his lifetime. Fontenelle hedged his bets by praising Leibniz for his range and energy rather than for any enduring intellectual achievements; and the prolific Encyclopedist Louis de Jaucourt, whose laudatory Life of 1734 was frequently reissued throughout the 18th century, deliberately continued the story after Leibniz’s death. The first modern biography, properly wary of anachronism, was published by Gottschalk Guhrauer in 1842, and, dull as it is, it has remained authoritative ever since.

Maria Rosa Antognazza’s heroic labours mean that Guhrauer can at last be sent back to the stacks: she has re-evaluated all the sources and constructed a lively and thoroughly documented story that is unlikely to be seriously challenged, even on matters of detail. She has also done her best to turn the facts of this life-that-was-not-one into a coherent narrative. As a schoolboy Leibniz immersed himself in various works on the reform of logic which he found in his father’s library, and when he was about 12, if Antognazza is right, he became captivated by the idea of an ‘alphabet’ whose characters would correspond not to the sounds of speech but to the ultimate structures of human thought. When he was 19 he carried the idea further in a university dissertation on the Ars combinatoria, suggesting that once the true elements of thought had been identified, there should be no difficulty in generating an infinite range of infallibly accurate judgments, simply through the mechanical manipulation of the symbols designating them. This youthful vision of a universal logical science, Antognazza argues, provided Leibniz with the all-embracing ‘project’ to which he would dedicate himself for the rest of his life.

Antognazza is not wrong: Leibniz did indeed keep dropping hints about his work on a ‘higher science’, and in 1675 boasted that ‘nothing can well be imagined which will contribute more to the perfection of the human mind,’ adding of course that ‘its nature cannot well be conveyed in few words’ and that the time for divulging its mysteries had not yet come. In 1688 he was writing memoranda to himself about the extraordinary utility of a ‘combinatory’ based on ‘the expression of thoughts through characters’, claiming that his techniques, once published, would lead not only to the immediate resolution of theoretical disputes of all kinds, but also to the reconciliation of the various branches of Christianity and the dawning of an age of perpetual peace.

This is my opinion: it will hardly be possible to end controversies and impose silence on the sects, unless we resolve complex arguments into simple calculations, and substitute well-defined symbols for terms with vague or uncertain meanings . . . . Once this has been done, however . . . disputes between philosophers will become as unnecessary as disputes between accountants. All we need do is . . . take up our pens, or sit down at our abacus, and say to one another, calculemus.

Let us calculate indeed: let us calculate the chances of two parties in fundamental disagreement concurring over the translation of disputed terms into ‘well-defined symbols’, and let us calculate, too, the supposed improbability that two accountants could ever disagree. Antognazza may be right in thinking that Leibniz’s calculemus is the secret thread that links his intellectual projects together, but it is hardly going to save him from the condescension of posterity.