George MacDonald Ross Leibniz
Originally published: Oxford University Press (Past Masters) 1984
Electronic edition : Leeds Electronic Text Centre July 2000
• Abbreviations
• Introduction
• 1 Life and character
Early years (1646-67) o
o Alchemist, jurist and polymath (1667-72)
o Paris (1672-6)
o Librarian and mining engineer (1676-86)
o Historian and archivist (1687-97)
o Diplomat and academician (1698-1714)
o Last years (1714-16)
o Character sketch
• 2 Mathematics
o The cult of the virtuoso
o Binary arithmetic
o The infinitesimal calculus
The priority dispute o
• 3 Science
o Force and energy
Dynamics and kinematics o
o Entropy
o The relativity of space
• 4 Logic
o The role of logic
o Definition
o Real and semi-mental beings
o Truth and necessity
o Discovery and proof
o Improving the syllogism
• 5 Metaphysics
o Philosophical Method
o Scholastics versus moderns
o Cartesians versus atomists
o Mechanists versus vitalists
o Phenomenlists versus realists
o Efficient versus final causation • 6 God and man
o Mysticism
o Theodicy
o Man's place in nature
o Freedom and determinism
• 7 Influence
• Further reading
o Biography
o Translations
o Commentaries
• Index
Abbreviations
All the quotations are my own translations. I have not specified any particular edition for the Monadology , which is included in most collections, and is referred to here by paragraph in the normal way. The rest are from the following editions:
; C Opuscules et fragments inédits de Leibniz [Unpublished Short Works and
Fragments of Leibniz], ed. Louis Couturat (Paris, 1903)
; D God. Guil. Leibnitii Opera Omnia [Leibniz's Complete Works], ed. Louis
Dutens, 6 vols, (Geneva, 1768)
; E God. Guil. Leibnitii opera philosophica quae extant [Leibniz's Extant
Philosophical Works], ed..Johann E. Erdmann, 2 vols in one (Berlin, 1840)
; G Leibniz, G. W., Die Philosophischen Schriften [The Philosophical Writings],
ed. C. I. Gerhard, 7 vols, (Berlin, 1875-90)
; S Leibniz' Deutsche Schriften [Leibniz's German Writings], ed. G. E. Guhrauer,
2 vols, (Berlin, 1838-40)
Introduction
Traditionally, university courses on the history of modern philosophy have been structured round a pantheon of seven great philosophers: three ‘continental rationalists ’: Descartes, Spinoza and Leibniz; three ‘British empiricists ’: Locke, Berkeley and Hume; and Kant. The empiricists were supposed to have believed that all our knowledge was built up out of the data of sense, whereas the rationalists were supposed to have restricted genuine knowledge to what could be deduced from indubitable truths of reason. Kant, on the other hand, created a new synthesis out of what was right in both empiricism and rationalism. Needless to say, this way of viewing the history of philosophy was invented by Kant himself. It has, however, had a remarkably long run for its money.
Historians of philosophy have always found particular difficulty in forcing Leibniz into this Kantian mould, since his approach was markedly less rationalist than that of either Descartes or Spinoza. During the present century, there has been a growing
tendency among professional philosophers to see logic as central to their discipline. Consequently the focus of interest in Leibniz's thought has shifted to his work on formal logic, and the extent to which his philosophy can be interpreted as derived from his logic. However, this approach leaves many questions unanswered, and commentators have been positively embarrassed by the many quirkier aspects of Leibniz's philosophical work. These obviously have nothing to do with logic. In fact, Leibniz stood on the interface between the holistic and vitalist worldview of the Renaissance, and the atomistic and mechanistic materialism that was to dominate the eighteenth and nineteenth centuries. As we shall see, many of his ideas were too radical for his own age, and were taken up only much later – sometimes not until the
present century. It would be rash to judge him merely by those ideas which have subsequently become part of our view of the world. As with all great philosophers, his work no doubt contains hitherto unrecognised potential.
Another common distortion is to see Leibniz as primarily a philosopher, as if his role
in life were the same as that of the twentieth-century professional philosopher. Not only was he never employed as a professor of philosophy, but the range of his interests was so wide that his philosophical work was no more than one activity among many. He was, as the Germans quite rightly call him, an Universalgenie – a
‘universal genius ’. A balanced account of his achievement must place his philosophy
in the context of everything else he did. Only then is it possible to appreciate how Leibniz, far from being the extreme ‘rationalist ’ Kant made him out to be, was really himself aiming to create a new synthesis out of the apparently irreconcilable conflicts between earlier traditions in various spheres of intellectual activity. 1 Life and character
; Early years (1646-67)
; Alchemist, jurist and polymath (1667-72)
; Paris (1672-6)
; Librarian and mining engineer (1676-86)
; Historian and archivist (1687-97)
; Diplomat and academician (1698-1714)
; Last years (1714-16)
; Character sketch
Early years (1646-67)
Gottfried Wilhelm von Leibniz was born in Leipzig, on Sunday 1 July 1646. His father, Friedrich Leibnütz (1597-1652), was Professor of Moral Philosophy at Leipzig University. His mother, Catherina Schmuck (1621-64), was Friedrich's third wife. Leibniz had a half-brother Johann Friedrich (d. 1696), and a sister Anna Catherina (1648-72), whose son Friedrich Simon Löffler was eventually his sole heir. During his
twenties, Leibniz changed the spelling of his name from ‘-ütz ’ to ‘-iz ’: he himself
never used the ‘-itz ’ form, which became the normal spelling during his own lifetime, and which has only recently gone out of fashion.
Little is known about Leibniz's early education, beyond what he tells us in incidental reminiscences, which probably exaggerate the extent to which he was self-taught. He learned to read from his father, well before going to school at the age of seven. He claims that he taught himself Latin from an illustrated Livy, and that by the age of eight he was avidly reading his late father's books. It is hard to imagine what he can have made of them at first, since he was not fluent in Latin until the age of twelve, and was only then beginning Greek. But they certainly formed the basis of his later massive erudition in the classics, the Church Fathers, and scholastic philosophy. On top of this, his school syllabus was itself very demanding, including German literature and history, Latin, Greek, theology and logic. This last was of particular interest to him, and at the age of thirteen he was already trying to improve on the Aristotelian theory of the categories, despite discouragement from his teachers.
Leibniz moved on to Leipzig University after Easter 1661, when he was still only fourteen (young, but not exceptionally so in those days). He followed the standard two-year arts course, which included philosophy, rhetoric, mathematics, Latin, Greek and Hebrew. After graduating, he could proceed only by studying for a doctorate in one of the ‘higher ’ faculties of Theology, Law, or Medicine. He opted for Law, but before starting his course, he spent the short summer term at the nearby university of Jena. Here he came into contact with more unorthodox ideas, in particular Erhard Weigel's Neopythagoreanism, according to which Number is the fundamental reality of the universe.
Following his return to Leipzig, Leibniz spent the next three years working at a series of ‘disputations ’ which he had to publish and defend in open debate at each stage (or
‘degree ’) of his student career. In addition to bachelor's and master's disputations in law, in his final year he wrote a Dissertation on the Art of Combinations, by which he
‘habilitated ’, that is, became qualified to lecture in philosophy. However, he did not
exercise his right to teach philosophy, since such lectureships were purely honorary, and he was already heavily in debt to his relatives. Rather, he had his eyes on one of twelve established law tutorships, which went to doctors of law whenever vacancies occurred, in order of date of graduation. Unfortunately, there were too many doctoral candidates that year, and the younger ones, including Leibniz, were told to wait until a later degree day. He took this very badly, and suspected a conspiracy directed against him personally by the Dean's wife, for motives which he never explained. So he moved on to the little university of Altdorf, just outside Nuremberg, which was then a major centre of science and technology. Almost as soon as he had registered (4 October 1666), he submitted his already prepared doctoral thesis, and was formally awarded the degree the following February. He so impressed the Altdorf academics, that he was offered a professorship, but by that time he had changed his mind about
an academic career, and decided instead to become more involved in the outside world.
Alchemist, jurist and polymath (1667-72)
Leibniz's first job was a stopgap, and he may already have had it while still officially a student at Altdorf. It was the secretaryship of a society of Nuremberg intellectuals interested in alchemy (not Rosicrucians, as has often been asserted). It is unclear what his duties were – on alchemical questions Leibniz consistently adhered to the tradition of secretiveness. In contrast with his contemporary Isaac Newton, it is unlikely that he ever did any actual laboratory work, but he certainly acquired a reputation as an adept with deep theoretical understanding of the art. To his dying day he retained a close interest in alchemy (he talked about it with his doctor on his death-bed), and he periodically arranged tests of the claims of various alchemists. His declared motives were scientific: if transmutation were a practical possibility, the process should yield valuable information about the structure of matter. But in fact he also hoped to make his fortune from it. Thus, in about 1676, he entered into a formal profit-sharing agreement with two practising alchemists (G. H. Schuller and J. D. Crafft), his side of the bargain being to provide capital and technical advice: he was always a soft touch for people wanting to borrow money for alchemical experiments. His main reservation about gold-making was that gold would lose its value if it could be made too cheaply.
Whatever his precise relationship with the Nuremberg alchemists, he did not stay with them for long. Sometime during the summer he was on the move again, intending to travel ‘to Holland and beyond ’. By chance he met up with Baron Johann Christian von Boineburg, the former chief min ister of the Elector of Mainz, Johann Philipp von Schönborn. Impressed by Leibniz's alchemical erudition, as well as by his obvious employability in state service, Boineburg persuaded him to accept his patronage, and go home with him to Frankfurt-am-Main, just outside Mainz. Boineburg soon managed to get him appointed as assistant to the Elector's legal adviser, who was working on a recodification of civil law. About a year and a half later, Leibniz was promoted to the rank of Assessor in the Court of Appeal.
Despite this appointment, he was still very much Boineburg's protégé, and for the next five years he spent as much time in Frankfurt as in Mainz. Leibniz's close relation ship with Boineburg was important, not merely for launching him on his career, but also at an intellectual and personal level. In particular, Boineburg and other members of his circle were converts from Lutheranism to Catholicism. Leibniz very nearly followed their example, and it says much for his sincerity that in later years, when offered the prestigious librarianships of the Vatican (in 1689), of Paris (in 1698), and perhaps also of Vienna, he turned them down only because he was not prepared to go through a formal conversion. How ever, despite his loyalty to Lutheranism, he moved easily in Catholic circles, and was ideally placed to further the reunification of the churches, which was one of his life's ambitions. With Boineburg's encouragement, he
drafted a number of monographs on religious topics, mostly to do with points at issue between the churches, such as the doctrine of transubstantiation.
As we shall see in Chapter 4, one of the corner-stones of Leibniz's philosophy was his vision of a ‘universal encyclopaedia ’, which would incorporate all knowledge into a single system. Many of his activities were intended as contributions towards this long-term goal, including his employ ment on legal recodification at Mainz, since he believed that natural law constituted a proper part of human knowledge. As it stood, German law comprised a chaotic mixture of the Roman code, traditional Germanic common law, and the statute and case law of the various states. Leibniz hoped to reduce it to order by defining all legal concepts in terms of a few basic ones, and deducing all specific laws from a small set of incontrovertible principles of natural justice. Among his papers there survive many draft attempts at such a system, and he published a number of short treatises on the topic during his Mainz period (for example, the New Method of Teaching and Learning Jurisprudence of 1667 ).
Although the focus of his interests moved away from law as he got older, he kept on returning to this youthful project. However, not only was it a huge task to reduce the whole of natural law to a system, but he never began to solve the problem of
extending it to civil legislation.
More generally, Leibniz's scheme for a universal encyclopaedia required a pooling of existing knowledge, of research in hand, and of future efforts. There had already been attempts to encompass all knowledge in a single work, for example J. H. Alsted's seven-volume Encyclopaedia of 1630, which Leibniz once thought of adapting to his
own purposes. But the vast bulk of current knowledge was in books scattered throughout the libraries of Europe, and he soon saw that the most feasible way of centralising access to it would be to compile a master subject-catalogue. At the time the only useful subject-catalogue in existence was that of the Bodleian Library at Oxford, and Leibniz had no knowledge of it. In 1670 he produced as a model a catalogue of Boineburg's rich book collection; but despite repeated pleas, he was never allowed to do the same for any of the major libraries which were later in his charge, and only recently has his dream of the librarian as specialist in information storage and retrieval again been taken up by professional librarians. As for setting up a central register of new discoveries, Leibniz devised a scheme for a review of books, which he called a nucleus librarius, to include abstracts of all new
serious publications. His long-term plan was to expand it to cover earlier publications, unpublished works, research in progress, and a cumulative subject-index. Twice he applied for the necessary imperial licence (in 1668 and 1669), but on each occasion he was turned down, presumably because of fears that it would harm the retail book trade. However, despite the failure of the more grandiose scheme, he continued to do what he could in the same general direction. Throughout his life he kept a card-index of all the important books he read (an immense number), he was a regular contributor to such review journals as existed (notably the Journal des Sçavans, founded in 1665,
and the Acta Eruditorum, founded in 1682); and much later, in 1700, he started his own journal, the Monatliche Auszug, under the editorship of his assistant Johann
Georg von Eckhart. This, however, folded after only two years.
The need to co-ordinate research naturally suggested the foundation of learned and scientific societies. Like many of his contemporaries, Leibniz dreamed up various Utopian schemes for communes of researchers, and he also proposed exhibitions and museums for popularising and funding science. Until he was influential enough for his plans to have any real chance of success, the only practical step was for him to join such societies as already existed. With this in mind, he composed a number of treatises on scientific topics, two of which he had printed with dedications to the Royal Society of London, and to the Paris Academy. He was elected to the former on 19 April 1673, but he had to wait until 13 March 1700 to be made an external member of the latter.
Although scientific societies and periodicals were gradually coming into existence during the seventeenth century, by far the most important medium of intellectual co-operation and dissemination of ideas was the exchange of letters. These were often widely distributed among the acquaintances of the correspondents, and it was also common for collections of such letters to be published in book form. For example, in 1697 Leibniz published a selection from his correspondence, mainly with Jesuit missionaries, about China, under the title Novissima Sinica (‘The Latest from China ’).
Boineburg was an avid letter-writer, and he helped Leibniz to build up his own circle of correspondents by putting him in touch with intellectuals from all over Europe. Within a few years, Leibniz was in correspondence with literally hundreds of people at a time on almost every subject under the sun – science, mathematics, law, politics,
religion, philosophy, literature, history, linguistics, numismatics, anthropology. He was obsessive about preserving his letters, and over 15,000 still survive. It is on these, and on a comparable mass of private notes and drafts, that we rely for most of our knowledge of his work, especially in the areas of philosophy, logic and mathematics. As he once wrote, ‘Anyone who knows me only by my publications does not know
me at all ’ (D vi i 65). Most of the manuscript material is in Latin, which was still (though not for much longer) the lingua franca of the scholarly world. He often corresponded in French (even with fellow Germans), but hardly ever in German. When he did, he fre quently lapsed into Latin because of the lack of abstract technical terms in German. As a keen nationalist he much regretted the fact, and proposed a German Academy to enrich and promote the German language. He occasionally tried to write philosophy in a German free of Latinate borrowings, very much in the spirit of the largely successful eighteenth-century movement for linguistic purity. Although Leibniz's interests were clearly developing in a scientific direction, he still hankered after a literary career. All his life he prided himself on his poetry (mostly Latin), and boasted that he could recite the bulk of Virgil's Aeneid by heart. During
his time with Boineburg he would have passed for a typical late Renaissance humanist. His Latin style was still elaborate and florid, he never missed any opportunity to
parade his classical learning, and his principal publication was an edition of the Antibarbarus of the sixteenth-century Italian humanist Mario Nizolio. Leibniz was broadly sympathetic with Nizolio's theme, which was that a pure style in Latin was a surer route to knowledge and wisdom than the logic and linguistic barbarism of university philosophy. In 1673 Leibniz promised to do the Delphin Classics edition of
Martianus Capella (the fifth-century author of a fantastic allegory on the seven liberal arts), but he never got round to it. In 1676 he translated Plato's Phaedo and Theaetetus
into Latin, and was the first modern scholar to detect a sharp contrast between the philosophy of the historical Plato, and the mystical and superstitious ‘Neoplatonism ’ (or ‘ Pseudo Platonism ’, as Leibniz called it) of Plato's later followers.
Leibniz also applied his mind to political questions. For example, soon after his arrival in Mainz, he published a short treatise using deductive arguments to solve the question of the Polish succession. A more long standing problem was the French threat to Germany, now seriously weakened by the Thirty Years War. Leibniz periodically came up with anti-French ideas, such as undercutting the brandy trade with cheap rum from West Indian sugar, and in 1684 he published an anonymous satire on Louis XIV's bellicosity, under the title Mars Christianissimus (Mars being
the god of war, and Louis being known as Rex Christianissimus, ‘The Most Christian
King ’'). While still under Boineburg's patronage, he devised a plan to distract Louis away from Northern Europe with an enticing scheme for a French conquest of Egypt (the strategy he suggested was almost identical to the one actually carried out by Napoleon a century and a half later). Boineburg was so impressed by the plan, that he arranged for Leibniz to go to Paris to try and lay it before the French government. Paris (1672-6)
On arriving in Paris in the spring of 1672, and while waiting for an opportunity to carry out his political objective, Leibniz set about getting himself known in intellectual circles. He soon had a wide range of acquaintances, including the philosophers Arnauld and Malebranche, and the mathematician Huygens. Through his philosophical contacts, he managed to get access to the unpublished writings of the two greatest French philosophers of the previous generation, Pascal and Descartes, and some of the latter survive only through the copies he himself made. As we shall see, his close but critical study of Descartes' work was one of the major influences on his mature philosophical system. But at this stage, his main interest was in mathematics. Because of the narrowness of his mathematical education in backward Germany, he had arrived in Paris with exaggerated ideas of his own achievements. After a number of embarrassing encounters with various leading mathematicians, mainly French and English , he was forced to realise that he still had a lot to learn. Far from being discouraged, he immersed himself in mathematical studies under the guidance of Huygens, and by the time he left Paris he had already made most of the discoveries that were to earn him his leading place in the history of the subject.
But Leibniz's official reason for being in Paris came to nothing: he never found an opportunity to present his Egyptian plan to the King. In November 1672, Boineburg sent his son Philipp Wilhelm to Paris to finish his education under Leibniz's charge. He arrived in the company of his brother-in-law, the Elector's nephew Melchior Friedrich von Schönborn, who was on a diplomatic mission. This meant that Leibniz had both continued financial support, and the status of a semi-official attaché. Most importantly, he took part in a trip to London, in January 1673, which enabled him to make personal contact with members of the Royal Society, in particular its secretary, his fellow German Henry Oldenburg. The Society had given a mixed reception to his treatise, The Theory of Concrete Motion, which he had sent them (see p. 8 above), but
they were very intrigued by another of his projects which he had brought along to show them. This was the prototype of a mechanical calculator he had been working on while still in Germany.
He was very proud of his invention. He once thought of commemorating it with a medal bearing the motto SUPERIOR TO MAN, and much later he had a machine made for Peter the Great of Russia to send to the Emperor of China as an example of superior Western technology. Its immediate applications were obvious: it would save considerable labour and improve accuracy in accountancy, administration, surveying, scientific research, production of mathematical tables and so on. This was all more significant than we might now appreciate, since at the time even educated people rarely understood multiplication, let alone division (Pepys had to learn his multiplication tables when already a senior administrator). For the long term, he envisaged a larger version of his calculator being used to mechanise all reasoning
processes, once all possible thoughts had been given a number through his projected ‘Universal Characteristic ’ (see Chapter 4 below). Instead of fruitless arguing, people
would say, ‘Let us calculate ’ – and they could do so by setting the dials and cranking
the handle of his machine (one of a number of Leibnizian schemes satirised in Swift's Voyage to Balnibarbi).
The calculator itself was a considerable advance on earlier adding machines, such as Wilhelm Schickard's of 1623, or Pascal's of 1642. Leibniz designed it specifically as a multiplier and divider, and invented a number of devices which became standard in later technology – in particular the stepped reckoner (or ‘Leibniz wheel ’), which had cogs of varying lengths. However, despite spending a small fortune on the project right up to the end of his life, he never developed a version which could do carrying completely automatically. One of his models still survives, and is now in the Hanover State Library.
While in Paris, Leibniz was full of other technological ideas. The one he had most fully worked out was a watch with two symmetrical balance wheels working in tandem, of which he demonstrated a model to the Paris Academy in April 1675. Others were a device for calculating a ship's position without using a compass or observing the stars, a method for determining the distance of an object from a single observation point, a compressed-air engine for propelling vehicles or projectiles, a
ship which could go under water to escape enemy detection (though he rejected space flight on the grounds that the air would be too thin), an aneroid barometer (subsequently reinvented by Vidi of Paris in 1843), and various improvements to the design of lenses.
Leibniz's trip to London was cut short by the news of the sudden deaths of both his patrons: of Boineburg in December 1672, and of the Elector in February 1673 . He arrived back in Paris in early March, but continued as the young Boineburg's tutor till his appointment came to an end in September 1674. He was now twenty-eight, but despite his acknowledged brilliance, he had no settled career. Although he had been offered jobs at the courts of Hanover and of Denmark, what he really wanted was a research post attached to the Paris Academy. Eventually he was forced to recognise that no such position was forthcoming, and since he was running seriously into debt, he reluctantly accepted the post of Court Councillor at Hanover. His appointment was officially from January 1676, but he managed to delay his arrival until December of that year. He left Paris in October, and took a roundabout route via London and Holland. His stay in London was very brief. In Amsterdam he got to know the pioneering microscopist Antonie van Leeuwenhoek, who had recently made the first observations of bacteria, protozoa and spermatozoa. Leibniz also had four days of intense discussions with the famous lens-grinder and philosopher, Benedict de Spinoza at the Hague.
Librarian and mining engineer (1676-86)
The administration at Hanover was typical of that of the hundred or so independent states under the titular leadership of the German Emperor in Vienna. The autocratic head of state, in this case Duke Johann Friedrich of Brunswick- Luneburg, acted through a council composed largely of lesser aristocrats and law graduates, some of whom were delegated more specialist functions. Leibniz managed to negotiate partial relief from normal council duties because of the burden of his particular responsibilities as librarian, political adviser, in ternational correspondent and, increasingly, as technological adviser.
His duties as librarian were onerous, but fairly mundane: general administration, purchase of new books and second- hand libraries, and conventional cataloguing. In 1679 he had to cope with the transfer of the library from the suburban Herrenhausen palace to Hanover itself, and two years later with its removal to more extensive accommodation in a rear wing. From 1698 it was housed in a separate building, with living quarters for the librarian. (The ‘ Leibniz-Haus ’ was destroyed in World War II,
but a replica was inaugurated in 1983.) In 1690 Leibniz also undertook overall responsibility for the much more prestigious Bibliotheca Augusta at Wolfenbüttel,
about 70 kilometres south-east of Hanover. He was expressly forbidden to reorganise it along the lines of any of his pet schemes, but he was at least able to oversee the drawing up of a main-entry alphabetical author catalogue. In 1705 the books were removed to the armoury while a grand new library was being built. Unfortunately,