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- Herausgeber: John Wiley & Sons
- Kategorie: Geisteswissenschaft
- Serie: Classic Thinkers series
- Sprache: Englisch
Few philosophers have left a legacy like that of Gottfried Wilhelm Leibniz. He has been credited not only with inventing the differential calculus, but also with anticipating the basic ideas of modern logic, information science, and fractal geometry. He made important contributions to such diverse fields as jurisprudence, geology and etymology, while sketching designs for calculating machines, wind pumps, and submarines. But the common presentation of his philosophy as a kind of unworldly idealism is at odds with all this bustling practical activity. In this book Richard. T. W. Arthur offers a fresh reading of Leibniz's philosophy, clearly situating it in its scientific, political and theological contexts. He argues that Leibniz aimed to provide an improved foundation for the mechanical philosophy based on a new kind of universal language. His contributions to natural philosophy are an integral part of this programme, which his metaphysics, dynamics and organic philosophy were designed to support. Rather than denying that substances really exist in space and time, as the idealist reading proposes, Leibniz sought to provide a deeper understanding of substance and body, and a correct understanding of space as an order of situations and time as an order of successive things. This lively and approachable book will appeal to students of philosophy, as well as anyone seeking a stimulating introduction to Leibniz's thought and its continuing relevance.
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Table of Contents
Classic Thinkers
Title page
Copyright page
Acknowledgements
Note on the Text and Translations
Abbreviations
Chronological Sketch
1: Introduction
Historical Context
Leibniz's Schooling
University and Scholastic Studies
Leibniz's Early Career
Paris
Hanover
Italian Sojourn
Back in Hanover
2: Logic, Language and the Encyclopaedia Project
Combinatorics and the Alphabet of Human Thoughts
Nominalism, Abstraction and Real Definition
Universal Language and the Encyclopaedia Project
From Combinatorics to Blind Thought
Leibniz's Philosophy of Natural Language
3: Natural Philosophy and the Science of Life
Worlds within Worlds
Atoms, Souls and Animal Generation
Machines of Nature
Life, Programs and Final Causes
4: Mathematical Philosophy
From Indivisibles to Fictions
Infinite Series, the Differential Calculus and the Law of Continuity
Contingent Existents and Possible Worlds
Truth, Contingency and Incommensurables
Applying the Calculus
5: The Reform of Metaphysics
Metaphysical Problems and Insights
Leibniz's Reaction to Spinoza's Philosophy
The Mature Theory: Minute Perceptions and Innate Ideas
Leibniz's Theory of Substance: Objections and Replies
6: Dynamics: The Physics and Metaphysics of Action
The Insufficiency of Mechanism
The Full Cause Principle and the Conservation of Force
Further Development: Application and Reception
The Metaphysics of Activity and Perfection
7: The Philosophy of Space and Time
Leibniz's Nominalist Approach to Relations
Space and Time, Immensity and Eternity
Space as the Order of Situations
Time as the Order of Successive Things
8: Morals and Politics
Justice, Natural Law and Voluntarism
Determinism, Freedom and the Lazy Fallacy
Necessity, Certainty and Hypothetical Necessity
Spontaneity, Freedom and Divine Concurrence
Theological Projects
9: Leibnizian Posterity
Select Bibliography
Index
Classic Thinkers
Copyright © Richard T. W. Arthur 2014
The right of Richard T. W. Arthur to be identified as Author of this Work has been asserted in accordance with the UK Copyright, Designs and Patents Act 1988.
First published in 2014 by Polity Press
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ISBN-13: 978-0-7456-5374-7
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ISBN-13: 978-0-7456-8637-0 (epub)
ISBN-13: 978-0-7456-8636-3 (mobi)
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Acknowledgements
Many people have helped to make this book better than it might otherwise have been. It is a pleasure to acknowledge Barry Allen, who co-taught a graduate seminar with me on Deleuze, Spinoza and Leibniz, and the students in that seminar who read early drafts of some chapters; and also the students, undergraduate and graduate, in my course on Leibniz and English Philosophy, for whom the manuscript was a set text. Their reactions to it and excellent weekly comments and discussions helped me to frame my treatment of many points. I also benefited greatly from the comments and suggestions of Ohad Nachtomy and a second (anonymous) reader for Polity Press, and am much indebted to my sons Alexander and Thomas Arthur for advice on how to frame chapter 1, to my colleagues Stefan Sciaraffa, Violetta Igneski and Stefan Rodde for feedback on chapter 8, to Liam Dempsey and David Wright for comments on the whole draft, to Stephan Meier-Öser for supplying me with the latest edited versions of some passages from Leibniz's writings, and above all to my wife Gabriella Colussi Arthur for her encouragement and critical advice. To all of you, and to Emma Hutchinson, Pascal Porcheron and everyone at Polity Press, many, many thanks!
Note on the Text and Translations
Leibniz wrote mostly in Latin, somewhat less in French, and occasionally in German. All translations here are the author's own translations from standard editions of Leibniz's original Latin and French (except where explicitly noted otherwise). For the convenience of the reader wishing to see a given passage in fuller context, references are also given to available English-language translations where these exist, e.g. (A VI iii 518/DSR 75).
The titles of Leibniz's books and papers are all given in English; for ease of reference, the original-language titles are also given in the Chronological Sketch.
Abbreviations
Chronological Sketch
1
Introduction
Gottfried Wilhelm Leibniz was one of the most prolific thinkers of all time. ‘Often in the morning when I am still in bed,’ he wrote, ‘so many thoughts occur to me in a single hour that sometimes it takes me a whole day or more to write them out’ (quoted from Mates 1986: 34). These thoughts might have included designs for a new wind pump to drain the mines of the Harz mountains or for a calculating machine based on binary arithmetic, sketches for a treatise on geology or etymology, another draft of a logical calculus that was two hundred years ahead of its time, or a new derivation of Newton's law of gravitation on strictly mechanical principles. Even before getting up, Leibniz would usually have written lengthy letters on such subjects to one or two learned correspondents. He might also have penned a proposal to his employer the Duke of Hanover for a universally accessible state medical system, a legal brief in support of the Duke's electoral claim to certain territories, a deposition aimed at church reunification, or tried to mediate in the dispute among the Jesuits over the interpretation of Chinese religious rites. In short, Leibniz was an indefatigable one-man industry.
Yet all this worldly activity seems at odds with the usual understanding of Leibniz as a philosopher. He is perhaps best known for his monads or unities of substance. These he conceived as enduring entities constituting what is real in bodies and their motions. But although in those respects they are like material atoms, Leibniz characterized monads as ‘possessing something analogous to perception and appetite’ (NE 318), where perceptions (or states) of monads are representations of the whole of the rest of the universe, and their appetites are tendencies toward future states, governed by a law specific to each individual. Consequently, Leibniz is usually understood as an idealist who wished to reduce the whole of reality to mind-like entities and their intentional states: each monad is a world apart, constituted only by its own perceptions, sequenced according to its own internal law. On the usual understanding, moreover, these monads do not even exist in space and time. For, as Leibniz famously argued against Isaac Newton (1642–1727) and Samuel Clarke (1675–1729), space and time are relations; but he also held that relations, far from being independently existing entities, are supplied by a perceiving mind. On this reading, then, Leibniz's philosophy appears as a thorough-going idealism.
This presents a perplexing contrast. Leibniz was a ‘natural philosopher’, making active contributions to geometry, mechanics, dynamics, optics, geology and the life sciences. But why would someone on the cutting edge of both theoretical and empirical developments in these fields have developed a philosophy apparently so hostile to the physical world? We know that Leibniz understood himself to be attempting a rapprochement between the new ‘mechanical philosophy’ of Descartes, Gassendi and Boyle, and the Aristotelian philosophy taught in the universities. But both parties understood the physical world to exist in an unambiguous way: for the mechanical philosophers, it was constituted by bodies in motion, bodies being understood as parts of matter extended in length, breadth and depth, whose motion could be treated geometrically; for the Aristotelians, bodies or ‘corporeal substances’ possessed ‘substantial forms’, which they used to explain all types of goal-directed behaviour: plants tending to face the light, heavy bodies tending to fall to Earth, and so forth. Now what kind of rapprochement would Leibniz have achieved if he was asking both parties to deny the existence of matter and motion, and of the corporeal substances that they took to be the very stuff of the physical world?
Interpreters have generally answered that question by an appeal to a distinction between Leibniz's public and private philosophies: the ‘optimistic, orthodox, fantastic, and shallow’ philosophy ‘designed to win the approbation of princes and princesses’, as Bertrand Russell puts it (Russell [1946] 1972: 604), and the ‘profound, coherent, largely Spinozistic, and amazingly logical’ philosophy he had developed in his unpublished manuscripts. On this view, Leibniz was happy to promote his philosophy in public as solving such problems as the interaction between body and mind by proposing that both bodies and minds unfold their states independently and perfectly in step, like two clocks that keep perfect time; and generally to speak of bodies and corporeal substances in a realistic vein. But in his private philosophy bodies are no more than the coherent appearances of perceiving substances.
I see no such schism between private and public in Leibniz's philosophy, but only differences in presentation, resulting from his cooperative approach to building knowledge. Although Leibniz worked hard to produce general principles that he thought could promote science and its application, as well as heal religious rifts, he knew this could only be achieved through dialogue with others. And in order to promote dialogue, he would bend or colour his views to maximize the chances of productive exchange.
A big difficulty in trying to present Leibniz's philosophy, however, is the sheer profusion and ambitious scope of the projects in which he was engaged, either at the bidding of his employers in court or on his own account, which virtually guaranteed he would bring few of them to completion. As a result of this almost permanent distraction, Leibniz produced no definitive masterwork, such as Spinoza's Ethics or Kant's Critique of Pure Reason. He did publish a long book on the problem of evil in 1710, the Theodicy, but, like his posthumously published New Essays, the work is too discursive and polemical to serve as an introduction to the main themes of his thought. Consequently, his philosophy is usually introduced through the study of two summaries he gave of his metaphysics, the Discourse on Metaphysics of 1686 and the Monadology of 1714 (both these titles are the creations of later editors). The first presents his views in a context heavily conditioned by his desire to engage Antoine Arnauld in correspondence. Arnauld (1616–98) was a co-author of the famous Port Royal Logic, and a leading Catholic theologian and critic of Descartes, whose approval would aid Leibniz (a tolerant Lutheran) in his ambition to bring about a reconciliation of faiths. But for a modern reader unfamiliar with this context, it is hard to understand the mélange of issues from theology, logic, metaphysics and physics that Leibniz chooses to stress. The second work, the Monadology, although in many ways an admirably succinct summary of Leibniz's metaphysics, by and large fails to give much argument for his views, the contexts in which they were generated, or the problems they were designed to resolve. As a result, Leibniz's philosophy comes across, in Hegel's words, ‘as a string of arbitrary assertions, following one upon another without any necessity in their connection, like a metaphysical romance’ (Hegel 1836: 454).
The usual reception of Leibniz is also conditioned by the need to fit him into a simple narrative about the history of philosophy, where he is seen as one of the ‘great rationalists’ along with Descartes and Spinoza, whose dogmatism is opposed by the British empiricist philosophers beginning with Locke. But Leibniz was not an academic with an allegiance to any one school. He was a court diplomat, who thought that a political career would better enable him to achieve his goals of reforming scientific knowledge and helping to bring about the reunification of the Church. Seen in this light, his contributions to science, such as his correction of Descartes's law of the conservation of force, were not side-issues, but an integral part of his programme for the advancement of learning which he hoped would repair the theological rifts that were dividing seventeenth-century Europe. Leibniz was not trying to undermine the mechanical philosophy by reducing things to ideas and intentions, but rather trying to improve it by providing it with a proper foundation that could lead to new discoveries and advancements, as well as reconcile it with accepted articles of faith.
Accordingly, I shall approach Leibniz here in a way that I think is in keeping with his philosophy, although it will be an unusual methodology for a book of this kind. Instead of beginning with the themes and principles of his mature philosophy, and then structuring his philosophy around them, I take a genetic approach, trying to show how Leibniz's views arose by reference to the problems he was trying to solve, in their own historical context. In so doing, I will concentrate on his youthful writings, most of which are scattered Latin drafts that do not exist in any convenient compilation, and all of which I have translated. This genetic approach courts some obvious dangers: a reader encountering Leibniz for the first time might remember him more for views he gave up, or confuse his earlier attempts with his mature solutions to some of these problems, or simply rue the fact that not much space is left to discuss developments in his mature writings. And of course, it is more difficult to understand anyone in historical context: the various scientific, political and theological problems that occupied Leibniz, such as the correct measure of force or church reunification, will seem remote from today's philosophical concerns. But the reward is to see Leibniz at his best, as a profound and creative thinker always pushing the boundaries of knowledge, anticipating and engendering new approaches, many of them of surprising contemporary relevance.
Another advantage of this genetic approach is that it allows me to tackle some of the issues of interpretation obliquely, rather than head on. Instead of assuming that Leibniz had a definite metaphysical system, consisting in certain dogmatically asserted premises that were more or less impervious to his scientific and political pursuits, I will try to show how his metaphysics developed through the attempt to solve various more specific problems in the life sciences, theology, physics and mathematics. From this perspective it will emerge that Leibniz never intended to deny that substances have real bodies, but he meant rather to convey a deeper appreciation of what it is to be a substance or to be a body. Nor did he intend to deny that things exist in spatial relations, or that states of substances really succeed one another in time; rather he wanted to show how a correct understanding of space as an order of situations and time as an order of successive things would rule out a metaphysics in which extension is taken to be a substance, or space and time are depicted as existing independently of the things in them.
This results in a picture of Leibniz's metaphysics very different from the idealistic interpretation described above, and it may be worth briefly stating it to orient readers familiar with the issues. On my reading, Leibniz's corporeal substances simply are his embodied monads, whose bodies are aggregates of subordinate substances.1 A corporeal substance is a unity by virtue of what is substantial in it, namely the form which gives it a unity of function and purpose through time. The body it has at any instant derives its reality from the substances presupposed in all its parts, although it is not itself a substance, and has at any time only a perceived unity. Similarly, motions derive their reality from an underlying instantaneous force existing at any instant. Thus Leibniz's commitment to corporeal substances is quite genuine, although by that term he means something different from what either the Cartesians or the Aristotelians understood by it. ‘It is really not surprising that the Cartesians have failed to understand the nature of corporeal substance,’ he tells his correspondent Burchard de Volder in June 1704, ‘since they consider extension as something absolute, ineffable, irresolvable, and primitive’ (GP ii 269/LDV 305). Extension, Leibniz insists, must be the extension of something, and what that something is he explains in terms of his new concept of force: it is the diffusion of a passive force of resistance. This passive force is complemented by an active force, which is his reinterpretation of the ‘substantial form’ or ‘first entelechy’ that Aristotle claimed to be the active principle of perfection in a body. Together the active and passive forces constitute corporeal substance. But more on these matters below.
Now let us turn to the context in which Leibniz's views were formulated. How did he come by his ambitions, and how did he seek to achieve them?
Historical Context
The political world into which Leibniz was born in 1646 was one riven with conflict. The German nation at that time was the Holy Roman Empire, an entity created already several hundreds of years before as a result (on two separate occasions) of a German king coming to the aid of a Pope in need of protection. In the seventeenth century the Empire included most of central Europe, including Burgundy, Bohemia and northern Italy. It was comprised of hundreds of imperial states ruled over by various dukes, counts, margraves and princes subservient to the Emperor, and at the time of Leibniz's birth had been at war – the Thirty Years War (1618–48) – for almost three decades. Peace negotiations were under way, but war did not cease until the Peace of Westphalia two years later. Hostilities had begun with the Bohemian revolt of 1618, in which Protestant estates rose up to defend their religious liberties against an attempt to impose Catholicism on them by the Habsburgs. When the Calvinist Palatine Elector came to the throne in Bohemia, the war widened along confessional lines, with Leibniz's state of Saxony entering into the fray, later to be joined by the fellow Lutheran states of Denmark and Sweden. Although military hostilities ceased in 1648, the truce, in recognizing the rights of Lutherans to practise their religions in Lutheran territories, and Calvinists in Calvinist territories, only confirmed the division of the Empire into three unreconciled religious confessions.
The intellectual world, too, was in turmoil. Leibniz lived in the heyday of what we now call the ‘Scientific Revolution’, when the Aristotelian philosophy of the Schools (the European universities) was under sustained attack from modern thinkers. After the demolishing of the older Aristotelian cosmology by Galileo Galilei (1564–1642) and Johannes Kepler (1571–1630) in central Europe, the Copernican worldview was widely accepted, even if in the Catholic countries it was theologically dangerous to embrace it as literal truth. Still in a state of flux, however, was the natural philosophy that would support Copernicanism: by what means did the planets stay in orbit around the Sun? If heavy bodies do not fall to the ground because of their natural motion to the centre of the Earth, as Aristotle and the Scholastics had taught, then what explains terrestrial gravity?
René Descartes (1596–1650) had famously exhorted his contemporaries to make a clean break with Aristotle's conception of the natural world. Where Aristotle had populated the world with individual substances modelled on living creatures, each with its own form or soul, acting in accordance with ends appropriate to its nature, Descartes introduced a radical dichotomy between the material and the mental. For him, created substances are of two kinds: corporeal substances or bodies; and mental substances or minds (a human being, of course, as a mind with an associated body, is a kind of composite of the two). Since matter is identical with extension, there can be no vacuum: the material world is full (a plenum). Bodies, or material substances, are simply divisible portions of this continuously extended plenum, distinguishable by their different motions. As such, they are entirely passive. They can react, as when one body is moved by the impact on it of another, but they cannot initiate any action. God has imbued all the matter in the world with a certain quantity of motion, and this gets redistributed among the bodies as they mutually collide, subject to the three laws of motion that Descartes expounds. Mental substances, on the other hand, are immaterial, and not divisible into parts. They are characterized by completely different qualities, such as willing, perceiving, believing and thinking. Mind, in fact, is essentially a thinking thing, a conclusion Descartes derives through his famous cogito, ergo sum, ‘I think, therefore I am’.
Thus on Descartes's austere philosophy, it is simply anthropocentrism to think of the planets as having souls (as Kepler did); he was highly sceptical whether any organisms apart from humans were animate, or contained souls. Just as the appearance of a force for resisting motion could be explained in terms of a redistribution of quantity of motion of the bodies (without assuming that they had an inherent inertia or laziness, as Kepler had proposed), so the motion of the planets could be explained entirely mechanically in terms of the actions on them of the matter of the fluid heavens without assuming planetary intelligences. Descartes's definition of bodies as quantities of extension, on the other hand, possessing a certain quantity of motion at each instant, facilitated the replacement of the qualitative Aristotelian physics with one in which mathematics, the science of quantity, would have immediate purchase. All natural phenomena were to be explained in terms of the motion, shapes and sizes of particles subject to mathematical laws, in accordance with both atomism and Plato's privileging of geometry; but matter was strictly incapable of initiating any action, so that the behaviour of animals and other substances could no longer be explained by analogy with human behaviour, or ascribed to the teleological (goal-directed) workings of a substantial form.
This new ‘mechanical philosophy’ of Descartes caught the imagination of his contemporaries, even if they reserved judgement on his denial of souls to animals and his identification of matter with movable extension. His main rival, the French scholar Pierre Gassendi (1592–1655), conceived matter as consisting in atoms moving in an otherwise empty space, drawing his inspiration from the atomist philosophy of Epicurus of the third century bc, and moulding Epicureanism, Stoicism and other ancient heathen learning into a grand synthesis compatible with Christianity. In England, Henry More (1614–87) initially welcomed Descartes's philosophy as a kind of modernized Platonism, but later became virulently anti-mechanist, balking at the Frenchman's denial of extension to spirits and of souls to the higher animals. Other leading lights of the age maintained a neutrality between atomism and the plenum. Robert Boyle (1627–91), for example, sought to extend the application of the mechanical philosophy into chemistry, showing how much of what had been discovered in the alchemical tradition could be understood in terms of collisions of corpuscles. As to whether these corpuscles should be understood as Gassendian atoms or as divisible Cartesian corpuscles, though, Boyle was agnostic, declaring the question empirically undecidable.
Above all, what appealed to Descartes's contemporaries about his philosophy was the rejection of substantial forms and the promise of successful explanations of natural phenomena using mathematics. Descartes, of course, was by no means the first to propose either. But the appeal of his philosophy was much enhanced not only by its rigorous formulation and presentation, but also by its own successes in achieving new knowledge, particularly his ground-breaking Geometry and novel contributions to optics and meteorology, to which his famous Discourse on the Method (1637) served as an introduction.
Beyond that, however, there was much controversy. Descartes maintained that once God had freely decided upon the laws of nature and created the world, all the possible states of the universe would eventually come to pass in a determined order. This seemed to commit him to a version of necessitarianism, since there would be no possible states of affairs that did not actually come to pass. After Descartes's death, the issue became acute when Baruch Spinoza (1632–77) endorsed the Cartesian position on the necessity of the sequence of states of the universe, but dismissed the attribution of a will to God as anthropomorphism, rendering the Divine Being as a non-creating, non-judging intelligence – to the horror of his Christian contemporaries.
A second theological difficulty with Cartesianism was its rejection of all teleology in the physical world. How could material things, acting out of mere mechanical necessity, possess the means to reproduce and display the optimal forms, designs and behaviours mandated by Divine Providence? These designs and behaviours, especially in the biological sphere, suggested there was more to nature than Descartes's version of the mechanical philosophy would allow. Third, there was trouble for Descartes in making his philosophy fit with the Catholic interpretation of the sacrament of the Eucharist as transubstantiation. Although Lutherans interpreted this in terms of Christ's ‘real presence’ in the bread and wine, Catholic orthodoxy required that when the bread was converted into Christ's body and the wine into his blood, in each case its substance was literally changed, despite its remaining the same in appearance. This was hard to reconcile, to say the least, with Descartes's insistence that the substance of body is simply extension. As Leibniz wrote to Duke Johann Friedrich in 1679, ‘if a body's nature consists in extension, as Descartes claims, it would without any doubt involve a contradiction to maintain that it might exist in many places at once’ (A II i 487/L 261). In these latter respects, Gassendi's philosophy appeared as an attractive alternative to Cartesianism, for Gassendi did not deny teleology in the natural world. Moreover, since his atoms were not simply lumps of extension, but contained active principles, there was scope in his philosophy for maintaining that the different substances of Christ's body (or blood) and the bread (or wine) could give rise to the same appearances.
Leibniz's Schooling
The young Leibniz was not immune to the attractions of the mechanical philosophy in its Gassendian guise. In a letter to Nicolas Rémond of July 1714, he confided that he had held Gassendi's philosophy in high esteem ‘when I was starting to abandon the opinions of the School, while still myself a schoolboy’, and that ‘I gave myself over completely’ to atoms and the void (GP iii 620/L 657). In another letter, to Thomas Burnett in 1697, he recalled how when he was ‘not yet fifteen’ he had spent days wandering in a grove on the outskirts of Leipzig called the Rosenthal deliberating on whether to keep substantial forms, before finally deciding in favour of the mechanical philosophy. These accounts tally, as Leibniz graduated from the Latin school in his home town of Leipzig to go to university there in April 1661, when he would still have been a few months shy of his fifteenth birthday.
That someone so young could be ‘seduced by the flattering ease with which things could be understood’ in the new philosophy (Leibniz 1991: 809) is perhaps understandable, if we can get past the sheer precociousness of Leibniz's considering questions like this at such an age. It becomes all the more remarkable, though, when his early education is taken into account, for few thinkers of his time had been so thoroughly immersed in Scholasticism. Leibniz's father was Friedrich Leubnitz (or, as he sometimes spelled it, Leibnütz) (1597–1652), a name Leibniz later held to be of Sorbian (Lusatian) origin, tracing his ancestry to Lubeniecz, a family of Polish nobles.2 Friedrich had held the chair of moral philosophy at the University of Leipzig, where he was by all accounts a very conservative Lutheran scholar, deeply immersed in Aristotle's Nicomachean Ethics and the study of theology. A pillar of Leipzig society, Friedrich Leubnitz had represented the university in his capacity as actuary in the surrender of the city in 1633, and also served as dean of the faculty and notary. He anticipated great things from his precocious son, to whom he was in the habit of reading histories. But he was not to see the fruits of this parental tuition, for he died at the age of only fifty-four, leaving two children by his first wife, and two more, Gottfried himself (aged six) and Anna Catharina (aged four), by his third wife, Catharina. Nevertheless, before his early demise he had instilled in the boy a love of history, which was only heightened two years later, when Leibniz gained access to his father's library. This had been kept under lock and key by family and teachers wary of the heterodox views young Gottfried might find there, until a visiting nobleman scholar had managed to persuade them to give him access.
This episode is significant in itself, for it highlights a certain tension between the extreme religious orthodoxy of Leibniz's immediate environment in Leipzig and the attractions of the more tolerant attitudes to religion that he was to find in the books in his father's library. Leipzig was anything but tolerant, and any hint of Catholicism, or, even worse, of the rival Protestant sects of Calvinism or Zwinglianism, was met with outright hostility. Leibniz's mother Catharina, daughter of the prominent Leipzig jurist Wilhelm Schmuck, was a pious and fervent Lutheran, and raised her children accordingly. There is a reflection of this family piety in the stern warnings Leibniz received from his siblings years after his mother's early death in 1664 not to abandon his faith, and to return to the fold in Leipzig – first from his half-brother in 1669 when he had left Leipzig to take a position in the Catholic court of Mainz, and then from his younger sister in 1672 when he had arrived in Paris. Yet these warnings fell on deaf ears: by then Leibniz had long been committed to the less provincial world he had found earlier in the books of his father's library. Quickly mastering Latin with the help of the pictures in Livy's illustrated Roman history, the boy had progressed from history to philosophy, managing to orient himself by identifying some conceptual landmarks, and then comparing and contrasting different positions taken on them. As he advanced in his teenage years to weightier tomes, he devoured the classics of Plato, Aristotle, Archimedes, Cicero, Seneca and others, and then works by mainstream theologians, Luther, Calvin and their followers, as well as Roman Catholics, and even writings of unorthodox sects such as the Jansenists and Arminians. But what appealed to him the most among the theological writings, according to his later testimony, were the writings of Georg Calixt (1586–1656), a Lutheran professor of moral philosophy based in Helmstedt, who had advocated the reconciliation of Lutheranism not only with Calvinism but with a reformed Roman Catholicism. Calixt, it should be noted, was anathema to the theologians at his father's university, who had led the opposition to his conciliatory position.
There is more to be said, of course, about just how Leibniz managed such astonishing progress in wading through what was hardly normal reading matter for an adolescent. What he appears to have done is to have applied an innovative learning method inspired by Ramus (Pierre de la Ramée 1515–72) that was percolating through the German schools as well as into the tomes in his father's library. According to this method, as outlined in various handbooks, the way to approach a new subject is as follows: first, you assemble lists of categories or topics that appear in the reading; then you set them in a logical order, by making divisions and subdivisions of categories; then you collect a wide variety of opinions on these topics, and compare and contrast them, looking for points of agreement and disagreement, and ways of reconciling contradictions. This enables you to master the subject in an orderly way, but also makes it easier to recall what you have learned. Writing later about his adoption of such methods as a boy, Leibniz reports that it gave him two decisive advantages: ‘first, that I did not fill my head with empty assertions (resting on learned authority rather than an actual evidence); second, that I did not rest until I had penetrated to the root and fibre of each and every doctrine and reached its very principles, from which I would be able to discover by my own efforts everything that I needed to discuss’ (GP vii 185).
The result of this approach to his early self-education was Leibniz's lifelong preference not only for a comparative and ecumenical approach to received doctrines, but also a desire always to try to refine and improve upon what he was presented with, rather than remaining content with merely understanding it. In fact, the influence of this Ramist (or ‘semi-Ramist’) method of learning explains a great deal about his approach to philosophy, as we shall see. Ramus himself had offered a set of basic categories (the so-called praedicamenta), but these were improved upon by Bartholomew Keckermann (1571–1609) and writers of the Herborn school, Alsted, Bisterfeld and Comenius, whose works Leibniz had eagerly devoured in his father's library. In addition, as we will discuss in chapter 2, these authors also tried to improve upon the Aristotelian logic on which this method was based by giving combinatorial methods of combining simple concepts into complex ones. In this way they transformed the method from one that merely aided in learning to one in which the ordering of concepts was supposed to reflect the order of things themselves. The exposure to neo-Ramist methods bred in Leibniz a lifelong respect for Aristotelian logic and the possibility of improving it, as well as planting the seeds for his idea of a universal language based on logic.
University and Scholastic Studies
In fact, Leibniz's break with Scholasticism was not as complete as might be supposed from his remarks about his schoolboy conversion quoted above. This is made clear in his exchange of letters with the prominent jurist Hermann Conring (1606–81) in 1678. For when Conring takes exception to Leibniz's firm commitment to mechanism, and jibes that he might have obtained a better opinion of the Schoolmen's metaphysics if only he had read them (Conring to Leibniz, 26 February 1678: GP i 191), Leibniz responds (19 March) that when he began his university studies he ‘did in fact read them, more immoderately and eagerly than my teachers approved’, to the extent that ‘they feared I would cling too tightly to these rocks’ (GP i 197/L 190). One of the fruits of these studies was the dissertation Leibniz wrote for his bachelor's degree at Leipzig in 1663 on the Principle of Individuation, under the supervision of his professor, Jakob Thomasius (1622–84). This was a traditional problem of the schools: what is it that gives each substance its individuality? In his thesis Leibniz gives a traditional solution indebted to the influential Spanish Jesuit, Francisco Suárez (1548–1617), that it is the ‘whole entity’ of each individual substance (not just its matter and form treated abstractly) that makes it distinct. But by the time he writes to Conring in 1678, his view has undergone some radical changes, and he now favours the Scholastic idea that it is the substantial form itself that is the principle that individuates corporeal substances. As he writes to Conring, ‘Who would deny substantial forms, that is, essential differences between bodies?’ (196/189).
But this is no retreat from mechanism. In his previous letter to Conring, Leibniz had firmly declared that ‘everything in nature happens mechanically’, to which Conring had replied trenchantly, ‘if you want this to be understood in a Cartesian sense, I for my part do not hesitate to pronounce it a most absurd statement’ (Conring to Leibniz, 26 February 1678: GP i 191). Leibniz's response is uncompromising, one of the most eloquent statements of the mechanist creed ever made: ‘I recognize nothing in the world but bodies and minds, and nothing in mind but intellect and will, nor anything else in bodies insofar as they are separated from mind but magnitude, figure, situation, and changes in these, whether partial or total. Everything else is merely said, not understood’ (to Conring, 19 March 1678: GP i 197f./L 189).
So how could Leibniz say in the same letter that he accepted substantial forms? The answer lies in a careful attention to his words. He has said that, apart from geometric properties and their changes, there is nothing in bodies ‘insofar as they are separated from mind’. And by 1678 (indeed, as early as 1668) Leibniz considered mind, or at least a mind-like principle involving memory of its body's past states, to be the key to individuating bodies. Over the next few years he will build this idea into his new conception of substance and the ‘rehabilitation of substantial forms’ announced in the Discourse on Metaphysics. The idea that each individual substance is individuated by a concept implicitly containing its whole history will develop into his predicate-in-notion principle, and the uniqueness of each such actually existing substance will be enshrined in his Principle of the Identity of Indiscernibles, according to which no two created individuals are exactly alike.
In addition to individuation, there were two other Scholastic problems Leibniz studied in his university days on which, he assured Conring, ‘you would have been seen me making some singular and profound comments’, namely ‘the composition of the continuum and the concurrence of God’ (GP i 198/L 190). It will be worth saying something here about these two issues too, for they also continued to dominate Leibniz's thinking into his maturity. They are, as Leibniz describes them in the preface to his Theodicy of 1710, ‘the two famous labyrinths in which our reason very often loses its way’ (GP vi 29/T 53). The ‘concurrence of God’ concerns the issue of the compatibility of human freedom with divine foreknowledge of human actions. It is the ‘great question of freedom and necessity, above all in the production and origin of evil’ that is the topic of the Theodicy itself. In the preface to that work he writes:
Even if God did not concur in evil actions, one would still find difficulty in the fact that He foresees and permits them, despite His being able to prevent them through His omnipotence. That is why some philosophers and even some theologians have preferred to deny Him detailed knowledge of things, above all of future events, rather than admit something that they believed clashed with His goodness. The Socinians and Conrad Vorst incline toward this opinion. … They are without doubt very much mistaken. (34/58)
But equally mistaken, Leibniz continues, are those who fall into the opposite extreme associated with the great Islamic philosopher Averroës (Ibn Rush'd, 1126–98) and his followers, namely that of believing that God is responsible for all the human actions He determines, thus compromising divine goodness. In keeping with his aversion to extremes, Leibniz follows Suárez in trying to delineate a middle way between these poles, to explain how it is that ‘God concurs in all the actions of His creatures … without being the author of sin’ (37/61). Leibniz's distinctive solution, as we shall see, depends on his articulation of the notion of uncreated possible worlds, whole worlds of individuals each of whose existence is compatible with the others', but which God chooses not to create. For given His goodness and omnipotence, God is bound to create the best of all these possible worlds. He foresees all the consequences of all the actions of humans in such a world, including free ones, and chooses to create the world in which goodness is maximized.
The other labyrinth ‘consists in the discussion of continuity and the indivisibles that appear to be elements in it, which necessarily involves consideration of the infinite’ (29/53). Here Leibniz has in mind a cluster of problems that was exercising his contemporaries: if matter is continuously extended as the Cartesians claimed, then it appears to be just parts within parts, with no smallest units out of which it could be composed; but then, so critics objected, it cannot be a true unity, or even a collection of such, and therefore cannot be substantial. Similarly, if motion consists in the tendency of each body to continue moving at an instant, then a body's motion over time should consist in an infinite sum of such instantaneous tendencies. But no matter whether these tendencies are considered finite, zero or infinitely small in magnitude, this leads to contradiction, and one can say the same about the composition of matter from indivisibles. Leibniz devoted his considerable talents to this cluster of problems throughout his career, making contributions to the understanding of the infinite and the infinitely small that very few other thinkers have matched. Also, as we shall see below, it was as a solution to the above difficulties of the continuum that his theory of substance was largely designed. But he never managed to find the time to write a treatise on this second labyrinth, and as late as 1710 we find him still hoping to find the opportunity to give a full account of his solution to this labyrinth by pointing out how the insurmountable difficulties result from ‘a lack of a true conception of the nature of substance and matter’ (29/53).
As we shall also see, guiding Leibniz in his devising of solutions to these three problems is a very intimate knowledge of traditional views on substance that he learned from his immersion in the Scholastic literature, not only the works of Suárez and other Iberian scholars like Pedro de Fonseca (1528–99), but especially the tomes of now forgotten authors like Julius Caesar Scaliger (1484–1558) and Jacopo Zabarella (1533–89), whose interpretation of Aristotle had greatly influenced the Lutheran scholars whom the young Leibniz was lapping up.
Leibniz's Early Career
Despite his obvious talent for philosophy, however, Leibniz chose not to become a professor like his father. How much this had to do with his being snubbed by the University of Leipzig after his habilitation in the faculty of philosophy in 1666 is not clear. But by then he had in any case opted for a career in law rather than philosophy. After enrolling in summer school at the University of Jena in 1663 to hear the mathematical lectures of Erhard Weigel, by February 1664 Leibniz had obtained a master's degree in philosophy, with his thesis An Essay of Collected Philosophical Problems of Right – although any feeling of satisfaction at this achievement would have been crushed by the loss of his mother to a respiratory infection nine days later. In short order he then earned a bachelor's degree in law at Leipzig in 1665, on the topic of conditional judgements in law, and for his habilitation in 1666 submitted a thesis, Dissertation on the Combinatorial Art, which was in many ways definitive for Leibniz's whole subsequent vision of how to do philosophy, as we will see in chapter 2. (Indeed, it was well enough regarded that it was republished in 1690 without his permission.) To complete his qualifications for a position in the faculty of law at Leipzig, he now needed a licence and a doctorate in law, so he duly applied for admission to the law faculty.
