Leibniz

Richard T.W. Arthur

• Publisher: Polity
• Year: 2014
• Print ISBN: 9780745653754, 9780745653747
• eBook ISBN: 9780745686370
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

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.

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 an...

Table of contents

• Cover
• Classic Thinkers
• Title page
• Copyright page
• Acknowledgements
• Note on the Text and Translations
• Abbreviations
• Chronological Sketch
• 1: Introduction
• 2: Logic, Language and the Encyclopaedia Project
• 3: Natural Philosophy and the Science of Life
• 4: Mathematical Philosophy
• 5: The Reform of Metaphysics
• 6: Dynamics: The Physics and Metaphysics of Action
• 7: The Philosophy of Space and Time
• 8: Morals and Politics
• 9: Leibnizian Posterity
• Select Bibliography
• Index