Maria Rosa Antognazza's Leibniz: An Intellectual Biography is the first full-length biography of Leibniz to appear since Eric J. Aiton's of 1985.Footnote ¹ It is the third book in English to appear from this author, following Leibniz on the Trinity and the Incarnation,Footnote ² and the co-authored study (with Howard Hotson) Alsted and Leibniz.Footnote ³ It joins a set of other intellectual biographies in this series (on Descartes, Locke, Kant, Habermas, Kierkegaard, Comte) from Cambridge University Press, and it is a remarkable work of synthesis and analysis, historically detailed and assembled with care and precision. Where Aiton, a historian of science, focused on Leibniz's scientific career and mathematical work, Antognazza aims for a balanced account, placing special emphasis, however, on the theological side of Leibniz's life and its role in his philosophical endeavours. She traces his career from his childhood in Leipzig, the centre of a thriving academic culture and book trade, through his years as an attaché to the Elector of Mainz, then as “librarian, historian and mining engineer” to successive Dukes of Brunswick, to his last years and the demoralizing battles with the Newtonians. She provides extensive information about his education, travels and audiences; his many correspondents; his somewhat fewer personal friends; and the circumstances of his major and minor writings. There is an extensive bibliography of primary and secondary sources, including full details of every text of Leibniz published in his lifetime or afterwards.

To readers who know Leibniz (1646–1716) only as a metaphysician, as the discoverer of the windowless monads and the pre-established harmony, his taste for theological controversy and political manoeuvring, and the quantity and in some cases quality of his work in the applied sciences will come as a surprise. Antognazza's claim is that the three spheres of Leibniz's activity—the pure theory of the metaphysics of the supersensible and mathematics; the practical sciences of chemistry, medicine and engineering; and the sociopolitical problems of church and state—were components of a single effort to perfect the world through the unification of the churches, the establishment of political peace and a rational and efficient legal system, and the development of the mechanical arts and knowledge of nature and numbers.

Antognazza characterizes Leibniz as a man of “synthesis and reconciliation” (5), as an opponent of sects and schisms who could see the good in all theologies, and the sense in all extant systems of philosophy, including the nature-philosophy and ethics of the Chinese. His self-chosen sobriquet “Wilhelmus Pacidius” reflects his remarkable lack of irritability. While Spinozism was arguably his philosophical bête noire, Antognazza maintains, somewhat controversially, that he “genuinely admired the learning and sharpness of Spinoza's thought and would continue to respect him as a person even as he disagreed with him as a philosopher” (168). She further portrays Leibniz as a worshipful humanitarian whose goal is “the improvement of the human condition and thereby the celebration of the glory of God in His creation” (5). She stresses the unity of his thought and its dependence on a few basic principles; the early coalescence of his aims and ideals; and their sources in the German Ramist pedagogy of Alsted, Comenius, Keckermann and Bisterfeld.

Good biographies can do two things. They place their subject in response mode, encountering their parents, teachers, books, ideas, demands, friends, enemies, obstacles and opportunities, and deciding, acting and writing in certain ways as a result of those encounters. While advancing age brings with it more control and less susceptibility, people remain beneficiaries and victims of chance meetings throughout adult life. At the same time, good biographers depict their subjects as active in self-fashioning, as choosing their influences, and as doing so in light of what Bernard Williams used to call “ground projects.”Footnote ⁴ Antognazza delivers both a sense of contingency and a sense of necessity driven by an internalized project. She fills in the sketch of Mueller and Kroenert's day-to-day account of Leibniz's activities,Footnote ⁵ and shows the reader the acts and encounters, the series of small triumphs, as Leibniz transforms himself from a provincial German-speaking nobody into a celebrated mathematician and physicist, and also the emotions—disappointment, grief—attached to his setbacks. Whether she correctly identifies the ground project is a large question, to be explored in some detail below.

One important contingency in Leibniz's case was the large library left by his father, a Lutheran professor of moral philosophy at the University of Leipzig “who based his teaching on the Nichomachean Ethics of Aristotle and saw a struggle between the ‘Christian philosophy’ and the ‘Diabolic philosophy’ led by Apollo (alias Lucifer).” The father recognized his son's precocity, read aloud to him and instilled in him a love of history, but died when Leibniz was six years old. While Leibniz's mother and half-brother by one of his father's previous marriages were pious, comparatively intolerant and not intellectual, and while his first teachers disapproved of his reading, a “nobleman of the neighbourhood” persuaded Leibniz's mother to unlock the library, and, with no adults to interfere, the eight-year-old discovered the world of books, including unbound material (one wonders if Diabolic philosophy was mixed in with it) as well as history, jurisprudence, philosophy and theology.

Aristotelian physics and logic, a smattering of Plato and the “moderns” Hobbes and Gassendi, who advocated different forms of materialism derived from the ancient atomists, as well as scores of other ancient and Renaissance authors, rounded out this reading, and by 1669, when Leibniz was in his early twenties, he was also familiar with the Elements of Euclid and the physics of Huygens and Galileo. After leaving the Universities of Jena, where he studied briefly; Leipzig, where he narrowly failed to earn a doctorate in law on account of the machinations of jealous older students; and Altdorf, where he succeeded, he became the secretary of a secret Nuremberg alchemical society, then an adviser to the Catholic convert Baron Johann Christian von Boineburg in Mainz, a post that enabled him to make scientific contacts and connections with the Royal Society and with Hobbes in England and also with French mathematicians and philosophers. In this period, Leibniz appeared to be working on a number of levels, on the one hand attempting to construct a synthetic metaphysics in which the concept of “substance” could satisfy the interpretations of the Eucharist of Catholics and Protestants alike, thereby pleasing his employer and calming theological tensions, and on the other trying to bring his interest in the mechanical philosophy and mathematical analysis of the “moderns” into alignment with what was to be his lifelong emotional preference for the dynamic natural philosophy of Aristotle and idealism of Plato. His falling in with the best mathematicians of his time in Paris in 1672 and discovering his own aptitude for mathematics and mathematical physics was another important contingency, as were his early encounters with the metaphysics of Spinoza through Spinoza's confidant, Walter Tschirnhaus, which aroused as well as frightened him. The characteristics that make Leibniz so different from Descartes and Spinoza, his fellow “rationalists”—his wide erudition and reconciling ambitions, his embrace of mechanism coupled with his rejection of material substance, and his belief in a value-laden universe—are very plausibly explained by these early encounters.

At the same time, Antognazza shows us the steadiness and persistence of Leibniz's concern for improvement, specifically improvement through invention and reformation: his desire at one time or another to repair the schism of the churches with a universal religion, to devise a perfect language that would end all merely verbal disputes, to reform the constitution of the Holy Roman Empire, to reorganize the legal system, and to introduce state-supported schools and vocational training to reduce poverty (196). His endeavours of the 1680s included plans for a new health system with trained, publicly funded physicians, pharmacies, published dietary recommendations and the careful recording of statistics on causes of mortality. Of particular note was his application of the methods of probability—only recently understood as relevant to more than games of chance—to serious purposes in the provision of life insurance, pensions and annuities for spreading risk and providing security (217). The list of his projects is almost interminable: the mining machines, the silkworm farm, the academy of arts and sciences (part technology museum and part circus), the mineral dye factory, the Viennese oil streetlamp project.

These sections of the book raise interesting questions about patronage and public-spiritedness, and the manner in which a seventeenth-century intellectual managed to balance or tried to balance the free exercise and perfecting of his own thinking with the need to earn a living and to satisfy an employer's demands. The depth of Leibniz's concern with public welfare as depicted by Antognazza was not shared by his most famous contemporaries. Descartes and Locke had much narrower concerns, and even Hobbes and Spinoza, for all their interests in civic peace and the elimination of religious conflict, did not devote themselves to the cause of the widow and the orphan or the development of industrial processes. Not until the late eighteenth century does this degree of public-spiritedness seem to resurface, and this raises a puzzle; for it is usual to think of welfarism as part and parcel of later secularization movements. Seventeenth-century philosophers seem more concerned with individual reform and salvation—even “secular salvation”Footnote ⁶—than with improving living conditions or devising annuities for the elderly in this vale of tears.

The cognitive dissonance between curiosity and faith, between the mundane and eternity, tormented the devout Pascal (the designer of the first omnibus service for Paris).Footnote ⁷ Leibniz experienced no such conflict, according to Antognazza. Indeed, her position is that Leibniz's projects are intrinsically related to his worshipful impulses, which are directed to a personal God and the support of the Christian religion, reflecting the local context and Lutheran atmosphere in which his character was formed. To the majority of Leibniz's contemporaries in central Europe, she maintains, the purpose of philosophy “was not to pursue [it] as a purely theoretical exercise, withdrawn from the world in splendid isolation; not . . . to use the new philosophies to sweep aside the intellectual rubbish accumulated over the centuries, as Bacon and Descartes had proposed” (23). Rather, the new science “might be used to reform, harmonise, bolster, and defend all that was best in the old theological, ecclesiastical and political order.”

Leibniz's zeal for improvement and reform implies that he faced a world that appeared to him rife with poverty, sickness, end-of-life misery, bad education, unemployment and warfare, disorganized in its legal system and constitutionally defective. Metaphysicians must either avert their gazes from this spectacle, or rationalize it, or immerse themselves in another fantasy world, and ever since Voltaire's Candide it has been standard to ridicule Leibniz's famous doctrine that the world is the best of all possible worlds and constantly improving too. But actually Leibniz does not pay much attention to earthquakes, hailstorms, birth defects and other natural evils supposed to present a problem for theists, though he does worry about sin. His writings on the theodicy question—how belief in the perfect justice and goodness of an omnipotent God can be maintained in light of experience—are in some respects similar to Malebranche's in appealing to the universality, simplicity and fruitfulness of the laws of nature, as laid down by God, in a way consistent with his perfection, as the unavoidable cause of all human troubles. But his real appeal in this connection from very early on, as Antognazza shows (145), is to the notions of plenitude and compossibility; the universe contains the maximal set of entities that can coexist with one another, and because existence is good as such (as the ontological argument requires) the set of all that is is the most perfect that can be. This conclusion would have led to Spinozism—the identification of the world with God—if Leibniz had not insisted that God is a distinct supramundane entity who either continuously creates the world by bringing its entities or “substances” from a state of potentiality to a state of actuality in a series of pulses, or creates it once for all and never intervenes thereafter. One might add that his view that the human world, including the natural world under human cultivation, is constantly improving, its potential perfection gradually coming into actuality, is not a theologically standard view, insofar as it suggests that human effort is the source of such perfection as is not already realized in the universe and that perfection in the immanent realm of human activity is attainable. This opinion won Leibniz credit in the minds of eighteenth-century reformers, including Lessing, Kant, and Herder, and he deserves credit for challenging the Protestant traditions of inherent sinfulness (which he regards on the model of inertia rather than on the model of a festering canker) and special election; indeed, his suggestion that in the fullness of time even the sinners in hell might be released created a later stir.

Leibniz's mathematics, developed in the early 1670s, are briefly but capably explained (155–63), as is the controversy with Newton and the Newtonians over the calculus that caused him such trouble forty years later. His general metaphysics are introduced midway through the book. Antognazza appears to subscribe to the view that, after some philosophical floundering, Leibniz's ontology was essentially in place by 1684 in his Discourse on Metaphysics (349), though she believes that some details were added in his blitz of publications in the 1690s, including the Specimen Dynamicum (1695), the articles written for the Berlin Acta Eruditorum and the Système nouveau de la nature et de la communication des substances for the Paris Journal des savants. A final polishing occurred in the much later Monadology and Principles of Nature and Grace. Although she avoids taking a position on the unity or disunity of Leibniz's underlying metaphysical scheme, she implicitly allies herself with Brown, who sees the monadology as prefigured in Leibniz's earliest meditations, and with Sleigh and Mercer.Footnote ⁸ By contrast, Garber has taken a developmental stance, arguing most recently that Leibniz began with a Hobbesian corpuscularian theory and ended with a rarefied form of idealism,Footnote ⁹ while Hartz and I have argued that Leibniz's dissatisfaction with the corporeal Epicurean atom and the purely mechanical universe led him to vacillate between an organic vitalism of “corporeal substances” and a more obscure theory of mind-like incorporeal atoms as the ground of appearances.Footnote ¹⁰ For a biographer, the refusal to take sides is sensible, pending a solution of the possibly interminable debate over Leibniz's “final system.”

In any event, according to Leibniz, “real unities”—the true “atoms of nature,” or “substances,” later “monads”—must lack parts, so as to be indestructible. At various times, these real unities were identified with persons, with embodied living animals of infinite complexity, and with unextended minds. The “matter” composing rocks, tables and so on is solid, lifeless and inert in appearance only, teeming with life and mind. Because they were as impenetrable as the traditional solid atom, all the changes that these incorporeal atoms or living animals experienced had to flow, Leibniz thought, from their internal natures and had to be completely determined from the moment of their creation. The forces treated by physics were “echoes” of a primitive force of appetition, and the empirical phenomenon of embryonic development furnished a model for the unfolding of the potential of an individual substance. Substances accordingly did not interact or communicate but harmoniously “mirrored” or conformed to the changes in one another in a way established at their creation.

The late texts laying out these doctrines are rightly described as “masterpieces amongst the classic texts of philosophy . . . [which] established Leibniz as the author of a strikingly innovative and beautifully economical metaphysics” (501). How the two levels of force, metaphysical and phenomenal, actually work, and how the incorporeal atoms or monads form or appear as animated, percipient organic bodies of infinite complexity ranging in size from the infinitesimally small to the size of large mammals (which might, of course, be much larger on the unexplored planets) is a problem that has given rise to many arguments over and dissertations on the rational reconstruction of Leibniz's ontology, arguments which Antognazza, as noted, wisely avoids going too far into.

There is good reason not to be overinvested in the question of Leibniz's real “system,” bearing down on it harder than this construction can bear. While he had excellent reasons to doubt that the solid, hard, massy atom surrounded by void was the basic building block of the universe—reasons that were pursued in later attempts by physicists to replace such atoms with force fields or to insist on their ideal or observer-relative character—he seems to have recognized that there was much left unexplained in his monadology. Paul Veyne asked whether the Greeks believed in their myths,Footnote ¹¹ and one sometimes wonders whether Leibniz believed in his system and was confident that he understood its precise details and ramifications himself. In the letter to the Lutheran theologian Christian Matthäus Pfaff of 1715 which Antognazza quotes as an example of deflationary playfulness, Leibniz remarks that “it is not for philosophers always to take things seriously. In framing hypotheses, as you rightly point out, they try out the force of their mental talents” (484). Yet his metaphysics did seem to have a place in his overall project for the betterment of everything. He seems to have feared that the penetration of Cartesianism and Spinozism in preference to his own new system would have morally unfortunate effects. His own view that all the future acts and experiences of a substance pre-exist in it did not seem fatalistic to him, insofar as the individual was not buffeted about or directed by any forces external to it and was the sole logical author of its own acts. Where both Descartes and Spinoza had been purposely vague about the immortality of the soul in the usual sense of the survival or resurrection of an embodied personality after death, Leibniz insisted that any living organism was physiologically immortal and that death was only a longish sleep and reconfiguration of the body into a smaller format that might one day expand and bestir itself again. On this view, all creatures persist forever, accumulating pleasures and pains, joys and woes, and cosmic justice can be secured within this infinitely long narrative.

Antognazza is surely right to emphasize Leibniz's habit of explaining to prospective patrons “how his programme as a whole [is] intended, as ever, to celebrate God's glory through the improvement of the human condition, though which the advancement of the sciences [is] the key instrument” (470). She cites his application for support for a scientific academy in his Letter to Peter the Great of 1712, in which Leibniz declares that although it is his advice on politics and the judiciary that is usually sought out, he regards the arts and sciences as the “higher calling” because “the sciences and the knowledge of nature and art, the wonders of God, his power, wisdom and goodness are especially manifest.” But when Leibniz declared as a twenty-seven-year-old that he had set jurisprudence and controversies behind him, having discovered the fascinations of mathematics and physics, was he really doing so because the new scientific and mathematical studies were intended to pave the way for a renewed advance on the Catholic Demonstrations, as Antognazza maintains (140)? Was it not the case that the young Leibniz became obsessed by mathematics—as happens in those who discover in themselves a flair for it—and needed to rationalize this obsession to himself and his employer by finding cosmic significance in a personal enthusiasm? I agree that “it was with Christian theology in mind that the young Leibniz eagerly worked to develop the ‘true notions’ of substance, mind, and body” (100). But it is far from clear that he drew the anti-Cartesian conclusion that body is not a substance and that the “substantial forms” of the Scholastics that he proposed to rehabilitate were invoked only or chiefly in order to save the incarnation and transubstantiation (104–5), rather than being turned to that use (cf. 119–20).

Leibniz grappled with the Christian mysteries: the Trinity, the Incarnation, the General Resurrection, and Eucharist, writing small tracts on these subjects between 1669 and 1690, and promising his patrons (234) to explain them thoroughly through his metaphysics. But except where the immortality of the soul was concerned, he did not provide much explanation, and it is difficult to see how his theory of self-propelled individual substances could really have been applied to the Trinity or the Eucharist. Despite Antognazza's repeated emphasis on Leibniz's desire to uphold the truths of revealed, as opposed to natural, religion, one suspects that the relationship between his metaphysics and natural religion was of more intimate concern to him, and that the promise of applied metaphysics was really intended to justify his philosophical researches—researches prompted by his interest in the history of philosophy and the ontologies of the ancient pagans and the modern innovators in physics. His general approach was not, as it turns out, detailed metaphysical explanation, but, as Antognazza says, the appeal to a distinction between faith and reason. “Mysteries are above human reason but cannot be against reason . . . As long as no contradiction has been positively proven, mysteries which have been proclaimed by the age-old tradition of the universal church as divine revelation can legitimately be held to be true” (259).

Essentially, there were three positions one could take on the Christian mysteries: that they were rationally explicable and ought to be believed; that they were rationally inexplicable yet ought to be believed, and that they were rationally inexplicable and ought to be rejected, with the ethical message of Christianity retained but its mythic elements discarded. Titles like Locke's The Reasonableness of Christianity (1695) and Toland's Christianity Not Mysterious (1696) suggest the first option, but are arguably directed to the defense of the third. Antognazza perhaps minimizes the unease associated with the position that the mysteries do not present any problem for reason as registered by late aseventeenth-century philosophers with their strenuous attention to questions of methodology and epistemological rigour. Leibniz's professed disapproval of Toland as a freethinker and of Locke as an advocate of “thinking matter” might seem to make his adherence to the second position unambiguous, and it is the one he adopts in his Theodicy of 1710—the only book published in his lifetime. Robert Boyle does the same in his Discourse of Things above Reason of 1681. But Boyle, as an experimental philosopher committed to Royal Society epistemological standards, was anything but complacent about this solution, and being an emotional person who needed no patron, he confessed his theological anxieties freely in writing. Leibniz never betrays the slightest anguish, but the notion of truth as whatever is delivered by age-old tradition seems very different from his explicit notion of truth as a property of propositions whose predicates are contained in their subjects. The discrepancy raises the old debate about the “exoteric” and “esoteric” aspects of Leibniz's philosophy. Why did Leibniz worry so much about the reactions of the theologians to his writings (482–3) if his philosophy was devoted either to the explanation of the mysteries or to the conformity of faith and reason? Was his monadological system not in fact an attempt to construct and present an ethical-political view of the cosmos, free of mystery, as an alternative to Descartes's value-neutral cosmos and his neo-Stoicism and to Spinoza's fully secularized and also basically Stoic ethics and democratic politics? Ian Hunter's political interpretation of Leibniz's hierarchical and retributivist metaphysics has a particularly convincing ring in this regard.Footnote ¹²

Behind the transcendental language of the late letter to Peter the Great, there is the reality of situation and character. Leibniz seems tired of legal wrangling, personalities and power, and the whole unstable, chaotic mess of Europe, and academic politics too, and to be feeling again the pull of engagement with nature itself. Nature, one imagines him thinking, unlike the social world, is ruled by a system of laws. The investigation of nature enables the individual to maintain control over his efforts and to create things that demonstrably do some good. The appeal to the glory of God in this context seems to convey both Leibniz's sense of fatigue with the political world and the supramundane appeal of scientific enquiry itself. Such a reading of Leibniz's theological references might fit better with Antognazza's recognition that Leibniz's religious beliefs evolved from a direct concern with Christian dogma to a form of deism with exceedingly modest theological requirements, though he remained anxious about the effects of widespread adoption of a rational, minimal, purified religion and refused to follow the Dutch–English trend towards legal and social toleration of theological diversity.

Leibniz had a talent for striking up correspondences, especially, despite his own unorthodoxies, amongst clerics, including Malebranche, de Volder and des Bosses, though he notoriously failed to ingratiate himself with the Jansenist Antoine Arnauld, or for that matter with Hobbes, Spinoza or Locke, though not for lack of trying. As a person, he comes across most engagingly in Antognazza's account of his relations with the two Sophies, the somewhat older Sophie von der Pfalz (1630–1714), the sister of Descartes's friend and intellectual correspondent the Princess Elizabeth, who became the Duchess of Hanover, and her daughter the much younger Sophie Charlotte (1668–1705), who became queen of Prussia. Leibniz conversed with and wrote to both women about metaphysics and natural philosophy, as well as politics and gossip, and the sudden death of Sophie Charlotte sent him into a state of shock and grief and uncharacteristic quiescence for six months. “I do not weep, I do not complain,” he wrote to a confidante, “but I do not know where I am. The loss of the queen seems like a dream, but when I awake from my slumber I find it only too real” (437). The duchess survived her daughter by many years but her death as well was a blow when it came in his own last years and in the midst of political wrangling over the Hanoverian succession in England.

Leibniz: An Intellectual Biography excels in its treatment of the theological context of Leibniz's writings and his personal and intellectual relations with patrons, correspondents, and antagonists, such as the Newtonians who plagued his last years with false accusations regarding the invention of the calculus. It is essential reading, not only for everyone wanting the full overview of Leibniz's achievements, but for historians interested in the relations between politics, philosophy and religion in the second half of the seventeenth century. It very effectively dismantles the popular image of Leibniz as a Panglossian wishful thinker and the inventor of a mad metaphysics of tiny twinkling mirrors, and it testifies to the significant differences in the way in which the historiography of philosophy is written in Great Britain from a generation ago, when the extraction and criticism of philosophical arguments or the rational reconstruction of a system in as close to axiomatic terms as possible was the ruling model. Correspondingly, it is not the book to read for a detailed discussion of Leibniz's views on metaphysics and natural science, on the physics of forces, cosmology, the history of nature and the theory of the living organism; nor for an account of the evolution of his theory of substance.

It is in this context, however, that one might consider Leibniz's reconciling aims as really emerging and as highly successful. Looking aside from the defense of the Christian mysteries, Leibniz appears to have been driven—albeit on account of the ethical demands that he thought Christian doctrine supported—to refute materialism and mortalism, and the associated doctrine that good and evil are perceptual qualities relative to observers. The “new system” was a synthesis of Democritean–Cartesian mechanism, Malebranchian occasionalism, Aristotelian dynamism, Platonic anti-materialism, and even Zeno's view that motion is unreal. This fusion even allowed for a mechanical treatment of perception and thought, with the proviso that experience, thought and vitality were at the same time the properties of simple, unextended substances. The system was intended to supersede each of the other major systems of early modern philosophy, whilst preserving the status of the laws of celestial and terrestrial motion, for Leibniz was eager to defend the status of the “mechanical philosophy” as necessary and sufficient for the explanation of particular effects, though not as metaphysically fundamental. His targets included Hobbes's soulless universe of corpuscles in motion and thinking matter; Descartes's mostly soulless universe, in which incorporeal minds operate the limbs of human physical machines made up of such corpuscles and transform impulses into conscious experiences; and Spinoza's single thinking and extended substance. The conviction that matter is mere appearance is common to Plato and the later Platonists, down to Marsilio Ficino and Ralph Cudworth, and Leibniz's early induction into this school of thought in Jena in as a seventeen-year-old, along with his first encounters with Gassendi's atomism and Hobbes's doctrine that thought is just motion, antedates the formation of his unity-of-the-churches vision.Footnote ¹³

We learn from this volume that Leibniz's successes did not match his ambitions. He did not succeed in reconciling the churches through metaphysics, or introducing the key elements of the welfare state, or even in making the Hartz mines profitable. His employer's disapproving letter presents the picture of a distracted man trying to do too much: “He wants to achieve everything, and therefore delights in endless correspondence and shuttling here and there striving to satisfy his insatiable curiosity, but he has either no talent or no inclination to pull anything together and bring it to a close” (490). What comes through clearly is nevertheless a picture of remarkable creativity, the boundless production of new schemes, designs, and templates concocted from available conceptual materials, besides his social and engineering inventions, his innovations in both finite and infinitistic mathematics and in logic. He succeeded in his ambition to found an academy of sciences, the Berlin Academy, and it was in fact in the physical, geophysical, and life sciences that his work arguably had the most impact. Despite his alleged lack of talent or lack of mental discipline, Leibniz's influence—both positive and critical—on eighteenth-century metaphysics, natural history and philosophy of history was undeniable. His arguments against physical atomism were taken seriously by Euler, Châtelet and Kant; his marvellous history of the earth, the Protogaea, by Buffon; his optimism by Lessing and Herder; and his theory of the organism by Bordeu, Bonnet and others.Footnote ¹⁴ It became apparently only in the twentieth century how far he had come in laying the foundations of algebra and set theory in his unpublished writings.

Williams, in his discussion of ground projects, warns against imposing external measurements of success and failure:

Unfortunately, philosophical biography—indeed any biography—would be virtually impossible to write if this sentiment were taken too literally. As preserving one's own personal integrity does not require a blanket refusal to be a means to anyone else's ends, the identification and characterization of A's ground project is impossible in the absence of the identification and description of B's and C's rival and complementary projects, and its success depends to some extent on what becomes of theirs. Antognazza's narrative—even if she touches only lightly on some of the most important of those under way in Leibniz's period—makes this dependency clear, showing how Leibniz's delicate diplomacy and the strangely beautiful metaphysical imagery of mirrors, tranquil pools and infinitely complex organic machines were linked to the world of theological antagonism and smouldering exchanges.