LEIBNIZ AND THE TWO SOPHIES is a critical edition of all of the philosophically important material from the correspondence between the philosopher Gottfried Wilhelm Leibniz (1646-1716) and his two royal patronesses, Electress Sophie of Hanover (1630-1714), and her daughter, Queen Sophie Charlotte of Prussia (1668-1705). In this correspondence, Leibniz expounds in a very accessible way his views on topics such as the nature and operation of the mind, innate knowledge, the afterlife, ethics, and human nature. The correspondence (...) also contains the only known philosophical writings by Sophie and Sophie Charlotte, and thus provides a valuable insight into their views and concerns, as well as throwing light on their characters. The texts are accompanied by a substantial introductory essay which sets the context for the correspondence and analyzes its main philosophical themes. (shrink)

Maimonides’ Latin translation of Moreh Nevukhim | Guide for the Perplexed, was the most influential Jewish work in the last millennia (Di Segni, 2019; Rubio, 2006; Wohlman, 1988, 1995; Kohler, 2017). It marked the beginning of scholasticism, a daughter of Judaism raised by Jewish thinkers, according to historian Heinrich Graetz (Geschichte der Juden, L. 6, Leipzig 1861, p. xii). Printed by Gutenberg's first mechanical press, its influence in the West went as far as the Fifth Lateran Council (1512 — 1517) (...) "where scholars were encouraged to remove the difficulties which seemed to divide the whole of theology and philosophy (Leibniz, Théodicée, 11)." For centuries, the Guide revolutionized the curriculum of school instruction by reintegrating the natural laws of thought in the sphere of faith (the fourth of which became Leibniz’ Principle of sufficient reason). This complete collection of notes expounds the ideas of the Guide and features all the passages selected and rewritten by Leibniz. This first complete annotated bilingual translation of the original manuscripts in Latin serves as an entry point to the faith in conformity with Reason. This complete collection of notes expounds the ideas of the Guide as selected and rewritten by Leibniz, the famous mathematician inventor of computer arithmetic, considered the last universal genius. The first complete bilingual translation in three centuries features on the front cover Rembrandt's Philosopher in meditation, and a recommendation from Leibniz's himself on the back: "Rabbi Maimonides' excellent book, A Guide for the Perplexed, is more philosophical than I imagined and worthy of careful reading." According to Malbim’s translator, Noah Rosenbloom, the book’s epigraph indicates that nineteenth-century Rabbi Leibush ben Yehiel Michel Wisser, also known as Malbim, was familiar with Leibniz’ Theodicy. In Leibniz’ anthology of the Guide, the reader can get a detailed glimpse of Leibniz' impressions of Maimonides. The Foreword by Leibniz' translator Lloyd Strickland suggests that there were sympathies and perhaps even overlaps between the thoughts of both universal luminaries. -/- . (shrink)

This volume contains more than 60 original translations of papers written by the German philosopher Gottfried Wilhelm Leibniz (1646-1716). As well as contributing to Leibniz scholarship, it is intended to function as an introductory text for students.

La traducción al latín de la obra de Maimónides Moreh Nevukhim | Guía para Perplejos, ha sido la obra judía más influyente en los últimos milenios (Di Segni, 2019; Rubio, 2006; Wohlman, 1988, 1995; Kohler, 2017). Ésta marcó el comienzo de la escolástica, «hija del judaísmo nutrida por pensadores judíos, » según el historiador Heinrich Graetz (Geschichte der Juden, L. 6, Leipzig 1861, p. xii). Impresa por la primera imprenta mecánica de Gutenberg, su influencia en Occidente se extendió hasta el (...) Quinto Concilio de Letrán (1512-1517) « donde se instó a los eruditos a eliminar las dificultades que parecían dividir el conjunto de la teología y la filosofía (Leibniz, Teodicea, 11 ). » Durante siglos, la Guía revolucionó el currículo de estudios de la instrucción escolar al reintegrar en el ámbito de la fe las leyes del pensamiento (la cuarta de las cuales se convirtió en el principio de la razón suficiente de Leibniz). La colección completa de las notas que exponen las ideas de la Guía incluye todos los pasajes seleccionados y reescritos por Leibniz. Esta primera traducción bilingüe completa y anotada de los manuscritos originales en latín sirve como una puerta de entrada a la fe conforme a la Razón. -/- « El excelente libro del rabino Moisés Maimónides, Guía para perplejos, es más filosófico de lo que había imaginado y merece una lectura atenta. El autor, distinguido por su inteligencia filosófica, fue versado en matemáticas, en el arte de la medicina, y también en el conocimiento de las Sagradas Escrituras. » — GW LEIBNIZ, 1685. Antología de Leibniz de la Guía de Maimónides, Capítulo III. (shrink)

In this unpublished Latin fragment (which dates from May 1702) G. W. Leibniz criticizes the Cartesian conception of body and force and develops his own notion of matter, extension and his theory of forces. He argues against Descartes and Cartesians that 1) the essence of corporal bodies cannot be reduced to extension alone but the latter arise from the primitive force itself, 2) consequently Cartesian quantity of motion falls short to account the motive force of a moving body since (...) the true nature of physical bodies which can only be understood through a careful analysis of dynamical forces. -/- Mayıs 1702’de kaleme aldığı ve ölümünden sonra yayımlanan bu Latince fragmanda G. W. Leibniz, Kartezyen felsefenin cisim ve kuvvet anlayışını eleştirir ve kendi madde, uzam ve kuvvetler teorisini geliştirir. Leibniz, Descartes ve Kartezyenlere karşı 1) cisimlerin özünün yalnızca uzama indirgenemeyeceğini, bunun ilksel kuvvetin kendisinden kaynaklandığını, 2) sonuç olarak da Kartezyen hareket miktarının hareket eden bir cismin kuvvetini açıklamakta yetersiz kaldığını, çünkü fiziksel cisimlerin gerçek doğasının ancak dinamik kuvvetlerin dikkatli bir analiziyle anlaşılabileceğini ileri sürer. (shrink)

An English translation of a draft essay by Leibniz from 1715, in which Leibniz argues for the conclusion: "if humanity endured long enough in its current state, a time would arrive when the same life of individuals would return, bit by bit, through the very same circumstances. I myself, for example, would be living in a city called Hannover located on the Leine river, occupied with the history of Brunswick, and writing letters to the same friends with the (...) same meaning.". (shrink)

La traduction latine du livre de Maïmonide Moreh Nevukhim | Guide des égarés, a été l'ouvrage juif le plus influent des derniers millénaires (Di Segni, 2019 ; Rubio, 2006 ; Wohlman, 1988, 1995 ; Kohler, 2017). Elle marqua le début de la scolastique, fille du judaïsme élevée par des penseurs juifs, selon l'historien Heinrich Graetz (Geschichte der Juden, L. 6, Leipzig 1861, p. xii). Imprimée par la première presse mécanique de Gutenberg, son influence en Occident s'étendit jusqu'au Vème concile du (...) Latran (1512-1517) « où les savants furent encouragés à lever les difficultés qui semblaient diviser l'ensemble de la théologie et de la philosophie — (Leibniz, Théodicée, 11 ) ». Pendant des siècles, le Guide a révolutionné le programme d'instruction scolaire en réintégrant dans le domaine de la foi les lois de la pensée (dont la quatrième est devenue le principe de la raison suffisante de Leibniz). Cette collection complète de notes qui expose les idées du Guide fournit tous les passages sélectionnés et réécrits par Leibniz. Cette première traduction complète bilingue annotée des manuscrits originaux en latin sert de porte d'entrée à la foi conforme à la Raison. -/- « L'excellent livre du Rabbin Moïse Maïmonide, le Guide des égarés, est plus philosophique que je ne l'avais imaginé et mérite une lecture attentive. L'auteur, distingué par son intelligence en philosophie, était versé dans les mathématiques, l'art médical, et aussi dans la connaissance de Saintes Écritures. » — G. W. LEIBNIZ, 1685, Anthologie de Leibniz du Guide de Maïmonide, Chapitre III. (shrink)

An English translation of Leibniz's fragment "Horizon rerum humanarum... " in which he announces a plan to demonstrate "that the number of truths or falsehoods enunciable by humans as they are now is limited; and also that if the present condition of humanity persisted long enough, it would happen that the greatest part of what they would communicate in words, whether by talking or writing, would have to coincide with what others have already communicated in the past; and moreover (...) that new humans would lead an entire life that appears thoroughly the same to the senses as lives that others have already led." . (shrink)

Leibniz claims that for every possible substance S there is an individual concept that includes predicates describing everything that will ever happen to S, if S existed. Many commentators have thought that this leads Leibniz to think that all properties are had essentially, and thus that it is not metaphysically possible for substances to be otherwise than the way their individual concept has them as being. I argue against this common way of reading Leibniz’s views on the (...) metaphysics of modality. I develop a model in which individual concepts are innocent; that is, individual concepts are divine ideas that permit God to know everything that will ever happen to all possible substances, if created, but these individual concepts neither require that all properties are had essentially nor require that it is metaphysically necessary for substances to be the way their individual concepts have them as being. (shrink)

Leibniz’s mechanistic reduction of colors and other sensible qualities commits him to two theses about our knowledge of those qualities: first, that we can acquire ideas of sensible qualities apart from any direct acquaintance with the qualities themselves; second, that we can acquire distinct (i.e., non-confused) ideas of such qualities through the development of physical-theoretical accounts. According to some commentators, however, Leibniz frequently denies both claims. His views on the subject are muddled and incoherent, they say, both because (...) he is ambivalent about the nature of sensible qualities, and because he gets confused about confusion, losing sight of his own distinction between the confusion proper to perceptions and that proper to ideas. In opposition to this, I argue that the critics have misunderstood Leibniz’s views, which are both consistent over time and coherent. The key to understanding his position is to appreciate what he characterizes as a kind of redundancy in our ideas of sensible qualities, a crucial feature of his view overlooked by the critics. (shrink)

In this paper I argue that Leibniz's ethics is a kind of virtue ethics where virtues of the agent are explanatorily primary. I first examine how Leibniz obtained his conception of justice as a kind of love in an early text, Elements of Natural Law. I show that in this text Leibniz's goal was to find a satisfactory definition of justice that could reconcile egoism with altruism, and that this was achieved through the Aristotelian virtue of friendship (...) where friends treat each other as “other selves.” Following this decisive moment, Leibniz adopted an Aristotle‐inspired ethical framework where the virtuous agent is central for moral evaluations. I then show that, despite certain developments, Leibniz's ethics retained this essential feature throughout his career. In Leibniz's later writings, God constitutes the foundation of the moral realm, and the fundamental moral endeavor of human beings consists in the imitation of God. (shrink)

A fresh translation and in-depth commentary of Leibniz's seminal text, the Monadology. -/- Written in 1714, the Monadology is widely considered to be the classic statement of Leibniz's mature philosophy. In the space of 90 numbered paragraphs, totalling little more than 6000 words, Leibniz outlines - and argues for - the core features of his philosophical system. Although rightly regarded as a masterpiece, it is also a very condensed work that generations of students have struggled to understand. (...) -/- Lloyd Strickland presents a new translation of the Monadology, alongside key parts of the Theodicy, and an in-depth, section-by-section commentary that explains in detail not just what Leibniz is saying in the text but also why he says it. The sharp focus on the various arguments and other justifications Leibniz puts forward makes possible a deeper and more sympathetic understanding of his doctrines. (shrink)

Drawing on remarks scattered through his writings, I argue that Leibniz has a highly distinctive and interesting theory of color. The central feature of the theory is the way in which it combines a nuanced subjectivism about color with a reductive approach of a sort usually associated with objectivist theories of color. After reconstructing Leibniz's theory and calling attention to some of its most notable attractions, I turn to the apparent incompatibility of its subjective and reductive components. I (...) argue that this apparent tension vanishes in light of his rejection of a widely accepted doctrine concerning the nature of bodies and their geometrical qualities. (shrink)

In his essay against Eberhard, Kant denies that there are innate concepts. Several scholars take Kant’s statement at face value. They claim that Kant did not endorse concept innatism, that the categories are not innate concepts, and that Kant’s views on innateness are significantly different from Leibniz’s. This paper takes issue with those claims. It argues that Kant’s views on the origin of the intellectual concepts are remarkably similar to Leibniz’s. Given two widespread notions of innateness, the dispositional (...) notion and the input/output notion, intellectual concepts are innate for Kant no less than for Leibniz. (shrink)

The first collection of Leibniz's key writings on the binary system, newly translated, with many previously unpublished in any language. -/- The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today's digital computing. This book offers the first collection of Leibniz's most important writings on the binary system, all newly translated by (...) the authors with many previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. -/- As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz's original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory “headnote” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz's mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz's development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age. (shrink)

I argue that Leibniz consistently subscribes to the view that phenomena (thus bodies) have their being in perceiving substances. I then argue that this mentalistic conception of phenomenon coheres with three of his doctrines of body: (1) that bodies presuppose the unities or simple substances on which they are founded; (2) that bodies are aggregates of those substances; and (3) that bodies derive or borrow their reality from their simple constituents.

Leibniz's mill argument in 'Monadology' 17 is a well-known but puzzling argument against materialism about the mind. I approach the mill argument by considering other places where Leibniz gave similar arguments, using the same example of the machinery of a mill and reaching the same anti-materialist conclusion. In a 1702 letter to Bayle, Leibniz gave a mill argument that moves from his definition of perception (as the expression of a multitude by a simple) to the anti-materialist conclusion. (...) Soon afterwards, in the Preface to the New Essays, Leibniz gave a different mill argument. That argument depends upon there being no arbitrary and inexplicable connections in nature, because God would not create such things. Later, in the 'Monadology', Leibniz again used the mill example in arguing against materialism. That passage too, I argue, uses an argument from inexplicability rather than from Leibniz's definition of perception. (shrink)

Leibniz has been accused of being ambivalent about the nature of sensible qualities such as color, heat, and sound. According to the critics, he unwittingly vacillates between the view that these qualities are really just complex mechanical qualities of bodies and the competing view that they are something like the perceptions or experiences that confusedly represent these mechanical qualities. Against this, I argue that the evidence for ascribing the first approach to Leibniz is rather strong, whereas the evidence (...) for imputing the second approach to him is rather weak. The first, "mechanistic" approach should therefore be regarded as his considered view. (shrink)

This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646-1716) on various number systems, in particular binary, which he independently invented in the mid-to-late 1670s, and hexadecimal, which he invented in 1679. The chapter begins with the oft-debated question of who may have influenced Leibniz’s invention of binary, though as none of the proposed candidates is plausible I suggest a different hypothesis, that Leibniz initially developed binary notation as a tool to assist his investigations in mathematical (...) problems that were exercising him at the time, namely those concerning the divisibility of composite numbers, primality, and perfect numbers. The chapter then explores Leibniz’s development of binary, his little-known work on binary fractions and expansions, his use of binary as a symbol for creation in his philosophical-theology, and his response to the suggestion that there was a correlation between binary numeration and the hexagrams of the ancient Chinese divinatory text, the Yijing. The chapter then focuses on Leibniz’s work on other number systems, in particular his invention and exploration of hexadecimal as well as his work on duodecimal. The chapter concludes by revealing a hitherto unknown practical application of binary that Leibniz devised in the last year of his life. (shrink)

Leibniz claims that God acts in the best possible way, and that this includes creating exactly one world. But worlds are aggregates, and aggregates have a low degree of reality or metaphysical perfection, perhaps none at all. This is Leibniz’s tendency toward acosmism, or the view that there this no such thing as creation-as-a-whole. Many interpreters reconcile Leibniz’s acosmist tendency with the high value of worlds by proposing that God sums the value of each substance created, so (...) that the best world is just the world with the most substances. I call this way of determining the value of a world the Additive Theory of Value (ATV), and argue that it leads to the current and insoluble form of the problem of incompossibility. To avoid the problem, I read “possible worlds” in “God chooses the best of all possible worlds” as referring to God’s ideas of worlds. These ideas, though built up from essences, are themselves unities and so well suited to be the value bearers that Leibniz’s theodicy requires. They have their own value, thanks to their unity, and that unity is not preserved when more essences are added. (shrink)

According to intellectualists, the will is a rational inclination towards apprehended goodness. This conception of the will makes its acts intelligible: they are explained by (i) the nature of the will as a rational inclination, and (ii) the judgement of the intellect that moves the will. From this it follows that it is impossible for an agent to will evil as such or for its own sake. In explaining wrongdoing intellectualists cite cognitive error or the disruptive influences of the passions; (...) these considerations, however, seem involuntary and at least partly exculpatory. The intellectualist needs an account that renders wrongful actions intelligible without undermining their status as responsible. I argue that Leibniz has the theoretical tools to provide at least part of an answer to this problem. In sum, an agent is directly responsible for her wrongdoing if the cognitive error or the disruptive influence of the passions that help explain this wrongdoing do not completely undermine her acting freely; an agent is indirectly responsible for her wrongdoing if she is directly responsible for previous actions which partly resulted in her wrongdoing, even if the presence of cognitive error or disruptive influence of the passions completely undermines her acting freely. (shrink)

Leibniz's World-Apart Doctrine states that every created substance is independent of everything except God. Commentators have connected the independence of substance asserted by World-Apart to a variety of important aspects of Leibniz's modal metaphysics, including his theory of compossibility and his notion of a possible world (including what possible worlds there are). But what sort of independence is at stake in World-Apart? I argue that there is not a single sense of "independence" at stake, but at least three: (...) what I call "causal", "phenomenal", and "ontological" independence. Further, I distinguish two versions of each type of independence: what I call "basic" and "strict" versions. I argue that only basic versions can be legitimately attributed to Leibniz. In light of this result, I conclude, pace previous commentators, that World-Apart has little impact on Leibniz's modal metaphysics. (shrink)

Leibniz has long faced a challenge about the coherence of the distinction between necessary and contingent truths in his philosophy. In this paper, I propose and examine a new way to save genuine contingency within a Leibnizian framework. I conclude that it succeeds in formally solving the problem, but at unbearable cost. I present Leibniz’s challenge by considering God’s choice of the best possible world (Sect. 2). God necessarily exists and necessarily chooses to actualise the best possible world. (...) The actual world therefore could not be different, for if it were different it would be a distinct and inferior world and hence would not be created. In Sect. 3 I defend Leibniz from this challenge. I argue that while it is necessary for God to choose to create the best possible world, it is not necessary for any world to be the best possible. This is because the criterion for judging perfection can itself be contingent. Different criteria will judge different worlds as the best. Thus it is necessary for God to create the best, but not necessary which is the best. Distinguishing between possible worlds in Leibniz’s sense and in the modern sense allows a fuller exposition of this position. There are worries that can arise with the claim that the criterion of perfection is contingent. I consider two of the most pressing (Sect. 4). The first argues that the criterion is in God’s understanding and hence is necessary; the second alleges that a contingent criterion of perfection violates Leibniz’s cherished Principle of Sufficient Reason. These worries are well-grounded, and examining them reveals a deep incompatibility between this solution and Leibniz’s metaphysical views. I conclude that there is a real solution available, but that it is unacceptable to Leibniz or a Leibnizian. The search for a genuine solution that is genuinely Leibnizian goes on. (shrink)

Leibniz thinks that every created substance is causally active, and yet causally independent of every other: none can cause changes in any but itself. This is not controversial. But Leibniz also thinks that every created substance is existentially independent of every other: it is metaphysically possible for any to exist with or without any other. This is controversial. I argue that, given a mainstream reading of Leibniz’s essentialism, if one accepts the former, uncontroversial interpretation concerning causal independence, (...) then one ought also to accept the latter, controversial one concerning existential independence. This is a new way to defend the ‘existential independence’ interpretation. Moreover, this defense provides a new approach for defending the broadly ‘non-logical’ interpretive camp in the longstanding debate over Leibniz’s views on incompossibility, against perhaps the strongest objection leveled by advocates of the opposing broadly ‘logical’ interpretation. (shrink)

Leibniz Reinterpreted tackles head on the central idea in Leibniz's philosophy, namely that we live in the best of all possible worlds. Strickland argues that Leibniz's theory has been consistently misunderstood by previous commentators. In the process Strickland provides both an elucidation and reinterpretation of a number of concepts central to Leibniz's work, such as 'richness', 'simplicity', 'harmony' and 'incompossibility', and shows where previous attempts to explain these concepts have failed. This clear and concise study is (...) tightly focussed and assumes no prior acquaintance with Leibniz or optimism. It thus serves as an ideal entry point into Leibniz's philosophy. (shrink)

Leibniz claims that Berkeley “wrongly or at least pointlessly rejects abstract ideas”. What he fails to realize, however, is that some of his own core views commit him to essentially the same stance. His belief that this is the best (and thus most harmonious) possible world, which itself stems from his Principle of Sufficient Reason, leads him to infer that mind and body must perfectly represent or ‘express’ one another. In the case of abstract thoughts he admits that this (...) can happen only in virtue of thinking of some image that, being essentially a mental copy of a brain state, expresses (and is expressed by) that state. But here he faces a problem. In order for a thought to be genuinely abstract, its representational content must differ from that of any mental image, since the latter can represent only particular things. In that case, however, an exact correspondence between the accompanying mental image and the brain state would not suffice to establish a perfect harmony between mind and body. Even on Leibniz’s own principles, then, it appears that Berkeley was right to dismiss abstract ideas. (shrink)

Leibniz accepts causal independence, the claim that no created substance can causally interact with any other. And Leibniz needs causal independence to be true, since his well-known pre-established harmony is premised upon it. So, what is Leibniz’s argument for causal independence? Sometimes he claims that causal interaction between substances is superfluous. Sometimes he claims that it would require the transfer of accidents, and that this is impossible. But when Leibniz finds himself under sustained pressure to defend (...) causal independence, those are not the reasons that he marshals in its defense. Instead, deep into his long correspondence with Burchard de Volder, he gives a different sort of argument, one that has gone nearly unnoticed by commentators and has not yet been properly understood. In part, this is because the argument develops slowly over four years of correspondence. It emerges in early 1704, but it is formulated tersely and appears murky unless understood in light of Leibniz and De Volder’s tangled exchanges. There Leibniz argues that, on his distinctive ontology of an infinity of created substances, no two created substances could possibly causally interact, for roughly the same reasons that some Cartesians like De Volder deny interaction between minds and bodies on their substance dualist ontology. In this paper I draw out this lost argument, explain it and the metaphysics on which Leibniz builds it, and untangle Leibniz and De Volder’s exchanges concerning causation from which this argument results. (shrink)

Despite holding that all concepts are strictly speaking innate, Leibniz attempts to accommodate the common belief that at least some concepts are adventitious by appealing to his theory of ideal action. The essential idea is that an innate concept can be considered adventitious, in a sense, just in case its ideal cause is to be found outside the mind of the one who possesses the concept. I explore this attempt at accommodation and argue that it fails. [See external link (...) for English draft.]. (shrink)

In his early lecture note Versuch einiger Betrachtungen über den Optimismus (1759) a young supporter of metaphysical optimism called Immanuel Kant tested the Leibnizian optimism by posing some counter-arguments against it only to falsify them. His counter-arguments were very inventive and they feature often in modern scholarship on Leibniz. In this paper I will present Kant’s main arguments and evaluate them. I will argue that Kant’s understanding on Leibnizian optimism is little misguided and for this reason his own positive (...) counter-argument despite its ingeniousness is problematic. His second solution to the problem is comparable to the doctrine of metaphysical optimism, but fails also for the same reason as the first one. -/- . (shrink)

The reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold provides a systematic account of the structure of Leibniz’s metaphysics in terms of its mathematical foundations. However, in doing so, Deleuze draws not only upon the mathematics developed by Leibniz—including the law of continuity as reflected in the calculus of infinite series and the infinitesimal calculus—but also upon developments in mathematics made by a number of Leibniz’s contemporaries—including Newton’s method of fluxions. He also draws upon (...) a number of subsequent developments in mathematics, the rudiments of which can be more or less located in Leibniz’s own work—including the theory of functions and singularities, the Weierstrassian theory of analytic continuity, and Poincaré’s theory of automorphic functions. Deleuze then retrospectively maps these developments back onto the structure of Leibniz’s metaphysics. While the Weierstrassian theory of analytic continuity serves to clarify Leibniz’s work, Poincaré’s theory of automorphic functions offers a solution to overcome and extend the limits that Deleuze identifies in Leibniz’s metaphysics. Deleuze brings this elaborate conjunction of material together in order to set up a mathematical idealization of the system that he considers to be implicit in Leibniz’s work. The result is a thoroughly mathematical explication of the structure of Leibniz’s metaphysics. This essay is an exposition of the very mathematical underpinnings of this Deleuzian account of the structure of Leibniz’s metaphysics, which, I maintain, subtends the entire text of The Fold. (shrink)

Leibniz’s views on modality are among the most discussed by his interpreters. Although most of the discussion has focused on Leibniz’s analyses of modality, this essay explores Leibniz’s grounding of modality. Leibniz holds that possibilities and possibilia are grounded in the intellect of God. Although other early moderns agreed that modal truths are in some way dependent on God, there were sharp disagreements surrounding two distinct questions: (1) On what in God do modal truths and modal (...) truth-makers depend? (2) What is the manner(s) of dependence by which modal truths and modal truth-makers depend on God? Very roughly, Leibniz’s own answers are: (1) God’s intellect and (2) a form of ontological dependence. The essay first distinguishes Leibniz’s account from two nearby (and often misunderstood) alternatives found in Descartes and Spinoza. It then examines Leibniz’s theory in detail, showing how, on his account, God’s ideas provide both truth-makers for possibilities and necessities and an ontological foothold for those truth-makers, thereby explaining modal truths. Along the way, it suggests several refinements and possible amendments to Leibniz’s grounding thesis. It then defends Leibniz against a pair of recent objections by Robert Merrihew Adams and Andrew Chignell that invoke the early work of Kant. I conclude that whereas Leibniz’s alternative avoids collapsing into yet another form of Spinozism, the alternatives proposed by Adams, Chignell, and the early Kant do not. (shrink)

Leibniz endorses several tenets regarding explanation: (1) causes provide contrastive explanations of their effects, (2) the past and the future can be read from the present, and (3) primitive force and derivative forces drive and explain changes in monadic states. I argue that, contrary to initial appearances, these tenets do not preclude an intelligible conception of contingency in Leibniz’s system. In brief, an agent is free to the extent that she determines herself to do that which she deliberately (...) judges to be the best from several considered options that she could have brought about, had she come to the deliberative conclusion that these options were best. I develop a model which illustrates how Leibnizian agents could have come to different deliberative conclusions, and which thus illustrates how Leibnizian agents could have acted differently. (shrink)

One of the more exotic and mysterious features of Leibniz’s later philosophical writings is the harmony between the kingdom of nature and the kingdom of grace. In this paper I show that this harmony is not a single doctrine, but rather a compilation of two doctrines, namely (1) that the order of nature makes possible the rewards and punishments of rational souls, and (2) that the rewards and punishments of rational souls are administered naturally. I argue that the harmony (...) is best considered as Leibniz’s distinctive collation, development, and rebranding of these doctrines, which were not themselves unique to Leibniz, nor uncommon in the seventeenth century. There follows a detailed examination of various concrete examples of the harmony in operation, from which I show that it is essentially the culmination of Leibniz’s lifelong thinking about divine justice. (shrink)

This paper reconsiders Leibniz’s conception of the nature of possible things and offers a novel interpretation of the actualization of possible substances. This requires analyzing a largely neglected notion, the reality of individual essences. Thus far scholars have tended to construe essences as representational items in God’s intellect. We acknowledge that finite essences have being in the divine intellect but insist that they are also grounded in the infinite essence of God, as limitations of it. Indeed, we show that (...) it is critical to understand that this dependence on God’s essence is prior to the dependence on God through divine ideas. Here it is crucial to distinguish questions concerning the ontological status of essences from questions concerning their reality. This yields a fresh view of Leibniz’s theory of creation, which takes seriously his claim that the same thing is first a mere possibility but after creation an actually existent substance. (shrink)

Leibniz frequently uses the notion of expression, but it is not easy to see just how he understood that relation. This paper focuses on the particular case of the expression of God, which is prominent in the 'Discourse on Metaphysics'. The treatment of expression there suggests several questions. Which substances did Leibniz believe expressed God? Why did Leibniz believe those substances expressed God? And did he believe that all substances expressed God in the same way and for (...) the same reasons? In answering those questions the paper distinguishes two views about expression in the 'Discourse', considers Leibniz's reasons for holding that substances express their causes, and argues that Leibniz's views about emanative causation are important for understanding the unity of his apparently distinct views here. The paper concludes by looking briefly at how the 'Discourse' fits into the evolution of Leibniz's views on this issue over time. (shrink)

In the early years of the eighteenth century Leibniz had several interactions with John Toland. These included, from 1702 to 1704, discussions of materialism. Those discussions culminated with the consideration of Toland's 1704 Letters to Serena, where Toland argued that matter is necessarily active. In this paper I argue for two main theses about this exchange and its consequences for our wider understanding. The first is that, despite many claims that Toland was at the time of Letters to Serena (...) a Spinozist, we can make better sense of him as a sort of Hobbesian materialist. The second main point concerns reasons for materialism, and in particular a story Locke tells in the Essay about materialists' motives. Toland defends his materialism by arguing that matter is active, and argues that matter is active by using a conceivability argument. But this is not the crude conceivability argument that Locke suggests motivates materialists. This (together with reflecting on some of Hobbes's arguments) suggests that we might well tell a Lockean story about reasons for early modern materialism, but not Locke's story. (shrink)

The ancient doctrine of the eternal return of the same embodies a thoroughgoing rejection of the hope that the future world will be better than the present. For this reason, it might seem surprising that Leibniz constructs an argument for a version of the doctrine. He concludes in one text that in the far distant future he himself ‘would be living in a city called Hannover located on the Leine river, occupied with the history of Brunswick, and writing letters (...) to the same friends with the same meaning.’ However, his argument concludes not that the future will be absolutely identical to the present, but rather that any finite description of the present and future worlds would be identical. In this way, the argument leaves room for the promise of a different and better future—even if it is one that could not be recognized by us as such. (shrink)

Leibniz' first problem with contingency stems from his doctrine of divine creation (not his later doctrine of truth) and is solved via his concepts of necessity per se, etc. (not via his later concept of infinite analysis). I scrutinize some of the earliest texts in which the first problem and its solution occur. I compare his "per se modal concepts" with his concept of analysis and with the traditional concept of metaphysical necessity. I then identify and remove the main (...) obstacle to Leibniz' employment of these concepts by reflecting on his concept of a world and comparing and contrasting it with contemporary conceptions. Finally I sketch the place that this early problem and its solution had in the context of his mature philosophy. A disagreement between Sleigh and Adams which hinges on the assumption that there is just one problem with competing solutions is seen to dissolve in this light. (shrink)

Recently we proposed "quantum language" (or, the linguistic Copenhagen interpretation of quantum mechanics"), which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes=Kant epistemology. We believe that quantum language is the language to describe science, which is the final goal of dualistic idealism. Hence there is a reason to want to clarify, from the quantum linguistic point of view, the following problems: "brain in a vat argument", "the Cogito proposition", (...) "five-minute hypothesis", "only the present exists", "Copernican revolution", "McTaggart's paradox", and so on. In this paper, these will be discussed and clarified in quantum language. That is, these are not in quantum language. Also we emphasize that Leibniz's relationalism in Leibniz-Clarke correspondence is regarded as one of the most important parts of the linguistic Copenhagen interpretation of quantum mechanics. This paper is the revised version of the paper: Open Journal of Philosophy, 2018 Vol.8, No.5, 466-480). (shrink)

On 1 November 1755, the city of Lisbon in Portugal was virtually destroyed by the largest documented seismic event ever to hit Europe. It is often claimed that the catastrophe severely damaged the plausibility of Leibniz’s optimism, and even the wider project of theodicy. Leibniz died several decades before the Lisbon earthquake struck, and so was unable to address it and the challenges thrown up by it, which would have included an account of how the event was consistent (...) with God’s providence. Contemporary scholars are of the view that Leibniz explained natural disasters like earthquakes as nothing more than the unfortunate consequences of the normal workings of simple laws of nature, and that God permits such disasters to happen because it would be unworthy of him to overrule the laws he has established. There certainly is this line of thinking in Leibniz’s writings, but it is far from being the whole story, as we shall see. The aim of this paper is to determine what Leibniz’s response to the Lisbon earthquake would have been, had he lived to know about the event. (shrink)

I consider Leibniz's thoughts about Hobbes's materialism, focusing on his less-discussed later thoughts about the topic. Leibniz understood Hobbes to have argued for his materialism from his imagistic theory of ideas. Leibniz offered several criticisms of this argument and the resulting materialism itself. Several of these criticisms occur in texts in which Leibniz was engaging with the generation of British philosophers after Hobbes. Of particular interest is Leibniz's correspondence with Damaris Masham. Leibniz may have (...) been trying to communicate with Locke, but ended up discussing Masham's version of the argument for materialism that Leibniz attributed to Hobbes. (shrink)

In 1682, Leibniz published an essay containing his solution to the classic problem of squaring the circle: the alternating converg-ing series that now bears his name. Yet his attempts to disseminate his quadrature results began seven years earlier and included four distinct approaches: the conventional (journal article), the grand (treatise), the impostrous (pseudepigraphia), and the extravagant (medals). This paper examines Leibniz’s various attempts to disseminate his series formula. By examining oft-ignored writings, as well as unpublished manuscripts, this paper (...) answers the question of how one of the greatest mathematicians sought to introduce his first great geometrical discovery to the world. (shrink)

• It would be a moral disgrace for God (if he existed) to allow the many evils in the world, in the same way it would be for a parent to allow a nursery to be infested with criminals who abused the children. • There is a contradiction in asserting all three of the propositions: God is perfectly good; God is perfectly powerful; evil exists (since if God wanted to remove the evils and could, he would). • The religious believer (...) has no hope of getting away with excuses that evil is not as bad as it seems, or that it is all a result of free will, and so on. Piper avoids mentioning the best solution so far put forward to the problem of evil. It is Leibniz’s theory that God does not create a better world because there isn’t one — that is, that (contrary to appearances) if one part of the world were improved, the ramifications would result in it being worse elsewhere, and worse overall. It is a “bump in the carpet” theory: push evil down here, and it pops up over there. Leibniz put it by saying this is the “Best of All Possible Worlds”. That phrase was a public relations disaster for his theory, suggesting as it does that everything is perfectly fine as it is. He does not mean that, but only that designing worlds is a lot harder than it looks, and determining the amount of evil in the best one is no easy matter. Though humour is hardly appropriate to the subject matter, the point of Leibniz’s idea is contained in the old joke, “An optimist is someone who thinks this is the best of all possible worlds, and a pessimist thinks.. (shrink)

Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation (...) by means of automated theorem provers and finite model builders. The fundamental theorem of Leibniz’s theory is derived using these tools. (shrink)

Leibniz’s account of probability has come into better focus over the past decades. However, less attention has been paid to a certain domain of application of that account, that is, the application of it to the moral or ethical domain—the sphere of action, choice and practice. This is significant, as Leibniz had some things to say about applying probability theory to the moral domain, and thought the matter quite relevant. Leibniz’s work in this area is conducted at (...) a high level of abstraction. It establishes a proof of concept, rather than concrete guidelines for how to apply calculations to specific cases. Still, this highly abstract material does allow us to begin to construct a framework for thinking about Leibniz’s approach to the ethical side of probability. (shrink)

At the end of 1671 and start of 1672, while in the service of the Archbishop and Elector of Mainz, Leibniz composed his Egypt Plan, which sought to persuade Louis XIV to invade Egypt. Scholars have generally supposed that Leibniz’s rationale for devising the plan was to divert Louis from his intended war with Holland. Little attention has been paid to the religious benefits that Leibniz identified in the plan, and those who do acknowledge them are often (...) quick to downplay them. This tendency to downplay or even dismiss the religious benefits Leibniz claimed of the Egypt Plan is undermotivated and stems from a very superficial reading of the documents that together comprise it. In this paper I argue that we should take seriously Leibniz’s claim that a French invasion of Egypt would bring religious benefits, and that he saw them as important and intrinsically desirable inasmuch as he came to believe that the execution of the plan would lead to the flowering of co-operation and brotherhood among Christians in a show of inter-denominational koinonia, that is, fellowship with other Christians in the participation of shared goals. (shrink)

Leibniz argues that there must be a fundamental level of simple substances because composites borrow their reality from their constituents and not all reality can be borrowed. I contend that the underlying logic of this ‘borrowed reality argument’ has been misunderstood, particularly the rationale for the key premise that not all reality can be borrowed. Contrary to what has been suggested, the rationale turns neither on the alleged viciousness of an unending regress of reality borrowers nor on the Principle (...) of Sufficient Reason, but on the idea that composites are phenomena and thus can be real only insofar as they have a foundation in substances, from which they directly ‘borrow’ their reality. The claim that composites are phenomena rests in turn on Leibniz's conceptualism about relations. So understood, what initially looked like a disappointingly simple argument for simples turns out to be a rather rich and sophisticated one. (shrink)

Although the historical reputation of Gottfried Wilhelm Leibniz (1646–1716) largely rests on his philosophical and mathematical work, it is widely known that he made important contributions to many of the emerging but still inchoate branches of natural science of his day. Among the many scientific papers Leibniz published during his lifetime are ones on the nascent science we now know as hydrology. While Leibniz’s other scientific work has become of increasing interest to scholars in recent years, his (...) thinking about hydrology has been neglected, despite being relatively broad in extent, including as it does papers on the ‘raising of vapours’ and the formation of ice, as well as the separation of salt and fresh water. That list can now be extended still further following the discovery of a previously unpublished letter of Leibniz’s on the causes of the devastating Lombardy flood of October and November 1705. This letter, which will be the focus of our paper, reveals the depth of Leibniz’s understanding of key hydrological processes. In it, he considers various mechanisms for the flood, such as heavy rains on high ground, underwater earthquakes, and a mountain collapse. Over the course of the paper we examine each of these mechanisms in depth, and show that Leibniz was in the vanguard of hydrological thinking. We also show that the letter contains one of the first scholarly attempts to apply aspects of the still-forming notion of the hydrological cycle to account for a flood event. (shrink)

To explain why God is not the author of sin, despite grounding all features of the world, the early Leibniz marginalized the divine will and defined existence as harmony. These moves support each other. It is easier to nearly eliminate the divine will from creation if existence itself is something wholly intelligible, and easier to identify existence with an internal feature of the possibles if the divine will is not responsible for creation. Both moves, however, commit Leibniz to (...) a necessitarianism that is stronger than what prominent interpreters such as Robert Sleigh and Mogens Lærke have found in the early Leibniz, and stronger than the necessitarianism that threatens his later philosophy. I defend this reading of Leibniz and propose that some features of Leibniz’s later metaphysics, including his “striving possibles” doctrine, are an artifact of the effort to rescue the early theodicy from its unwelcome implications. (shrink)