The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are often (...) seen as part of the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence. (shrink)

This essay develops a interpretation of Leibniz’ theory of motion that strives to integrate his metaphysics of force with his doctrine of the equivalence of hypotheses, but which also supports a realist, as opposed to a fully idealist, interpretation of his natural philosophy. Overall, the modern approaches to Leibniz’ physics that rely on a fixed spacetime backdrop, classical mechanical constructions, or absolute speed, will be revealed as deficient, whereas a more adequate interpretation will be advanced that draws (...) inspiration from an invariantist conception of reality and recent non-classical theories of physics. (shrink)

In the texts of the middle years (roughly, the 1680s and 90s), Leibniz appears to endorse two incompatible approaches to motion, one a realist approach, the other a phenomenalist approach. I argue that once we attend to certain nuances in his account we can see that in fact he has only one, coherent approach to motion during this period. I conclude by considering whether the view of motion I want to impute to Leibniz during his middle years ranks (...) as a kind of realism or rather as some kind of phenomenalism or idealism. (shrink)

Response to critical comments by Edward Slowik on my article 'Leibniz on Motion and the Equivalence of Hypotheses' in The Leibniz Review 18 (2008).

Abstract -/- The indistinction between repose and uniform movement exposed in the principle of inertia marks one of the most famous dissertations: the discussion between Newton and Leibniz. Through their respective conceptions of space, both seek to solve the problem of indistinction. The relational space of Leibniz, supported by the principle of sufficient reason and the identity of indiscernibles leads to the kinematic solution of the problem of inertia. The objective of this paper is to show the contribution (...) of Leibniz, in terms of relations of order, by distinguishing between equality by identity and equality by equivalence. Under a philosophical approach we link identity, equivalence and equality as relations of order with the indiscernibility between different states of movement. We expose first the principle of sufficient reason and the identity of indiscernibles. Under Bernoulli's principle of indifference, we argue that we distinguish between equality in abstract and equality in concrete. As a third part, we present the relationship between the identity of the indiscernibles and the predicate of equality under logical analysis. Finally we present the conclusions. -/- . (shrink)

We show in this paper that the answer to the question in the title is in the negative. In modern optics, Snell’s law of reflection is derived using Leibniz’s calculus method that identifies the least time path, chosen by rays of light in going from a given point A, to another given point B, undergoing reflection at a point P on their way. We demonstrate, taking two examples of reflection: (1) at a plane reflector and (2) at elliptical reflector, (...) that Snell’s law of reflection is not a consequence of least time path principle and, that Leibniz’s method of derivation of Snell’s law of reflection is invalid. In (1), we prove that, if a light ray is reflected at point P on a line, along the least time path APB, then at every point Pi on that line, rays from A are reflected to point B, satisfying Snell’s law. However, paths, APB and APiB do not have equal travel times. In (2), we prove that, if a light ray is reflected along the least time path APB, from focus A to focus B incident at point P on an ellipse, satisfies Snell’s law, then points Pi, not lying on the ellipse, also reflect light rays from A to B, satisfying Snell’s law. However, the paths APB and APiB do not have equal travel times. Thus, both examples prove that least time path is not a criterion for reflection and, that Snell’s law of reflection is not a consequence of least time path principle. (shrink)

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)

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)

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.

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)

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)

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)

It is often claimed that one can avoid the kind of underdetermination that is a typical consequence of symmetries in physics by stipulating that symmetry-related models represent the same state of affairs (Leibniz Equivalence). But recent commentators (Dasgupta 2011; Pooley 2021; Pooley and Read 2021; Teitel 2021a) have responded that claims about the representational capacities of models are irrelevant to the issue of underdetermination, which concerns possible worlds themselves. In this paper I distinguish two versions of this objection: (...) (1) that a theory’s formalism does not (fully) determine the space of physical possibilities, and (2) that the relevant notion of possibility is not physical possibility. I offer a refutation of each. (shrink)

I propose a straightforward reconciliation of Leibniz’s conception of bodies as aggregates of simple substances (i.e., monads) with his doctrine that bodies are the phenomena of perceivers, without in the process saddling him with any equivocations. The reconciliation relies on the familiar idea that in Leibniz’s idiolect, an aggregate of Fs is that which immediately presupposes those Fs, or in other words, has those Fs as immediate requisites. But I take this idea in a new direction. Taking notice (...) of the fact that Leibniz speaks of three respects in which one thing may immediately presuppose others--i.e., with respect to its being, its existence, and its reality--I argue that a phenomenon having its being in one perceiving substance (monad) can plausibly be understood to presuppose other perceiving substances (monads) in two of these respects. Accordingly, good sense can be made of both the claim that a phenomenon in one monad is an aggregate of other monads (in Leibniz’s technical sense of 'aggregate') and the (equivalent) claim that the latter monads are constituents of the phenomenon (in his technical sense of 'constituent'). So understood, the two conceptions of body are perfectly compatible, just as Leibniz seems to think. (shrink)

The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, (...) the geometrical meaning of the double contradiction is considered as follows. A tangent at a point on a convex curve is iterated. Then, the slope of the tangent at the point is sandwiched by two kinds of lines. The first kind of line crosses the curve at the original point and a point to the right of it. The second kind of line crosses the curve at the original point and a point to the left of it. Then, the double contradiction can be applied, and the slope of the tangent is determined as a single value. Finally, the meaning of this method for the foundation of mathematics is considered. We reflect on Dehaene’s notion that the foundation of mathematics is based on the intuitions, which evolve independently. Hence, there may be gaps between intuitions. In fact, the Ancient Greeks identified inconsistency between arithmetic and geometry. However, Eudoxus developed the theory of proportion, which is equivalent to the Dedekind Cut. This allows the iteration of an irrational number by rational numbers as precisely as desired. Simultaneously, we can define the irrational number by the double contradiction, although its existence is not guaranteed. Further, an area of a curved figure is iterated and defined by rectilinear figures using the double contradiction. (shrink)

The notion of Providence is born with the Greek word prόnoia which, however, originally meant "premeditation" (of a crime) or "design" of an artefact, and had nothing to do with religion. It was Plato in the Timaeus who adopted the word from the common language to indicate the rational and benevolent principle that inspired the anonymous God, which he defined as dēmiourgόs (also this word originally meant a professional technician, for example, a doctor or an architect) in his work of (...) shaping the cosmos. The doctrine of divine Providence was taken up by Middle Platonism, and with it the need to "justify" the divinity for the presence of evil in the world, what Leibniz will call "theodicy". Stoicism also supported Providence, but here there is no "theodicy" because in Stoic philosophy rationality and beneficial purpose are intrinsic to the cosmic process and therefore there is no external architect to be charged and absolved. Christian authors of the first centuries recycled the arguments of the Platonists in support of Providence, despite the fact that the word prόnoia never appears in the New Testament, nor is there any Hebrew equivalent in the Tanak. Perhaps there is some compatibility problem between the philosophical theory of Providence and the biblical-Christian view of God. (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)

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)

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)

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)

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)

This paper is concerned with the relation between two notions: that of two solutions or models of a theory being related by a symmetry of the theory and that of solutions or models being physically equivalent. A number of authors have recently discussed this relation, some taking an optimistic view, on which there is a suitable concept of the symmetry of a theory relative to which these two notions coincide, others taking a pessimistic view, on which there is no such (...) concept. The present paper arrives at a cautiously pessimistic conclusion. (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.

I argue that an individual has aspects numerically identical with it and each other that nonetheless qualitatively differ from it and each other. This discernibility of identicals does not violate Leibniz's Law, however, which concerns only individuals and is silent about their aspects. They are not in its domain of quantification. To argue that there are aspects I will appeal to the internal conflicts of conscious beings. I do not mean to imply that aspects are confined to such cases, (...) but the best way to start is to recognize them experientially. We can feel the conflicts within ourselves. In doing so we can feel some of our aspects. I will try to enhance our understanding of the concept of aspect by listing and formalizing some principles for its use. After that I will argue that all sorts of individual things have aspects, not just people who are conflicted. (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)

This paper corrects a mistake I saw students make but I have yet to see in print. The mistake is thinking that logically equivalent propositions have the same counterexamples—always. Of course, it is often the case that logically equivalent propositions have the same counterexamples: “every number that is prime is odd” has the same counterexamples as “every number that is not odd is not prime”. The set of numbers satisfying “prime but not odd” is the same as the set of (...) numbers satisfying “not odd but not not-prime”. The mistake is thinking that every two logically-equivalent false universal propositions have the same counterexamples. Only false universal propositions have counterexamples. A counterexample for “every two logically-equivalent false universal propositions have the same counterexamples” is two logically-equivalent false universal propositions not having the same counterexamples. The following counterexample arose naturally in my sophomore deductive logic course in a discussion of inner and outer converses. “Every even number precedes every odd number” is counterexemplified only by even numbers, whereas its equivalent “Every odd number is preceded by every even number” is counterexemplified only by odd numbers. Please let me know if you see this mistake in print. Also let me know if you have seen these points discussed before. I learned them in my own course: talk about learning by teaching! (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)

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 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 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 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 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)

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)

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)

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 is not commonly numbered amongst canonical writers on toleration. One obvious reason is that, unlike Locke, he wrote no treatise specifically devoted to that doctrine. Another is the enormous amount of energy which he famously devoted to ecclesiastical reunification. Promoting the reunification of Christian churches is an objective quite different from promoting the toleration of different religious faiths – so different, in fact, that they are sometimes even construed as mutually exclusive. Ecclesiastical reunification aims to find agreement at (...) least on the most important doctrines. Religious toleration involves accepting and respecting disagreement even on the most important doctrines. If one regards these two projects as alternative rather than complementary strategies for dealing with religious diversity, Leibniz might more readily be characterised as an ecumenist rather than a tolerationist. Such appears to be the conclusion, at any rate, implicit in the balance of critical literature on these topics: whereas a steady stream of studies has discussed Leibniz’s project of ecclesiastical reunification, only a meager trickle has been devoted to his views on toleration; and some of these studies go so far as to conclude that Leibniz had no doctrine of toleration at all. This paper will attempt to show, on the contrary, that a robust, many-layered, and unusually inclusive doctrine of toleration can be gleaned from Leibniz’s writings. This doctrine operated at least at three different levels: philosophical, theological, and pragmatic. As this implies, the doctrine of religious toleration, rather than being in collision with Leibniz’s core project of ecclesiastical reunification, was an essential element of that very project: it should be seen, in other words, not as a competing goal, but as a necessary first step toward ecclesiastical reunification. Yet at the same time it will also emerge that Leibniz’s doctrine of toleration was no mere function of this intra-Christian project of reunification: rather it was a still more fundamental principle which extended beyond the ecumenical project as well. It had the resources for accepting and respecting irreducible religious diversity and disagreement on points of importance not only between Christian communities, but also between Christians and non-Christians, including, in principle, even the atheists. These points will emerge from a discussion of statements on the philosophical, theological, and pragmatic justifications of religious toleration scattered throughout Leibniz’s sprawling corpus of writings. (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 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)

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)

What would Gottfried Wilhelm Leibniz have said about today’s problem of consciousness? Some philosophers claim that Leibniz was one of the first to argue that there is an ‘explanatory gap’ between our knowledge of matter and our knowledge of consciousness, and that he thought this posed a problem for materialism (see for example Churchland 1995: 191-2; Kriegel 2015: 49; Seager 1991; Searle 1983: 267-8). This is supposed to be the point of the famous passage in the Monadology (1714), (...) in which Leibniz argues that perception is ‘inexplicable in terms of mechanical reasons’... (shrink)

Formal criteria of theoretical equivalence are mathematical mappings between specific sorts of mathematical objects, notably including those objects used in mathematical physics. Proponents of formal criteria claim that results involving these criteria have implications that extend beyond pure mathematics. For instance, they claim that formal criteria bear on the project of using our best mathematical physics as a guide to what the world is like, and also have deflationary implications for various debates in the metaphysics of physics. In this (...) paper, I investigate whether there is a defensible view according to which formal criteria have significant non-mathematical implications, of these sorts or any other, reaching a chiefly negative verdict. Along the way, I discuss various foundational issues concerning how we use mathematical objects to describe the world when doing physics, and how this practice should inform metaphysics. I diagnose the prominence of formal criteria as stemming from contentious views on these foundational issues, and endeavor to motivate some alternative views in their stead. (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)

This paper presents a simple pair of first-order theories that are not definitionally (nor Morita) equivalent, yet are mutually conservatively translatable and mutually 'surjectively' translatable. We use these results to clarify the overall geography of standards of equivalence and to show that the structural commitments that theories make behave in a more subtle manner than has been recognized.

This paper explores the development of Leibniz’s metaphysics of the Incarnation in the context of his philosophy. In particular it asks to what extent Leibniz’s repeated endorsement of the traditional analogy between the union in humankind of soul (mind) and body, and the union in Christ of divine and human natures, could be accommodated by his more general metaphysical doctrines. Such an investigation highlights some of the deepest commitments in Leibniz’s theory of substance as well as detect (...) in it some unresolved tensions. The paper comes to the conclusion that puzzling points of Leibniz’s metaphysics of the Incarnation, rather than being problems specific to his theology, uncover tensions in his theory of substance as such – tensions converging on the vexed question of whether there can or cannot be genuine corporeal substances in Leibniz’s mature philosophy. (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)

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)

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)