Leibniz's Views Research Articles

The young Leibniz's tentative acceptance of physical occasionalism

AbstractIn this article, I revisit Leibniz's early views on physical causation, more specifically, his relation to physical occasionalism focusing on the period from 1668 to 1676. An in‐depth analysis of the Confession of Nature against the Atheists taken together with the Catholic Demonstrations, Leibniz's correspondence with Jakob Thomasius from 1668/69, and the Pacidius Philalethi (1676) serve as evidence that his position leads to physical occasionalism. This receives further confirmation by taking into account Leibniz's familiarity with Weigel's occasionalism in contrast to Leibniz's later encounter of French occasionalism à la Cordemoy, La Forge, or Malebranche. Leibniz's exposure to Weigel's occasionalism, in turn, helps us better understand Leibniz's later critical reaction to occasionalism and how occasionalism helped him develop his own distinct views on causation as expressed in his mature philosophy.

Law and Physics in Leibniz

abstract: In this paper I argue that there is a structural parallelism between law and physics in Leibniz since his early years, which has significant influence on the formation of his views. I start by examining Leibniz's early physical system and an analogy with juridical laws that he uses to explain the structure of physical laws. Then, I argue that this analogy stems from an envisioned parallelism between law and physics. Finally, I illustrate the significance of this legal-physical parallelism by arguing that it underlies some of Leibniz's mature views. Most importantly, I argue that the parallelism explains the origin of architectonic principles or optimality principles in Leibniz's mature physics.

Leibniz's Moral Psychology of an Evil Person

Abstract Our focus in this article concerns Leibniz's views on evil. Our goal is to examine which are the consequences of his conception of moral agency for the moral psychology of the genuinely evil person. For Leibniz, moral failure is an epistemic error since it involves some false practical judgement. Moral maxims may be represented in blind or symbolic cognitions, but then moral agents can misrepresent the evil consequences of their behaviour. Finally, we discuss Leibniz's view on habits that may help virtuous persons strive for perfection but also enable evil persons to continue sinning.

Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work

This paper is concerned with the status of mathematical fictions in Leibniz’s work and especially with infinitary quantities as fictions. Thus, it is maintained that mathematical fictions constitute a kind of symbolic notion that implies various degrees of impossibility. With this framework, different kinds of notions of possibility and impossibility are proposed, reviewing the usual interpretation of both modal concepts, which appeals to the consistency property. Thus, three concepts of the possibility/impossibility pair are distinguished; they give rise, in turn, to three concepts of mathematical fictions. Moreover, such a distinction is the base for the claim that infinitesimal quantities, as mathematical fictions, do not imply an absolute impossibility, resulting from self-contradiction, but a relative impossibility, founded on irrepresentability and on the fact that it does not conform to architectural principles. In conclusion, this “soft” impossibility of infinitesimals yields them, in Leibniz view, a presumptive or “conjectural” status.

Space, Law, and Justice in Leibniz: Leibniz as a Theorist of Spatial Justice

This article argues that Leibniz should be viewed as a predecessor of the idea of spatial justice and that Leibniz's heritage remains a valuable source for inspiration and critical reading of the contemporary literature on spatial justice. The article first demonstrates interdependency between Leibniz's conceptualisation of space and his conceptualisation of law and justice. This is the first time that this argument is made in relation to Leibniz, therefore significant space is devoted to justifying this argument. The article then proceeds to comparing Leibniz's views on space, law and justice to one of the most “spatial” contemporary articulation of the idea of spatial justice, namely that proposed by Andreas Philippopoulos-Mihalopoulos. The article concludes by pointing out some aspects of Leibniz's thought that are most valuable for the further study of law, space and spatial justice in contemporary scholarship.

Leibniz�s well-founded fictions and their interpetations

Leibniz used the term fiction in conjunction with infinitesimals. What kind of fictions they were exactly is a subject of scholarly dispute. The position of Bos and Mancosu contrasts with that of Ishiguro and Arthur. Leibniz's own views, expressed in his published articles and correspondence, led Bos to distinguish between two methods in Leibniz's work: (A) one exploiting classical `exhaustion' arguments, and (B) one exploiting inassignable infinitesimals together with a law of continuity. Of particular interest is evidence stemming from Leibniz's work Nouveaux Essais sur l'Entendement Humain as well as from his correspondence with Arnauld, Bignon, Dagincourt, Des Bosses, and Varignon. A careful examination of the evidence leads us to the opposite conclusion from Arthur's. We analyze a hitherto unnoticed objection of Rolle's concerning the lack of justification for extending axioms and operations in geometry and analysis from the ordinary domain to that of infinitesimal calculus, and reactions to it by Saurin and Leibniz. A newly released 1705 manuscript by Leibniz (Puisque des personnes...) currently in the process of digitalisation, sheds light on the nature of Leibnizian inassignable infinitesimals. In a pair of 1695 texts Leibniz made it clear that his incomparable magnitudes violate Euclid's Definition V.4, a.k.a. the Archimedean property, corroborating the non-Archimedean construal of the Leibnizian calculus. Keywords: Archimedean property; assignable vs inassignable quantity; Euclid's Definition V.4; infinitesimal; law of continuity; law of homogeneity; logical fiction; Nouveaux Essais; pure fiction; quantifier-assisted paraphrase; syncategorematic; transfer principle; Arnauld; Bignon; Des Bosses; Rolle; Saurin; Varignon

The Leibniz-Arnauld Correspondence: With Selections from the Correspondence with Ernst, Landgrave of Hessen-Rheinfels by G. W. Leibniz

Reviewed by: The Leibniz-Arnauld Correspondence: With Selections from the Correspondence with Ernst, Landgrave of Hessen-Rheinfelsby G. W. Leibniz Julia Jorati G. W. Leibniz. The Leibniz-Arnauld Correspondence: With Selections from the Correspondence with Ernst, Landgrave of Hessen-Rheinfels. Text established and translated and with an introduction by Stephen Voss. The Yale Leibniz series. New Haven: Yale University Press, 2016. pp. lix + 410 Cloth, $125.00. In February 1686, Gottfried Wilhelm Leibniz sent a letter to Antoine Arnauld, via their mutual friend Ernst, the Landgrave of Hessen-Rheinfels. This letter contained a short summary of Leibniz's most recent philosophical work, the Discourse on Metaphysics, and asked Arnauld for his reaction to it. Arnauld's response was extremely harsh: he called Leibniz's views shocking and useless (9) and advised him to stop engaging in metaphysical speculations (11). Yet, Leibniz did not let this discourage him. In the exchange that followed, Leibniz was intent on convincing Arnauld that the views contained in the Discourseare well supported and less radical than Arnauld initially thought. And while he never convinced Arnauld completely, he managed to allay some of Arnauld's worries. Along the way, the two men discussed topics such as divine foreknowledge, freedom, contingency, complete concepts, substancehood, causation, the laws of physics, and the special status of rational souls. The correspondence continued until March 1690—though Arnauld stopped responding to Leibniz's letters in August 1687. It is indisputably one of the most important philosophical texts from Leibniz's middle period and also sheds light on Arnauld's views. Even though various editions and translations of this correspondence have long been available, Stephen Voss's new edition greatly facilitates scholarly engagement with this text. Like other volumes of the invaluable Yale Leibniz series, it contains the original language text along with an English translation on facing pages, which is enormously convenient. The volume also includes two short but useful indices and multiple appendices: an edition and translation of manuscript variants as well as an edition and translation of seventeen annotations that Leibniz made in the margins of some of the letters years later. Moreover, an extremely rich 40-page introduction provides a summary of the correspondence and a vast amount of background information about the manuscripts, the correspondence and its intellectual milieu, and, of course, about the edition itself as well as its relation to other editions. Perhaps most importantly, Voss's edition is based on a much wider range of manuscripts than other editions; more on that later. The English translation is often more literal than other translations. This is intentional; Voss opted, as he puts it, to "teach us to hear Leibniz and Arnauld as they spoke in the seventeenth century" rather than to "teach them to speak to us in the twenty-first" (xxiv). Because the authoritative Akademie edition of the Arnauld correspondence has already been published ( Sämtliche Schriften und Briefe, series 2, volume 2, Berlin: Akademie Verlag, 2009), one might have expected Voss simply to reprint the French text from that edition. Instead, he produced a new edition, working from sixty-two extant manuscripts that are housed in multiple libraries and archives across Europe. Because the manuscripts of some of the letters that Leibniz sent to Arnauld are lost, Voss reconstructs their content on the basis of extant drafts and copies. These reconstructions are produced with great care: the textual basis for the reconstructions is meticulously documented in an appendix, and they include nothing that does not occur in any of the witnesses to the lost manuscript. This is one important respect in which Voss's approach differs from that of the Akademie and other editors, who merely establish the text of extant manuscripts instead of attempting to reconstruct a lost original. Another important difference is that Voss consulted many manuscripts that were not consulted by other editors. That alone would make Voss's edition indispensable for Leibniz scholars, even if it did not have other virtues. For a list of discrepancies between Voss's edition on the one hand and the Akademie edition as well as Geneviève Rodis-Lewis's edition ( Lettres de Leibniz à Arnauld d'après un manuscrit in...

Leibniz et Bayle: Confrontation et dialogue ed. by Christian Leduc, Paul Rateau, and Jean-Luc Solère

Reviewed by: Leibniz et Bayle: Confrontation et dialogue ed. by Christian Leduc, Paul Rateau, and Jean-Luc Solère Mara van der Lugt Christian Leduc, Paul Rateau, and Jean-Luc Solère, editors. Leibniz et Bayle: Confrontation et dialogue. Studia Leibnitiana 43. Stuttgart: Franz Steiner, 2015. Pp. 452 €64.00. Central to this volume are two philosophical powerhouses of the early modern period: Gottfried Wilhelm Leibniz and Pierre Bayle. Born in, respectively, 1646 and 1647, both made for an astonishing career in a variety of scholarly disciplines and reached, if not equal, then certainly comparable fame in the course of their lives. Nowadays, Bayle's reputation is eclipsed by that of Leibniz, who is the focus of yearly conferences and libraries of scholarship, while Bayle had to await the later twentieth century to be rediscovered. He has since been at the center of a quickly expanding body of scholarship, which continues to be sharply divided over the vexed question how to interpret his religious stance. This imbalance in the amount of scholarship devoted to the two thinkers partly has to do with their respective modes of philosophizing. Though it is an exaggeration to say that Leibniz was systematic where Bayle was critical, it is the case that Leibniz was more intent on building his own systems, Bayle on exposing the inherent weaknesses of others'. Leibniz left a corpus of philosophical treatises, monographs and essays, while Bayle left his arguments scattered in a variety of textual curiosity cabinets, combining philosophical argument with generous helpings of historical and literary digressions. But if this diverse treatment of Leibniz and Bayle seems warranted by the character of their philosophical oeuvres, it becomes questionable when one takes into account their intellectual itineraries, which crossed in various debates. As intellectual sparring partners, they engaged with each other's arguments with the highest degree of dedication, to such an extent that Leibniz's philosophical legacy would be unthinkable without Bayle. One of the major strengths of this collection of articles is to bring out Leibniz and Bayle in "confrontation and dialogue" and emphasize the dialectical and interactive component of their philosophical sparring sessions, which spanned decades and a wide variety of texts. The twenty-one articles collected in this bilingual volume (French-English) are grouped thematically into four categories. The articles in the first section, "Methods, Hypotheses and Truth," discuss both philosophers' views on epistemology, skepticism, truth and belief, and trace the evolution of their debate in these areas; a valuable contribution by Michael Hickson questions the common dichotomy that associates Leibniz with rationalism, Bayle with skepticism. The second section, "Pre-established Harmony and Plastic Natures," is oriented more towards the various stages within the development of Leibniz's system, and the role played by Bayle's criticism throughout this process. A crucial part in this is the debate on animal sensation and Bayle's attempt to disprove the logic of Leibniz's pre-established harmony via the thought-experiment of a dog that suddenly passes from a state of pleasure to a state of pain; and Bayle and Leibniz's differing views on Ralph Cudworth and plastic natures, which Bayle connects to the philosophical specter of Stratonism. [End Page 353] The third section, "Faith and Reason," focuses on Bayle and Leibniz's views on religion, theology, rationalism and fideism, sometimes questioning the assumption that Leibniz and Bayle were diametrically opposed with regard to reason and religious belief (Kristen Irwin). Other articles examine their respective views on quietism (Thomas Lennon) and the apocalypse (Hartmut Rudolph): this last article contains some unfortunate inaccuracies (e.g. the misattribution of Bayle's Critique Générale to Louis Maimbourg, 337). An especially insightful contribution by Paul Rateau discusses the figure of the virtuous atheist in Leibniz and Bayle. The fourth section, "Evil and Theodicy," is centered on one of the most influential interactions between Bayle and Leibniz, which would leave a huge impact on the eighteenth century: their debate on the problem of evil, various aspects of which are discussed by the articles in this section. Especially noteworthy is Gianni Paganini's contribution, which raises an important question with regard to the eclipse of the Book of Job from the...

Leibniz and the Foundations of Physics: The Later Years

This essay offers an account of the relationship between extended Leibnizian bodies and unextended Leibnizian monads, an account that shows why Leibniz was right to see intimate, explanatory connections between his studies in physics and his mature metaphysics. The first section sets the stage by introducing a case study from Leibniz's technical work on the strength of extended, rigid beams. The second section draws on that case study to introduce a model for understanding Leibniz's views on the relationship between derivative and primitive forces. The third section draws on Leibniz's understanding of the relationship between derivative and primitive forces in order to shed light, in turn, on his understanding of the relationship between extended, material bodies and unextended, immaterial monads. The fourth section responds to a likely objection by arguing that Leibniz's monads may, in a perfectly reasonable sense, be spatially located.

Leibniz on Causation - Part 2

Leibniz is almost unique among early modern philosophers in giving final causation a central place in his metaphysical system. All changes in created substances, according to Leibniz, have final causes, that is, occur for the sake of some end. There is, however, no consensus among commentators about the details of Leibniz's views on final causation. The least perfect types of changes that created substances undergo are especially puzzling because those changes seem radically different from paradigmatic instances of final causation. Building on my more general discussion of efficient and final causation in ‘Leibniz on Causation – Part 1,’ I will examine and assess some of the rival interpretations of Leibniz's account of final causation.

Leibniz on Causation – Part 1

AbstractLeibniz holds that created substances do not causally interact with each other but that there is causal activity within each such creature. Every created substance constantly changes internally, and each of these changes is caused by the substance itself or by its prior states. Leibniz describes this kind of intra‐substance causation both in terms of final causation and in terms of efficient causation. How exactly this works, however, is highly controversial. I will identify what I take to be the major interpretive issues surrounding Leibniz's views on causation and examine several influential interpretations of these views. In ‘Leibniz on Causation – Part 2’ I will then take a closer look at final causation.

LA TESIS DE LA ELECCIÓN DIVINA DE LO ÓPTIMO: UNA EXCEPCIÓN EN LA TEORÍA MODAL DE LEIBNIZ

La proposición "Dios elige lo mejor" constituye una verdad incuestionable para Leibniz, y una premisa fundamental en su explicación de la existencia del mundo, tanto como en su teodicea. Leibniz sintió la necesidad de clarificar su carácter modal, dada la importancia de tal cuestión en relación con la libertad divina. Sin embargo, en el abordaje de este problema, se vio conducido a infringir los criterios de su propia teoría modal, con el fin de justificar la contingencia de tal proposición. Este trabajo intenta mostrar que la posición principal sostenida por Leibniz, en torno a la modalidad de esta proposición, constituye una suerte de excepción en el marco de su doctrina modal, y que esta ambigüedad refleja las razones profundas de las oscilaciones constatables en sus escritos sobre esta temática.

Time as Relative

AbstractPhilosophical development of Leibniz's view that time is merely earlier–later order is necessary because neither Leibniz nor modern followers sufficiently answered the Newtonian charge that order does not give quantity. Logically, order is transitive, quantity, as in distance, is not. Quantity, as well as order, is naturally assumed in Newton's absolute time, so that to declare the mere relative order sufficient is to have to show how quantity can arise for it. The modern theory of the continuum, perfectly applicable to Newton's absolute, does not show this but assumes quantity. The development given here shows how interval, instant and simultaneity can be logically developed from Leibniz's insight.

Leibniz and the Necessity of the Best Possible World

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 actualize 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 Section 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.

WHAT DID RUSSELL LEARN FROM LEIBNIZ?

Russell’s rejection in 1898 of the doctrine of internal relations — the view that all relations are grounded in the intrinsic properties of the terms related — was a decisive part of his break with Hegelianism and opened the way for his turn to analytic philosophy. Before rejecting it, Russell had given the doctrine little thought, though it played an essential role in the most intractable of the problems facing his attempt to construct a Hegelian dialectic of the sciences. I argue that it was Russell’s early reading of Leibniz, in preparation for his lectures on Leibniz given at Cambridge in 1899, that most probably alerted him to the role the doctrine was playing in his own philosophy. Leibniz defended a similar doctrine and extricated it from difficulties like those faced by Russell by means of devices that were not open to Russell. Russell would have come across these views of Leibniz in writings by Leibniz that he read in the summer of 1898, just before he rejected the doctrine of internal relations.ReferencesF. H. Bradley. Appearance and Reality. Oxford: Clarendon Press, 1968. Originally published 1893.Nicholas Griffin. Russell’s Idealist Apprenticeship. Oxford: Clarendon Press, 1991.Nicholas Griffin. Russell and Leibniz on the Classification of Propositions. In Ralf Krömer and Yannick Chin-Drian, editors, New Essays on Leibniz Reception. Basel, Birkhäuser, pp. 85–127, 2012.http://dx.doi.org/10.1007/978-3-0346-0504-5G. W. Leibniz. Die Philosophischen Schriften von Leibniz, 7 Volumes. Edited by C.I. Gerhardt. Berlin, Weidman, 1875–90.G. W. Leibniz. The Philosophical Works of Leibnitz. Edited by G.M. Duncan. New Haven, Tuttle, Morehouse and Taylor, 1890.G. W. Leibniz. New Essays Concerning Human Understanding, Translated by A.G. Langley. London, Macmillan, 1896.G. W. Leibniz. The Monadology and other Philosophical Writings. Edited by R. Latta. Oxford: Oxford University Press, 1898.G. W. Leibniz. Philosophical Papers and Letters, 2 Volumes. Edited by L.E. Loemker. Chicago, University of Chicago Press, 1956.G. W. Leibniz. New Essays Concerning Human Understanding, Translated and Edited by Peter Remnant and Jonathan Bennett. Cambridge, Cambridge University Press, 1981.Massimo Mugnai. Leibniz’ Theory of Relations. Stuttgart: Steiner, 1992.Massimo Mugnai. Leibniz’s Ontology of Relations: A Last Word?. In Oxford Studies in Early Modern Philosophy, Volume IV. Edited by Daniel Garber and Donald Rutherford. Oxford, Oxford University Press, 2012.http://dx.doi.org/10.1093/acprof:oso/9780199659593.001.0001Walter H. O’Briant. Russell on Leibniz. Studia Leibniziana, 11: 159–222, 1979.B. Russell. An Essay on the Foundations of Geometry. New York, Dover, 1956.B. Russell. My Philosophical Development. London, Allen and Unwin, 1959.B. Russell. The Principles of Mathematics. London: Allen and Unwin, 1964.B. Russell. The Monistic Theory of Truth. In Philosophical Essays New York, Simon and Schuster, pages 131–46, 1968.B. Russell. A Critical Exposition of the Philosophy of Leibniz. London, Allen and Unwin, 1975.B. Russell, The Collected Papers of Bertrand Russell, vol. 1, Cambridge Essays, 1888–99, edited by Kenneth Blackwell, et al. London, Allen and Unwin, 1983.B. Russell. The Collected Papers of Bertrand Russell, vol. 2, Philosophical Papers, 1896–99, edited by Nicholas Grif?n and Albert C. Lewis. London, Routledge, 1989a.B. Russell. On the Relations of Number and Quantity (1897). In Russell [1989a], pages 70–82, 1989b.B. Russell. An Analysis of Mathematical Reasoning (1898). In Russell [1989a], pages 163–241, 1989c.B. Russell. The Classification of Relations (1899), in Russell [1989a], pages 138–46, 1989d.B. Russell. The Fundamental Ideas and Axioms of Mathematics (1899). In Russell [1989a], pages 265–305, 1989e.B. Russell. The Collected Papers of Bertrand Russell, vol. 3, Towards “The Principles of Mathematics”, 1900–02, edited by Gregory H. Moore. London, Routledge, 1993a.B. Russell. The Principles of Mathematics, 1899–1900 Draft. In Russell [1993a], pages 13–180, 1993b.B. Russell. The Collected Papers of Bertrand Russell, vol. 11, Last Philosophical Testament, 1943–68. Edited by John G. Slater. London, Routledge, 1997.

‘A Series of Generations’: Leibniz on Race

Summary In some very interesting recent work, Peter Fenves has sought to trace G. W. Leibniz's views on human diversity back to the philosopher's core philosophical concerns, in particular to his metaphysical picture of the world as consisting in causally unconnected substances, monads, that are ‘windowless’, ‘worlds apart’. In this article I argue by contrast that Leibniz's anthropological views develop quite independently of his core metaphysics, and are rooted instead in his significant work as a historian and genealogist. In this connection, he develops a conception of race as a ‘series of generations’, and of genealogy as ‘the explication of this series’, that will in turn ground much of his thought about not just human groups, but about living kinds in general. These conceptions, moreover, offer significant new insight into Leibniz's position with respect to the philosophical problem of the ontological status of species.

Emilie du Châtelet on the Existence and Nature of God: An Examination of Her Arguments in Light of Their Sources

Many commentators have suggested that the metaphysical portions of Emilie du Châtelet's Institutions de physique are a mere retelling of Leibniz's views. I argue that a close reading of the text shows that du Châtelet's cosmological argument and discussion of God's nature contains both Lockean and Leibnizian elements. I discuss where she follows Locke in her arguments, what Leibnizian elements she brings in, and how this enables her to avoid some of the mistakes commonly attributed to Locke's formulation of the cosmological argument. I show that while du Châtelet accepts the causal principle ex nihilo nihil fit, she does not utilize Locke's stronger causal principle. I also discuss her use of the principle of sufficient reason in both improving the Lockean cosmological argument and in proving the attributes of God.

Disentangling Leibniz's Views on Relations and Extrinsic Denominations

Disentangling Leibniz's Views on Relations and Extrinsic Denominations Anja Jauernig (bio) 1. Introduction Most commentators agree that Leibniz advocates some version of a doctrine of the ideality or reducibility of relations, but there is considerable disagreement on the question of what exactly this doctrine is supposed to amount to. This question is pressing because of the central place that Leibniz's theory of relations occupies in his philosophy. How one understands Leibniz's views on relations will influence how one understands Leibniz's complete concept doctrine, his (super)essentialism, the principle of the identity of indiscernibles, his account of compossibility, and his theory of space and time, to name just a few examples.1 [End Page 171] The most divisive question in this context is whether Leibniz is what I will call a "reductionist," i.e., whether he advocates some form of "reductionism" about relations. There are several ways in which this question could be understood, depending on how the term 'reductionism' is explicated. A reductionist about relations could be said to hold that all there is in the world are individuals and their intrinsic properties, or that a complete description of the world is possible in purely non-relational terms, or that all relations and extrinsic properties (strongly) supervene on intrinsic properties—which are popular ways in which Leibniz's views on relations and extrinsic denominations have been interpreted. The question of whether Leibniz is a reductionist splits commentators into two camps: those who answer the question in the affirmative,2 and those who answer it in the negative.3 Despite much good work on this topic, the proponents of the two camps have been talking past each other to a considerable extent. One of the main factors [End Page 172] hampering the discussion is the widespread, if only implicit, assumption that there must be one unified thesis, or, at most, a small number of closely related theses, that Leibniz is trying to articulate in his various pronouncements on relations and extrinsic denominations. On my view, this assumption is clearly false.4 Another obstacle to exegetical progress is the frequent inadequate appreciation of Leibniz's division of reality into different ontological levels. The failure to take this level distinction into account tends to obscure the complex and multi-faceted nature of Leibniz's views on relations and extrinsic denominations. Once Leibniz's various theses about relations and extrinsic properties have been sorted out, it becomes clear that both camps of commentators are correct about some aspects of Leibniz's views, even though the overall flavor of Leibniz's position on relations remains non-reductionist. The argument of this paper will proceed as follows. Section 2 covers some preliminaries and background material, including a sketch of Leibniz's tiered ontology. In section 3, I discuss Leibniz's thesis of the ideality of abstract relations. Section 4 explicates the sense in which all phenomenal extrinsic properties can be reduced to the perceptions of monads, and addresses the question of whether monads have irreducibly extrinsic properties. In section 5, I analyze Leibniz's notorious claims that there are no purely extrinsic denominations and that every extrinsic denomination has a foundation in the thing denominated, which I take to be concerned primarily with the phenomenal level of reality. I argue that these claims do not commit Leibniz to reductionism, but they warrant ascribing to him five other weaker theses about extrinsic denominations and their relation to intrinsic denominations. In the sixth and final section, I revisit Leibniz's much discussed project of reformulating relational sentences into non-relational ones, and identify two more Leibnizian theses about relations and extrinsic properties. 2. Preliminaries and Background The main focus of this paper is on Leibniz's views on relations and extrinsic properties in his mature philosophy, which I take to have been in place by the mid-1680s, at least as far as its main doctrines and principles are concerned, several changes in emphasis and presentation style notwithstanding.5 An important step toward disentangling these views is a careful appreciation of Leibniz's division of reality into several ontological levels. This level-distinction is widely acknowledged in the literature, but there are different views...

Continental idealism: Leibniz to Nietzsche

Standard accounts of nineteenth-century German philosophy often begin with Kant and assess philosophers after him in light of their responses to Kantian idealism. In Continental Idealism, Paul Redding argues that the story of German idealism begins with Leibniz. Redding begins by examining Leibniz's dispute with Newton over the nature of space, time and God, and stresses the way in which Leibniz incorporated Platonic and Aristotelian elements in his distinctive brand of idealism. Redding shows how Kant's interpretation of Leibniz's views of space and time consequently shaped his own 'transcendental' version of idealism. Far from ending here, however, Redding argues that post-Kantian idealists such as Fichte, Schelling and Hegel on the one hand and metaphysical sceptics such as Schopenhauer and Nietzsche on the other continued to wrestle with a form of idealism ultimately derived from Leibniz. Continental Idealism offers not only a new picture of one of the most important philosophical movements in the history of philosophy, but also a valuable and clear introduction to the origins of Continental and European philosophy.

Remarks on Possibilia in Leibniz, 1672-1676

n a recent article Fabrizio Mondadori studies in detail the scholastic background for Leibniz's view of possibilia . Mondadori concludes that, sharply distinguishes between the question of the possibility, and the question of the reality, of possibilia , and explicitly suggests that the reality - but not the possibility - of possibilia depends on the (actual) existence of 1 The expression 'the possibility of possibilia' might seem a bit cumbersome for making a simple point, namely that possibility for Leibniz depends on the principle of contradiction alone, so that possibilities are defined by freedom from contradiction (or by self-consistency) and depend on nothing else. In particular, and against Descartes' voluntarist view of the eternal truths, for Leibniz, possibility is independent of God's will. According to Leibniz, God finds all possibilities fully formed in his understanding. This point provides a central premise in Leibniz's early reasoning in the confessio philosophi that God is not to be regarded as the Author of sin. Sins are understood and then permitted existence by God as part of the most harmonious series of things, but they are found (among the ideas of all things) in God's understanding and are not willed or made by God. Thus, Leibniz's God cannot make something possible impossible or vice versa. This is governed by purely logical considerations stemming from the law of contradiction. Even if indeed cumbersome, this terminology (the possibility of possibilia ) brings out some of the historical context (in its traditional jargon) and highlights the contrast with the question of the reality of possibilia . 2 The thesis that the reality of possibila depends on God means that, according to Leibniz, possibilities are not free floating or self-sufficient like platonic forms; rather, they are conceived in God's understanding and are among the objects of his understanding. This gives rise to a difficult question: if God does not think certain possibilities, are they to be considered possible or not? In somewhat different words, does it make sense to claim that God does not conceive certain possibilities, i.e., self-consistent concepts? While possibilities are certainly independent from God's will, and depend on the principle of contradiction, they do not seem to be entirely independent from some thinking agent. As Massimo Mugnai notes, there are no ideas without the intellectual activity of someone thinking (be it God or man or some other rational