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)

Leibniz and Kant were heirs of a biblical theistic tradition which viewed miraculous activity in the world as both possible and actual. But both were also deep explanatory rationalists about the natural world: more committed than your average philosophical theologian to its thoroughgoing intelligibility. These dual sympathies—supernaturalist religion and empirical rationalism—generate a powerful tension across both philosophers’ systems, one that is most palpable in their accounts of empirical miracles—that is, events in nature that violate one or more of the natural (...) laws. The primary goal of this chapter is to exhibit their respective efforts to resolve this tension, and to show how Kant’s noumenal ignorance doctrine allows him to set aside some key difficulties that Leibniz’s model leaves unresolved. The chapter concludes with the unorthodox suggestion that both systems leave conceptual space for the idea that finite free beings, rather than just God, can produce empirical miracles. (shrink)

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 proposed the ‘Most Determined Path Principle’ in seventeenth century. According to it, ‘ease’ of travel is the end purpose of motion. Using this principle and his calculus method he demonstrated Snell’s Laws of reflection and refraction. This method shows that light follows extremal (local minimum or maximum) time path in going from one point to another, either directly along a straight line path or along a broken line path when it undergoes reflection or refraction at plane or spherical (concave (...) or convex) surfaces. The extremal time path avoided the criticism that Fermat’s least time path was subjected to, by Cartesians who cited examples of reflections at spherical surfaces where light took the path of longest time. Thereby it became the standard method of demonstration of Snell’s Laws. Ptolemy’s theorem is a fundamental theorem in geometry. A special case of it offers a method of finding the minimum sum of the two distances of a point from two given fixed points. We show in this paper that Leibniz’s calculus proof of Snell’s Laws violates Ptolemy’s theorem, whereby Leibniz’s proof becomes invalid. (shrink)

This paper examines the origin, range and meaning of the Principle of Action and Reaction in Kant’s mechanics. On the received view, it is a version of Newton’s Third Law. I argue that Kant meant his principle as foundation for a Leibnizian mechanics. To find a ‘Newtonian’ law of action and reaction, we must look to Kant’s ‘dynamics,’ or theory of matter. I begin, in part I, by noting marked differences between Newton’s and Kant’s laws of action and reaction. I (...) argue that these are explainable by Kant’s allegiance to a Leibnizian mechanics. I show (in part II) that Leibniz too had a model of action and reaction, at odds with Newton’s. Then I reconstruct how Jakob Hermann and Christian Wolff received Leibniz’s model. I present (in Part III) Kant’s early law of action and reaction for mechanics. I show that he devised it so as to solve extant problems in the Hermann-Wolff account. I reconstruct Kant’s views on ‘mechanical’ action and reaction in the 1780s, and highlight strong continuities with his earlier, pre-Critical stance. I use these continuities, and Kant’s earlier engagement with post-Leibnizians, to explain the un-Newtonian features of his law of action and reaction. (shrink)

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. (shrink)

For years philosophers argued for the existence of distinct yet materially coincident things by appealing to modal and temporal properties. For instance, the statue was made on Monday and could not survive being flattened; the lump of clay was made months before and can survive flattening. Such arguments have been thoroughly examined. Kit Fine has proposed a new set of arguments using the same template. I offer a critical evaluation of what I take to be his central lines of reasoning.

This paper focuses on Leibniz’s conception of modality and its application to the issue of natural laws. The core of Leibniz’s investigation of the modality of natural laws lays in the distinction between necessary, geometrical laws on the one hand, and contingent, physical laws of nature on the other. For Leibniz, the contingency of physical laws entailed the assumption of the existence of an additional form of causality beyond mechanical or efficient ones. While geometrical truths, being necessary, do not require (...) the use of the principle of sufficient reason, physical laws are not strictly determined by geometry and therefore are logically distinct from geometrical laws. As a consequence, the set of laws that regulate the physical laws could have been created otherwise by God. However, in addition to this, the contingency of natural laws does not consist only in the fact that God has chosen them over other possible ones. On the contrary, Leibniz understood the status of natural laws as arising from the action internal to physical substances. Hence the actuality of physical laws results from a causal power that is inherent to substances rather than being the mere consequence of the way God arranged the relations between physical objects. Focusing on three instances of Leibniz’s treatment of contingency in physics, this paper argues that, in order to account for the contingency of physical laws, Leibniz maintained that final causes, in addition to efficient and mechanical ones, must operate in physical processes and operations. (shrink)

A standard strategy for defending a claim of non-identity is one which invokes Leibniz’s Law. (1) Fa (2) ~Fb (3) (∀x)(∀y)(x=y ⊃ (∀P)(Px ⊃ Py)) (4) a=b ⊃ (Fa ⊃ Fb) (5) a≠b In Kalderon’s view, this basic strategy underlies both Moore’s Open Question Argument (OQA) as well as (a variant formulation of) Frege’s puzzle (FP). In the former case, the argument runs from the fact that some natural property—call it “F-ness”—has, but goodness lacks, the (2nd order) property of its (...) being an open question whether everything that instantiates it is good to the conclusion that goodness and F-ness are distinct. And in the latter case, the argument runs from the fact that that Hesperus has, but Phosphorus lacks, the property of being believed by the ancient astronomers to be visible in the evening sky to the conclusion that Hesperus and Phosphorus are distinct. Kalderon argues that both the OQA and FP fail because in neither case is there good reason to believe that both (1) and (2) are true. The reason we are tempted to believe that they are true is because we mistake de dicto claims for de re claims. In order for FP to go through, the truth of the following de re claims needs to be established: FP1) Hesperus was believed by the ancient astronomers to be visible in the evening sky. (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)

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)

Explications of the reconstruction of Leibniz’s metaphysics that Deleuze undertakes in 'The Fold: Leibniz and the Baroque' focus predominantly on the role of the infinitesimal calculus developed by Leibniz.1 While not underestimat- ing the importance of the infinitesimal calculus and the law of continuity as reflected in the calculus of infinite series to any understanding of Leibniz’s metaphysics and to Deleuze’s reconstruction of it in The Fold, what I propose to examine in this paper is the role played by other (...) developments in mathematics that Deleuze draws upon, including those made by a number of Leibniz’s near contemporaries – the projective geometry that has its roots in the work of Desargues (1591–1661) and the ‘proto-topology’ that appears in the work of Du ̈rer (1471–1528) – and a number of the subsequent developments in these fields of mathematics. 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. What is provided in this paper 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)

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)

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)

This dynamical interpretation of the continuum is based on a threefold perspective. First, detailed differentiation of all standard realms of Leibnizian Weltanschauung – (R real), (P phenomenal), (I ideal). Second, analysis of the scope of the Law of Continuity famously formulated by Leibniz and mapping it onto this (RPI) structure. Third, finding the precise place of dynamics and force in this (RPI) continuum.

Leibniz claimed that the universe, if God-created, would be physically and morally optimal in this conjoint sense: Of all possible worlds, it would be richest in phenomena, but its richness would arise from the simplest physical laws and conditions. This claim raises two difficult questions. First, why would this “richest/simplest” world be morally optimal? Second, what is the optimal balance between these competing criteria? The latter question is especially hard to answer in the context of a multiverse or multi-domain universe. (...) Leibniz focused on goodness as God’s motive in creation. “This is the cause of the existence of the best: that his wisdom makes it known to God, his goodness makes him choose it, and his power lets him produce it.” This article suggests that love is God’s motive. Since love entails acting to both benefit and be with the beloved, limitless love would entail God’s becoming as much unified reality as possible. The physical laws that govern the universe and its vast richness of phenomena appear to be those that we should expect if this claim is true and there are ways of testing the closeness of this fit. The claim that God has become the world (pandeism) also offers a satisfying resolution to the problem of evil. (shrink)

SUMMARYThis article investigates the context of a side line in Leibniz's critique of Locke on maxims. In an enigmatic and little-explored remark, Leibniz objects that Locke has overlooked some legal maxims that fulfil the function of ‘constituting the law’. I propose to read this remark against the background of the divergence between conceptions of legal maxims in the common law tradition and conceptions of legal maxims in the Roman law tradition. In a few remarks, Locke seems to echo the (...) common law emphasis on customs and conventions expressed by legal maxims. According to such a conception, reason would mainly fulfil the function of subsuming particular norms under more general conventional norms. By contrast, Leibniz uses the Roman law idea that some ‘rules of law’ express demands of natural reason and, thereby, express principles constitutive of natural law. This is why he proposes to reform vague and confused ‘brocards’ used by jurists in order to identify sound maxims that provide a natural-law foundation for legal institutions. (shrink)

Leibniz was born near the conclusion of the chaotic period of the Thirty Years War. He studied law and then spent much of his life in the service of nobility and royalty, particularly the House of Hanover that assumed the British Crown a few years before his death. Best known for his works on metaphysics, mathematics, and logic, Leibniz's extensive political correspondence and writings concerned the foundations of law, local and international political affairs and social problems, and moral and (...) political philosophy. (shrink)

The advance of mechanism in science and philosophy in the 17th century created a great interest to machines or automata. Leibniz was no exception - in an early memoir Drôle de pensée he wrote admiringly about a machine that could walk on water, exhibited in Paris. The idea of automatic processing in general had a large role in his thought, as can be seen, for example, in his invention of the binary code and the so-called Calculemus!-model for solving controversies. In (...) metaphysics, the idea of an automata was expressed most clearly in the 1695 article New System of the Nature of Substances and their Communication, and the ensuing correspondence with, among others, Foucher, Bayle, Lamy, Jaquelot and Masham. In the article Leibniz discusses the soul as a spiritual machine in the context of pre-established harmony, arguing that God can "give to a substance at the outset a nature or internal force which could produce in it an orderly way (as in spiritual or formal automaton; but a free one, in the case of a substance which is endowed with a share of reason) everything that is going to happen to it, that is to say, all the appearances or expressions it is going to have, and all without the help of any created thing." The basic idea of Leibniz's spiritual machine is that the soul or entelechy is an autonomous and spontaneous unity, consisting of internal active force and producing its own perceptions (both confused and distinct). It is a self-moving machine, driven by its perceptions and appetites, but it follows (without being conscious of it) a lawful series or programme created by God. The entelechy remains the same despite undergoing an infinite number of changes. To Foucher he explained that each state of the individual substance is a consequence of its preceding one, "as if there were only God and the substance in the world". Despite this, the spiritual machine is related not only to God, but through the pre-established harmony to bodies or natural machines. However, as it is not dependent on them, the spiritual machine is superiot to natural machines. In this paper I concentrate on three moral themes related to the spiritual machine: moral deliberation, moral identity and the goal of moral action. All these themes are more or less implicit in the New System, but are discussed in more detail in the ensuing correspondence after the publication of the article. Finally, the themes are given an extended discussion especially in the second book of New Essays on Human Understanding (1704, published 1765), written partly at the same time as some of the correspondence and unpublished related material. I will first give an overview of Leibniz's position concerning the spiritual machine or automaton in the New System and then go on to explore the three moral themes one by one, as they feature in the subsequent correspondence and in the New Essays. I will show that the three topics are essential to the function of the spiritual machine – to Sophie Charlotte Leibniz wrote: "...let us say that everything in bodies happens mechanically, or in accordance with laws of motion, and that everything in the soul happens morally, or in accordance with perceived good or evil." There are many texts that anticipate the views in the New System (notably the unpublished memoir De Affectibus of 1679) and Leibniz continued to discuss its themes later on (in addition to correpondence, for example, in Theodicy of 1710 and Monadology and Principles of Nature and Grace of 1714). Here I focus on the short-term development of Leibniz's views on the topic (around 1695-1705), but I argue that his basic view of the spiritual machine did not change much after finishing the dialogue with Locke in 1704. (shrink)

Photomechanical reprint of papers from 1970 to 1992 mostly in English, some in German or French: Foreword 1–4; LAW AS PRACTICE ‘La formation des concepts en sciences juridiques’ 7–33, ‘Geltung des Rechts – Wirksamkeit des Rechts’ 35–42, ‘Macrosociological Theories of Law’ 43–76, ‘Law & its Inner Morality’ 77–89, ‘The Law & its Limits’ 91–96; LAW AS TECHNIQUE ‘Domaine »externe« & domaine »interne« en droit’ 99–117, ‘Die ministerielle Begründung’ 119–139, ‘The Preamble’ 141–167, ‘Presumption & Fiction’ 169–185, ‘Legal Technique’187–198; LAW AS LOGIC (...) ‘Moderne Staatlichkeit und modernes formales Recht’ 201–207, ‘Heterogeneity & Validity of Law’ 209–218, ‘Leibniz & die Frage der rechtlichen Systembildung’ 219–232, ‘Law & its Approach as a System’ 233–255, ‘Logic of Law & Judicial Activity’ 258–288, ‘Kelsen’s Pure Theory of Law’ 289–293, ‘The Nature of the Judicial Application of Norms’ 295–314; LAW AS EXPERIENCE ‘The Socially Determined Nature of Legal Reasoning’317–374, ‘The Ontological Foundation of Law’ 375–390, ‘Is Law a System of Enactments?’ 391–398, ‘The Uniqueness of National Legal Cultures’ 399–411, ‘Institutions as Systems’ 413–424; LAW AS HISTORY ‘From Legal Customs to Legal Folkways’ 427–436, ‘Anthropological Jurisprudence?’ 437–457, ‘Law as a Social Issue’ 459–475, ‘Law as History?’477–484, ‘Rechtskultur – Denkkultur’ 485–489; w/ Curriculum Vitae & Bibliography, as well as Index & Indexes of normative materials & of names. (shrink)

Gottfried Wilhelm Leibniz (1646–1716) was a universal genius, making original contributions to law, mathematics, philosophy, politics, languages, and many areas of science, including what we would now call physics, biology, chemistry, and geology. By profession he was a court counselor, librarian, and historian, and thus much of his intellectual activity had to be fit around his professional duties. Leibniz’s fame and reputation among his contemporaries rested largely on his innovations in the field of mathematics, in particular his discovery of the (...) calculus in 1675. Another of his enduring mathematical contributions was his invention of binary arithmetic, though the significance of this was not recognized until the 20th century. These days, a good proportion of scholarly interest in Leibniz is focused on his philosophy. Among his signature philosophical doctrines are the pre-established harmony, the theory of monads, and the claim that ours is the best of all possible worlds, which forms the central plank of his theodicy. For Leibniz, philosophy was not the discovery of deep truths of interest only to other philosophers, but a practical discipline with the means to increase happiness and well-being. Philosophical truths, he believed, revealed the beauty and rational order of the universe, and the justice and wisdom of its creator, and accordingly could inspire contentment and peace of mind. Leibniz’s other intellectual projects were likewise geared toward the improvement of the human condition. He lobbied tirelessly for the establishment of scientific societies, devised measures to improve public health, and was actively engaged in projects to unite the churches and so end the religious strife that marred the Europe of his day. He was also engaged in politics for much of his career, and often took on a diplomatic role, sometimes officially and other times not. In the political sphere, Leibniz did not wield true power but was a man with influence, obtained in no small part by his cultivation of relationships with leaders and sovereigns both inside and outside Germany. The sheer range of Leibniz’s interests, projects, and activities can make him a difficult figure to study, and the vast quantity of his writings only compounds the problem (around fifty thousand of his writings survive). Nevertheless, even a sampling of Leibniz’s work is enough to get a sense of his vision, originality, and intellectual depth, and good secondary literature will only enhance this. The items in this bibliography were chosen with this in mind. (shrink)

This paper argues for an interpretation of Leibniz’s claim that physics requires both mechanical and teleological principles as a view regarding the interpretation of physical theories. Granting that Leibniz’s fundamental ontology remains non-physical, or mentalistic, it argues that teleological principles nevertheless ground a realist commitment about mechanical descriptions of phenomena. The empirical results of the new sciences, according to Leibniz, have genuine truth conditions: there is a fact of the matter about the regularities observed in experience. Taking this stance, however, (...) requires bringing non-empirical reasons to bear upon mechanical causal claims. This paper first evaluates extant interpretations of Leibniz’s thesis that there are two realms in physics as describing parallel, self-sufficient sets of laws. It then examines Leibniz’s use of teleological principles to interpret scientific results in the context of his interventions in debates in seventeenth-century kinematic theory, and in the teaching of Copernicanism. Leibniz’s use of the principle of continuity and the principle of simplicity, for instance, reveal an underlying commitment to the truth-aptness, or approximate truth-aptness, of the new natural sciences. The paper concludes with a brief remark on the relation between metaphysics, theology, and physics in Leibniz. (shrink)

We investigate the structure common to causal theories that attempt to explain a (part of) the world. Causality implies conservation of identity, itself a far from simple notion. It imposes strong demands on the universalizing power of the theories concerned. These demands are often met by the introduction of a metalevel which encompasses the notions of 'system' and 'lawful behaviour'. In classical mechanics, the division between universal and particular leaves its traces in the separate treatment of cinematics and dynamics. This (...) analysis is applied to the mechanical theories of Newton and Leibniz, with some surprising results. (shrink)

Kant and Leibniz are interested in explaining how a number of individuals can come together and form a single unified composite substance. Leibniz does not have a convincing account of how this is possible. In his pre-critical writings and in his later metaphysics lectures, Kant is committed to the claim that the idea of a world is the idea of a real whole, and hence is the idea of a composite substance. This metaphysical idea is taken over into his ethical (...) writings and becomes the idea of a realm of ends. I explain why a realm of ends, should be thought of as both a unum per se and as a real whole. A realm of ends is a whole of individuals unified by laws they have given themselves, that is, it is a community of autonomous individuals. Only such a community can be thought of as a composite individual. Such a whole will be real rather than ideal because the source of the unity of the whole is intrinsic to the whole, for what gives unity to the realm are laws and the sources of the laws are the individual members of the whole. It will be a unum per se because both the laws and the individuals constituting the realm are incomplete without one another. If this reading is correct, this requires a fundamental reevaluation of Kant’s notion of autonomy. To be autonomous is not, primarily, to be understood in terms of ruling oneself, but instead must be thought of primarily in terms of being a generative source of laws for an ideal community. (shrink)

In the autumn of 1667, the young Leibniz published a «new method» for the science of law. Producing a revised edition of that early work was to become his lifelong project, to the purpose of which he wrote, in the 1690s, a succession of new versions of most of its sections. The main reason for this enduring interest was probably the fact that the juridical part of the treatise was preceded with a more general one, encapsulating in a few pages (...) a systematic overview of the disciplines composing the baroque encyclopaedia, after the model of Johann Heinrich Alsted’s monumental Encyclopaedia septem tomis distincta. If Leibniz still depended on Alsted’s notion of philosophy as the «circle of disciplines», he deeply transformed that pre-Cartesian conception of knowledge by two decisive innovations: following Bacon, he defines each branch of demonstrative science as bearing on one single «quality», abstracted from the subjects in which it inheres; yet, contrary to Bacon, he no longer conceives of these qualities as the ultimate components of reality, but as those of our experience of it, marking the limit of the explanatory capacity of language. (shrink)

Apart from his critique of Kant, Maimon’s significance for the history of philosophy lies in his crucial role in the rediscovery of Spinoza by the German Idealists. Specifically, Maimon initiated a change from the common eighteenth-century view of Spinoza as the great ‘atheist’ to the view of Spinoza as an ‘acosmist’, i.e., a thinker who propounded a deep, though unorthodox, religious view denying the reality of the world and taking God to be the only real being. I have discussed this (...) aspect of Maimon’s philosophy in other places, and though the topic of the current paper has an interesting relation to certain doctrines of Spinoza, I will not develop this issue here. Neither of these two issues -- Maimon’s criticism of Kant or his original interpretation of Spinoza -- was considered by Maimon as his main contribution to philosophy. There is little doubt that if Maimon were asked to point out his single most important innovation he would have picked his doctrine of the Principle of Determinability [Satz der Bestimmbarkeit]. Regarding this doctrine Maimon writes: ... [T]he principle of determinability laid down in this work is a principle of all objectively real thought, and consequently of philosophy as a whole too. All the propositions of philosophy can be derived from, and be determined by it [woraus sich alle Sätze herleiten und wodurch sie sich bestimmen lassen]. … I have made available a supreme principle of all objectively real thought, viz., the principle of determinability... and have established as the ground of the whole of pure philosophy -- a principle which, if it is ever grasped, will, I hope, withstand every scrutiny. These claims may strike the reader as somewhat presumptuous, to say the least. But, if we pay attention to the last sentence of the passage, we can see that Maimon doubts whether his great finding will ever be understood. It is not unlikely that in this phrase (“wenn er nur einmal eingesehen werden wird”) Maimon was reacting to his own repeatedly unsuccessful attempts to explain the principle. The fate of Maimon’s principle has not been much better in the few works written on Maimon’s philosophy, and though almost all commentators agree that the principle of determinability is the linchpin of the positive philosophy Maimon was trying to develop, we do not yet have a clear explanation of this principle, or of the reason why Maimon assigns such importance to it. Recently, Oded Schechter developed an excellent reading of this principle, and in most aspects my view agrees with his (primarily, in its rejecting the attempt to explain the principle as a version of Leibniz’s predicate-in-subject [Praedicatum inest subjecto] containment thesis). My paper consists of two parts. The first is expository in nature. In this part, I spell out briefly the main aspects of Maimon’s principle of determinability and its aims. In the second part, I examine Maimon’s surprising claim that once we accept the principle of determinability, we have to deny the possibility of two subjects sharing the same predicate. Maimon provides several proofs for this highly counterintuitive claim, and I will try to clarify and evaluate these proofs. (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)

The Argument of the “Perpetual Miracle” and its Theological Implications: on Leibniz-Malebranche Relationships. One of Leibniz’s strongest arguments against the Occasionalists is that, since they see all natural laws only as constant connections, Occasionalists are unable to distinguish a natural law from a constantly repeated miracle. The paper shows that Leibniz’s argument is not entirely adequate as a criticism of Malebranche, in that it stems from a theology that is quite different to that of Malebranche. For Malebranche, miracles are the (...) effects of God’s “particular will” and are quite different even from God’s legal distribution of Grace. A miracle ruled by a law is, therefore, a conceptual impossibility. To Leibniz, miracles include everything that overrules creatures and their forces. Miracles may thus be governed by laws and, indeed, all miracles performed by God in our world are regulated by the laws of Leibniz’s Kingdom of Grace. (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.

During 17th century a scientific controversy existed on the derivation of Snell’s laws of reflection and refraction. Descartes gave a derivation of the laws, independent of the minimality of travel time of a ray of light between two given points. Fermat and Leibniz gave a derivation of the laws, based on the minimality of travel time of a ray of light between two given points. Leibniz’s calculus method became the standard method of derivation of the two laws. We demonstrate in (...) this article that Snell’s law of reflection follows from simple results of geometry. We do not use the concept of motion or the time of travel in our demonstration. That is, time plays no role in our demonstration. (shrink)

There are at least five ‘core’ notions of community found in Kant's works: 1. The scientific notion of interaction. This concept is introduced in the Third Analogy and developed in the Metaphysical Foundations of Natural Science. 2. A metaphysical idea. The idea of a world of individuals (monads) in interaction. This idea was developed in Kant’s precritical period and can be found in his metaphysics lectures. 3. A moral ideal. The idea of a realm of ends. 4. A political ideal. (...) The idea of a juridical community (or community of communities) governed by juridical laws. 5. A theological ideal. What Kant calls ‘the kingdom of heaven’, and which can be thought of as a community of holy beings, or angels. In this paper I focus on the relationship between the first, second and fourth of these notions. My argument is that Kant’s notion of a juridical community governed by juridical laws is modelled on the metaphysical idea of the world. This metaphysical idea of a world is, in turn, modelled on the category of community introduced in the first Critique and developed in his logic lectures. (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.".

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)

There is an old and powerful argument for the claim that divine foreknowledge is incompatible with the freedom to do otherwise. A recent response to this argument, sometimes called the “dependence response,” centers around the claim that God’s relevant past beliefs depend on the relevant agent’s current or future behavior in a certain way. This paper offers a new argument for the dependence response, one that revolves around different cases of time travel. Somewhat serendipitously, the argument also paves the way (...) for a new reply to a compelling objection to the dependence response, the challenge from prepunishment. But perhaps not so serendipitously, the argument also renders the dependence response incompatible with certain views of providence. (shrink)

Suppose Molinism is true and God placed Adam in the garden because God knew Adam would freely eat of the fruit. Suppose further that, had it not been true that Adam would freely eat of the fruit, were he placed in the garden, God would have placed someone else there instead. When Adam freely eats of the fruit, is he free to do otherwise? This paper argues that there is a strong case for both a positive and a negative answer. (...) Assuming such cases are possible under Molinism, we are left with a puzzling question: if Molinism is true, what can you do? (shrink)

Let (leeway) incompatibilism be the thesis that causal determinism is incompatible with the freedom to do otherwise. Several prominent authors have claimed that incompatibilism alone can capture, or at least best captures, the intuitive appeal behind Jorge Luis Borges's famous “Garden of Forking Paths” metaphor. The thought, briefly, is this: the “single path” leading up to one's present decision represents the past; the forking paths that one must decide between represent those possible futures consistent with the past and the laws (...) of nature. But if determinism is true, there is only one possible future consistent with the past and the laws and, hence, only one path to choose from. That is, if determinism is true, then we are not free to do otherwise. In this paper, I argue that this understanding of the Garden of Forking Paths faces a number of problems and ought to be rejected even by incompatibilists. I then present an alternative understanding that not only avoids these problems but still supports incompatibilism. Finally, I consider how various versions of (leeway) compatibilism fit with the Garden of Forking Paths as well as the broader question of whether metaphors, however intuitive, have any dialectical force in the debates over freedom. (shrink)

Is the virtue of the good citizen the same as the virtue of the good man? Aristotle addresses this in Politics 3.4. His answer is twofold. On the one hand, (the account for Difference) they are not the same both because what the citizen’s virtue is depends on the constitution, on what preserves it, and on the role the citizen plays in it, and because the good citizens in the best constitution cannot all be good men, whereas the good man’s (...) virtue is uniform. On the other hand, (the account for Identity) the two virtues are identical in the good men in the best constitution, in which all are good citizens, each possessing the ability for ruling and for being ruled. This nuanced answer can be seen as Aristotle’s synthesis of a Periclean view (contribution to state blots out personal wrongs) and a Socratic view (no good citizen is without justice). Its nuances reflect the extent to which Aristotle’s conceptions of good citizenship and the best constitution accommodate deviations of what is probable from the human ideal set out in his ethical writings. In the present chapter, I will first address three puzzles regarding the nuances of Aristotle’s answer. Second, I will consider one question about its implication: Does Aristotle’s account for Difference turn out to entail something ultra-Periclean: that no one can simultaneously be a good man and a good citizen in any constitution other than the best? I shall argue the negative. (shrink)

Goodman and Lederman (2020) argue that the traditional Fregean strategy for preserving the validity of Leibniz’s Law of substitution fails when confronted with apparent counterexamples involving proper names embedded under propositional attitude verbs. We argue, on the contrary, that the Fregean strategy succeeds and that Goodman and Lederman’s argument misfires.

Libertarian views of freedom claim that, although determinism would rule out our freedom, we are nevertheless free on some occasions. An odd implication of such views (to put it mildly) seems to be that indeterminism somehow enhances or contributes to our agency. But how could that be? What does indeterminism have to offer agency? This paper develops a novel answer, one that is centred around the notion of explanation. In short, it is argued that, if indeterminism holds in the right (...) places, then the best explanation of the history of the world necessarily cites facts about our agency. Along the way, alternative proposals regarding the significance of indeterminism are considered and, ultimately, rejected in favour of the one developed in this paper. (shrink)

Recently, several authors have utilized the notion of dependence to respond to the traditional argument for the incompatibility of freedom and divine foreknowledge. However, proponents of this response have not always been so clear in specifying where the incompatibility argument goes wrong, which has led to some unfounded objections to the response. We remedy this dialectical confusion by clarifying both the dependence response itself and its interaction with the standard incompatibility argument. Once these clarifications are made, it becomes clear both (...) (1.) that the dependence response does not beg the question against the proponent of the incompatibility argument and (2.) that the dependence response advances the dialectic whether it is developed as a version of Ockhamism or as a version of multiple-pasts compatibilism. (shrink)

Review of Causation and Free Will by Carolina Sartorio, Oxford University Press, 2016. viii + 188 pp. £35.00.

In the TACITUS project for using commonsense knowledge in the understanding of texts about mechanical devices and their failures, we have been developing various commonsense theories that are needed to mediate between the way we talk about the behavior of such devices and causal models of their operation. Of central importance in this effort is the axiomatization of what might be called commonsense metaphysics. This includes a number of areas that figure in virtually every domain of discourse, such as granularity, (...) scales, time, space, material, physical objects, shape, causality, functionality, and force. Our effort has been to construct core theories of each of these areas, and then to define, or at least characterize, a large number of lexical items in terms provided by the core theories. In this paper we discuss our methodological principles and describe the key ideas in the various domains we are investigating. (shrink)

I show that intuitive and logical considerations do not justify introducing Leibniz’s Law of the Indiscernibility of Identicals in more than a limited form, as applying to atomic formulas. Once this is accepted, it follows that Leibniz’s Law generalises to all formulas of the first-order Predicate Calculus but not to modal formulas. Among other things, identity turns out to be logically contingent.

In a series of articles, Kit Fine presents some highly compelling objections to monism, the doctrine that spatially coincident objects are identical. His objections rely on Leibniz’s Law and linguistic environments that appear to be immune to the standard charge of non-transparency and substitution failure. In this paper, I respond to Fine’s objections on behalf of the monist. Following Benjamin Schnieder, I observe that arguments from Leibniz’s Law are valid only if they involve descriptive, rather than metalinguistic, negation. Then I (...) show that the monist is justified in treating the negation in Fine’s objections as metalinguistic in nature. Along the way I make a few methodological remarks about the interaction between the study of natural language and metaphysics. I also present evidence that some of the linguistic environments which Fine relies on are, contrary to appearances, non-transparent. (shrink)