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)

Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.

Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.

The article is an investigation of a certain form of argument that refers to Leibniz’s Law as its inference ticket (where Leibniz’s Law is understood as the thesis that if x=y.

Stage theorists invoke the idea of counterpart relations to make sense of how objects are able to persist despite their claim that an object is identical with a single instantaneous stage. According to stage theorists, an object persists if and only if it has a later counterpart that bears the appropriate counterpart relation of identity to it. Whilst objects can and do persist, stages cannot and do not. This seems to amount to a refutation of Leibniz’s law. Stage theorists think (...) that the nature of the counterpart relation invoked depends on how it is that the object is referred to. In this paper, I argue that the context sensitivity that they invoke here gives stage theorists a response to the Leibniz’s Law Problem. (shrink)

Leibniz’s Law (or as it sometimes called, ‘the Indiscerniblity of Identicals’) is a widely accepted principle governing the notion of numerical identity. The principle states that if a is identical to b, then any property had by a is also had by b. Leibniz’s Law may seem like a trivial principle, but its apparent consequences are far from trivial. The law has been utilised in a wide range of arguments in metaphysics, many leading to substantive and controversial conclusions. This article (...) discusses the applications of Leibniz’s Law to arguments in metaphysics. It begins by presenting a variety of central arguments in metaphysics which appeal to the law. The article then proceeds to discuss a range of strategies that can be drawn upon in resisting an argument by Leibniz’s Law. These strategies divide into three categories: (i) denying Leibniz’s Law; (ii) denying that the argument in question involves a genuine application of the law; and (iii) denying that the argument’s premises are true. Strategies falling under each of these three categories are discussed in turn. (shrink)

The Philosophical Review, Vol. XCVI, No. 4 (October 1987). Categorically proves that Leibniz's Law (the principle that any instance of _for any x and y, if x=y, then if ...x..., then ..y..._ is true) is not a principle of which is true of natural language objectual quantification.

Moderate composition as identity holds that there is a generalized identity relation, “being the same portion of reality,” of which composition and numerical identity are distinct species. Composition is a genuine kind of identity; but unlike numerical identity, it fails to satisfy Leibniz’s Law. A composite whole and its parts differ with respect to their numerical properties: the whole is one; the parts (collectively) are many. Moderate composition as identity faces the challenge: how, in the absence of Leibniz’s Law, can (...) one characterize what counts as a genuine kind of identity? This paper explores a promising answer: a genuine kind of identity must satisfy a version of Leibniz’s Law restricted to properties that ascribe qualitative character. Strong composition as identity holds that there is only one identity relation, that it satisfies Leibniz’s Law, and that the parts are identical with the whole that they compose. Strong composition as identity faces the challenge of showing that numerical properties do not provide counterexamples to Leibniz’s Law, and doing so in a way that is compatible with the framework of plural logic that is needed to formulate the theory. The most promising way to do this is to hold that plural logic is fundamental at the level of our representations, but not fundamental at the level of being. At the level of being, portions of reality cannot be characterized as either singular or plural. It turns out that the proposed moderate theory and the proposed strong theory are one and the same. In spite of its many attractions, I reject it. The main issue has to do with whether slice-sensitive emergent properties are possible. I argue that they are, making use both of specific examples and general principles of modal plenitude. I do not claim that my arguments are irresistible. But they cannot be evaded as easily as a related argument against strong composition as identity given by Kris McDaniel. I critically examine McDaniel’s argument to pave the way for my own. (shrink)

We draw some metaphysical conclusions about colour and belief from some epistemological commonplaces. It turns out that this requires us to challenge orthodoxy on the causal efficacy of mental properties and to rewrite the standard argument against dualism, but in a way which is good news for functionalists about the mind.

Professor arthur prior has argued that because one thing can become two things we must abandon leibniz's law. ("time, Existence and identity" in 'papers on time and tense', Oxford, 1968). I argue that while it does often happen that one thing becomes two things, We need not say that in such cases one thing is identical with both the things it becomes. Fission need not be seen as preserving identity. Hence prior does not provide us with adequate reasons for (...) abandoning leibniz's law. (shrink)

Since Leibniz first put forward the sufficient reason law in his philosophical work "The Monadology" (1914), the issue of the law of sufficient reason has aroused heated discussions in the field of logic in our country. The question of whether the law of sufficient reason is the basic law of formal logic was particularly heated in the domestic logic circle in 1978-1980. Since then, there has been little discussion, but from the newly compiled formal logic textbooks published one after another, (...) no consensus has been reached. Although they didn't agree on the question of "whether or not", the two sides elaborated their arguments in detail and put forward some new opinions, thus creating new conditions for solving this problem scientifically. Firstly, this paper analyzes the different viewpoints of both sides of the argument. Secondly, it analyzes whether the law of sufficient reason is the basic law of formal logic from whether Leibniz put forward the law of sufficient reason. Finally, on this basis, a new transformation method is put forward. After this transformation, the law of sufficient reason is an important basic law of deductive logic, which can be juxtaposed with the other three logical laws, such as identity, and coordinated with the "three laws" and complement each other. (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.

The indiscernibility of identicals is incompatible with geach's theory of 'relative' identity, But consistent with the view that x is identical with y iff x is the same a as y, For some count-Noun 'a'. 'x is the same a as y' expresses identity only if x is an a, Otherwise it is merely an equivalence relation.

Neil Feit; Graduate Papers from the Joint Session 1995: On a Famous Counterexample to Leibniz's Law1, Proceedings of the Aristotelian Society, Volume 96, Issue.

This is the first volume compiling English translations of Leibniz's journal articles on natural philosophy, presenting a selection of 26 articles, only three of which have appeared before in English translation. It also includes in full Leibniz's public controversies with De Catelan, Papin, and Hartsoeker. The articles include work in optics, on the fracture strength of materials, and on motion in a resisting medium, and Leibniz's pioneering applications of his calculus to these issues by construing them as (...) mini-max and inverse tangent problems. Other topics covered by the articles include: criticisms of the Cartesian estimate of motive force and Leibniz's proposal of a different way of estimating force to replace it; a proposed theory of celestial motions and gravitation, and derivation of the inverse square law; challenge problems concerning the isochronous curve and the catenary; a sample of work on gaming theory; and Leibniz's critique of atomism. (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)

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)

(Accepted for an edition of Synthese that never saw light of day, and remained on my website. Written 2005.) Noting the status of the Law of Continuity as one of Leibniz’s most cherished axioms, Bertrand Russell charged that his philosophy nevertheless amounted to “a complete denial of the continuous”. Georg Cantor made a similar accusation of inconsistency about Leibniz’s philosophy of the actual infinite. But I argue that neither doctrine is inconsistent when the subtleties of Leibniz’s syncategorematic interpretation are properly (...) taken into account. Leibniz rejects the existence of infinite wholes: an infinite aggregate of actual things forms only a fictitious whole. Analogously, infinitesimals are only fictitious parts, this time of ideal wholes. That is, just as an actual infinity of terms can be understood syncategorematically as more terms than can be assigned a number, without there being any infinite numbers, so too the infinitely small can be given a syncategorematic interpretation by means of the Law of Continuity, without there existing any actual infinitesimals. By examining Leibniz’s justification of infinitesimals in his calculus, I argue that the syncategorematic interpretation is also applicable to series of changes, and thus exonerates Leibniz from Russell’s criticism: on this interpretation all naturally occurring transitions are continuous in that the difference between neighbouring states is smaller than any assignable. This means not that there exists a least difference, but that for any assignable finite difference, there exists a smaller one. Thus there is a true continuous transition, even though the states themselves and all assignable differences between them are actually discrete. (shrink)

Two of Leibniz's most studied and often quoted works appear in this volume. Published in 1686, the Discourse on Metaphysics consists of the philosopher's explanation of individual perception as an expression of the rest of the universe from a unique perspective. The whole world--the best of all possible worlds, as he famously remarks--is thus contained in each individual substance. The Monadology, written in 1714, offers a concise synopsis of Leibniz's philosophy, establishing the laws of final causes, which underlie (...) God's free choice to create the best possible world--a world that serves as dynamic and perfectly ordered evidence of the wisdom of its creator. Translated by George R. Montgomery. (shrink)

An English translation of Gottfried Wilhelm Leibniz's 1669 compilation Doctrina Conditionum.

Leibniz’s mature philosophical understanding of the laws of nature emerges rather suddenly in the late 1670’s to early 1680’s and is signaled by his embrace of three central theses.1 The first, what I’ll call the thesis of Contingency, suggests that the laws of nature are not only contingent, but, in some sense, paradigmatically contingent; they are supposed to provide insight into the very nature of contingency as Leibniz comes to understand it. The second, what I’ll call the thesis of Providence, (...) suggests that the laws of nature provide a basis for a new argument from design by showing how reflection on God’s ends can be positively useful in the practice of natural philosophy. The third, what I’ll call thesis of .. (shrink)

In this paper, we endeavour to give a historically accurate presentation of how Leibniz understood his infinitesimals, and how he justified their use. Some authors claim that when Leibniz called them “fictions” in response to the criticisms of the calculus by Rolle and others at the turn of the century, he had in mind a different meaning of “fiction” than in his earlier work, involving a commitment to their existence as non-Archimedean elements of the continuum. Against this, we show that (...) by 1676 Leibniz had already developed an interpretation from which he never wavered, according to which infinitesimals, like infinite wholes, cannot be regarded as existing because their concepts entail contradictions, even though they may be used as if they exist under certain specified conditions—a conception he later characterized as “syncategorematic”. Thus, one cannot infer the existence of infinitesimals from their successful use. By a detailed analysis of Leibniz’s arguments in his De quadratura of 1675–1676, we show that Leibniz had already presented there two strategies for presenting infinitesimalist methods, one in which one uses finite quantities that can be made as small as necessary in order for the error to be smaller than can be assigned, and thus zero; and another “direct” method in which the infinite and infinitely small are introduced by a fiction analogous to imaginary roots in algebra, and to points at infinity in projective geometry. We then show how in his mature papers the latter strategy, now articulated as based on the Law of Continuity, is presented to critics of the calculus as being equally constitutive for the foundations of algebra and geometry and also as being provably rigorous according to the accepted standards in keeping with the Archimedean axiom. (shrink)

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)

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis, (...) as propounded by John Bell. I find some salient differences, especially with regard to higher-order infinitesimals. I illustrate these differences by a consideration of how each approach might be applied to propositions of Newton’s Principia concerning the derivation of force laws for bodies orbiting in a circle and an ellipse. “If the Leibnizian calculus needs a rehabilitation because of too severe treatment by historians in the past half century, as Robinson suggests (1966, 250), I feel that the legitimate grounds for such a rehabilitation are to be found in the Leibnizian theory itself.”—(Bos 1974–1975, 82–83). (shrink)

entry for the Stanford Encyclopedia of Philosophy (SEP) This entry will attempt to provide a broad overview of the central themes of Leibniz’s philosophy of physics, as well as an introduction to some of the principal arguments and argumentative strategies he used to defend his positions. It tentatively includes sections entitled, The Historical Development of Leibniz’s Physics, Leibniz on Matter, Leibniz’s Dynamics, Leibniz on the Laws of Motion, Leibniz on Space and Time. A bibliography arranged by topic is also included. (...) A working draft is available here (comments, as always welcome): draft. (shrink)

Leibniz speaks, in a variety of contexts, of there being two realms—a "kingdom of power or efficient causes" and "a kingdom of wisdom or final causes." This essay explores an often overlooked application of Leibniz's famous "two realms doctrine." The first part turns to Leibniz's work in optics for the roots of his view that nature can be seen as being governed by two complete sets of equipotent laws, with one set corresponding to the efficient causal order of (...) the world, and the other to its teleological order. The second part offers an account of how this picture of lawful over-determination is to be reconciled with Leibniz's mature metaphysics. The third addresses a line of objection proposed by David Hirschmann to the effect that Leibniz's doctrine undermines his stated commitment to an efficient, broadly mechanical account of the natural world. Finally, the fourth part suggests that Leibniz's thinking about the harmony of final and efficient causes in connection with corporeal nature may help to shed light on his understanding of the teleological unfolding of monads as well. (shrink)

Leibniz’s Méditation sur la notion commune de la justice is his most important writing on justice as “wise charity” and “universal benevolence” ; we now observe the 300th anniversary of its composition, and a reproduction of part of Leibniz’s manuscript appears in the Appendix to this article. But Leibniz’s essay might with equal justice be called, “Meditation on the Common Notion of Platonism”—for the Méditation opens with a nearly-verbatim paraphrase of Euthyphro 9e-10e, moves on to reduce Hobbes to Thrasymachus in (...) Republic Book I, and ends with Platonic “ascent,” in the manner of Phaedrus and Symposium, from mere negative forbearance from harm to justice as wise love, caritas, Roman-law honeste vivere, and benevolent “aid to others”—as in Augustine’s Platonizing De Civitate Dei XIX). (shrink)

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)

Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, (...) Robinson regards Berkeley’s criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley’s criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz’s infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz’s defense of infinitesimals is more firmly grounded than Berkeley’s criticism thereof. We show, moreover, that Leibniz’s system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz’s strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity. (shrink)

Leibniz raises three main objections to the doctrine of occasionalism: (1) it is inconsistent with the supposition of finite substances; (2) it presupposes the occurrence of "perpetual miracles"; (3) it requires that God "disturb" the ordinary laws of nature. At issue in objection (1) is the proper understanding of divine omnipotence, and of the relationship between the power of God and that of created things. I argue that objections (2) and (3), on the other hand, derive from a particular conception (...) of the intelligibility of nature, a conception to which Leibniz is firmly committed and that occasionalists like Malebranche no less firmly reject. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Leibniz’s Political and Moral Philosophy in the Novissima Sinica, 1699–1999Patrick RileyThe Preface to Leibniz’s Novissima Sinica 1 contains an important but highly compressed and abbreviated quintessence of his theory of justice or jurisprudence universelle—a version so compressed and abbreviated that one must have a broader and fuller understanding of this universal jurisprudence before one can entirely appreciate what Leibniz has to say about Christian charity, Platonism, and geometry in (...) the Novissima Sinica itself. Above all, one wants to know why Leibniz, in the key paragraph of the Preface to Novissima Sinica, should describe the Chinese emperor as just and charitable and as a (more or less) “Platonic” geometer who is as wise as he is charitable. And why should Leibniz contrast this “wisely charitable” Chinese ruler with the Pontius Pilate who irresponsibly asked, “What is truth?” and then permitted the judicial murder of the very Christ who did most to make charity and justice coextensive by saying, “A new law I give unto you, that ye love one another”? 2 The wise course, therefore, is to throw enough light on Leibnizian universal jurisprudence in general to make his moral-political utterances in Novissima Sinica intelligible in particular.In 1693, four years before the publication of Novissima Sinica, Leibniz revealed the outlines of his jurisprudence universelle in the Codex Iuris Gentium:a good man is one who loves everybody, so far as reason permits. Justice, then, which is the virtue which regulates that affection which [End Page 217] the Greeks call philanthropy, will be most conveniently defined... as the charity of the wise man, that is, charity which follows the dictates of wisdom... Charity is a universal benevolence, and benevolence the habit of loving or of willing the good. Love then signifies rejoicing in the happiness of another..., the happiness of those whose happiness pleases us turns into our own happiness, since things which please us are desired for their own sakes. 3Slightly later, in La véritable piété, Leibniz indicated what this view of justice entails:those who... reduce justice to [mere] rigor, and who fail altogether to understand that one cannot be just without being benevolent... in a word, not only those who look for their profit, pleasure, and glory in the misery of others, but also those who are not at all anxious to procure the common good and to lift out of misery those who are in their care, and generally those who show themselves to be without enlightenment and without charity, boast in vain of piety which they do not know at all, whatever appearance they create. 4The central idea of Leibniz’s “universal jurisprudence,” which aims to find quasi-geometrical, eternal moral verities equally valid for all rational beings, human or divine, is that justice is “the charity of the wise” (caritas sapientis), 5 that it is not mere conformity to sovereign-ordained “positive” law given ex plenitudo potestatis (in the manner of Hobbes); nor is it mere “refraining from harm” or even “rendering what is due” (the neminem laedere and suum cuique tribuere of Roman law). 6 The equal stress on “charity” and on “wisdom” suggests that Leibniz’s practical thought is a kind of fusing of Platonism—in which the wise know the eternal truths such as absolute goodness (Phaedo 75d), which the gods themselves also know and love (Euthyphro 93-10e) and which therefore deserve to rule (Republic 443d-e) 7 —and of Pauline Christianity, whose key moral idea is that charity or love is the first of the virtues (“though I speak [End Page 218] with the tongues of men and of angels, and have not charity, I am become as sounding brass or a tinkling cymbal”). 8 Historically, there is nothing remarkable in trying to fuse Platonism and Christianity. Augustine’s thought (particularly the early De Libero Arbitrio) is just such a fusion. 9 But Leibniz was the last of the great Christian Platonists, and left the world just as Hume, Rousseau, and Kant were about to transform and “secularize” it.I. If one decomposes caritas sapientis into its parts, charity and wisdom, the provenance of both elements is clear enough... (shrink)

I have shown (to my satisfaction) that Leibniz's final attempt at a generalized syllogistico-propositional calculus in the Generales Inquisitiones was pretty successful. The calculus includes the truth-table semantics for the propositional calculus. It contains an unorthodox view of conjunction. It offers a plethora of very important logical principles. These deserve to be called a set of fundamentals of logical form. Aside from some imprecisions and redundancies the system is a good systematization of propositional logic, its semantics, and a correct (...) account of general syllogistics. For 1686 it was quite an accomplishment. It is a pity that Leibniz himself did not fully appreciate what he had achieved. It does seem to me that this was due in part, as the Kneales urge (Note 4), to his having kept the focus of his attention on traditional syllogistics. It is a great pity that he did not polish GI 195–200 for publication. The publication of GI 195, 198, and 200 would have most likely promoted further research. MAJR- Humanities, Social Sciences and Law. (shrink)

Larry Jorgensen aims to show that "Leibniz offers a fully natural theory of mind", recommending Leibniz to our contemporary discussion of naturalism. Readers of Leibniz will, however, hesitate to call him a naturalist. After all, he considered natural laws to be subordinated rules below general divine laws and rejected explaining the soul's action by bodily motion. Jorgensen does have a point, though, when he refers to Leibniz's frequent pleas for natural explanations and his continuity principle.Jorgensen's project unfolds in four (...) parts. The first offers a discussion of Leibniz's concept of nature and a clear presentation of Leibniz's principles, above all the... (shrink)

Leibniz sought to solve the metaphysical problem of reality, avoiding ontological premises. His intensional method was aimed at the logical solution of the problem, preserving the objectivity and unobstructed metaphysical research. Metaphysics can provide a certain level of coherence to the phenomena of physics and make them more real. Leibniz was convinced that physics, for its part, should be grounded in metaphysical principles. This promotes a reciprocal relationship between physics and metaphysics, where metaphysical principles derive their reality from physical principles, (...) and the two fields are interrelated. If we recognize the reality of the laws of physics, then we must also recognize the reality of the concept of substance. His position is that the laws of mathematical physics predict the existence of real substances, which makes it possible to move from mathematical objects to real substances. This method of substantiating the reality of substance and metaphysical principles can be considered as the foundations of the transcendental method. Leibniz's metaphysical approach is that necessary truths exist by themselves and do not depend on specific objects of study or perception. He regarded these truths as eternal. (shrink)

One of the most puzzling features of Leibniz’s deep metaphysics is the apparent contradiction between his claims that the law of continuity holds everywhere, so that in particular, change is continuous in every monad, and that “changes are not really continuous,” since successive states contradict one another. In this paper I try to show in what sense these claims can be understood as compatible. My analysis depends crucially on Leibniz’s idea that enduring states are “vague,” and abstract away from further (...) changes occurring within them at a higher resolution—consistently with his famous doctrine of "petites perceptions." As Leibniz explains further in a recently transcribed unpublished manuscript, these changes are dense within any actual duration, which is conceived as actually divided by them into states that are syncategorematically infinite in number and unassignably small. The correspondence between these unassignably small intervals between changes and the differentials of his calculus allows processes to be conceived as continuous, despite the discontinuity of the changes that occur in actuality. (shrink)

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis (...) (SIA), as propounded by John Bell. Despite many parallels between SIA and Leibniz’s approach —the non-punctiform nature of infinitesimals, their acting as parts of the continuum, the dependence on variables (as opposed to the static quantities of both Standard and Non-standard Analysis), the resolution of curves into infinitesided polygons, and the finessing of a commitment to the existence of infinitesimals— I find some salient differences, especially with regard to higher-order infinitesimals. These differences are illustrated by a consideration of how each approach might be applied to Newton’s Proposition 6 of the Principia, and the derivation from it of the v2/r law for the centripetal force on a body orbiting around a centre of force. It is found that while Leibniz’s syncategorematic approach is adequate to ground a Leibnizian version of the v2/r law for the “solicitation” ddr experienced by the orbiting body, there is no corresponding possibility for a derivation of the law by nilsquare infinitesimals; and while SIA can allow for second order differentials if nilcube infinitesimals are assumed, difficulties remain concerning the compatibility of nilcube infinitesimals with the principles of SIA, and in any case render the type of infinitesimal analysis adopted dependent on its applicability to the problem at hand. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Leibniz’s Universal Jurisprudence: Justice as the Charity of the Wise by Patrick RileySusanna GoodinPatrick Riley. Leibniz’s Universal Jurisprudence: Justice as the Charity of the Wise. Cambridge: Harvard University Press, 1996. Pp. xiii + 338. Cloth, $39.95.Leibniz’s political views are often downplayed, if not simply ignored, by philosophers focusing on his metaphysical accounts of substance and force. That Leibniz himself does not view these two areas as distinct is (...) forcefully argued in Patrick Riley’s detailed account of Leibniz’s theory of justice. Under Riley’s presentation, Leibniz’s definition of justice as the “charity of the wise” depends crucially on both his monadology and his theodicy. And his political maneuverings, particularly with France, are dominated by this unique definition of justice.Riley begins his argument by detailing Leibniz’s objections to Descartes’s voluntarism and Hobbes’s mechanistic view of human nature and the emphasis on power as the foundation of moral truths. The central Leibnizian theme to which Riley returns repeatedly is perfection. A perfect God does not act on whim or power but on reason. Monads are created with the freedom to strive toward perfection. Love, or charity, becomes perfect by becoming universal. Justice is not, as Hobbes claimed, that which is determined to be good for the whole by an absolute power, but a love or benevolence for the whole, striving through reason for the best. Wisdom is the heart of justice, not power. And for Leibniz, wisdom is inseparable from charity. God wills to actualize the best of all possible worlds out of love and wisdom, thus, wise charity.But Leibniz’s view of justice as wise charity is not without problems, most significantly the problem of freedom. In his first chapter, “Foundations,” Riley skillfully raises this problem in the context not only of Leibniz’s political stance on justice but also in the context of his metaphysics and theodicy. It is in the second chapter, “Monadology and Justice,” that Riley does the bulk of the work relating the metaphysics with the moral-political: “... on the knowledge of substance, and in consequence of the soul, depends the knowledge of virtue and of justice” (Leibniz, as quoted in Riley, 51). Political philosophy cannot be done correctly without first acquiring an adequate and proper account of substance, something the materialist Hobbes had failed to do. But because Leibniz has so closely linked his politics with his metaphysics, the perhaps insurmountable problem of freedom in his metaphysics hounds his politics. “If there are no autonomous persons with nonillusory ‘wills’, there cannot be ‘general benevolence’—for benevolence is just [End Page 470] ‘good willing’, and Leibniz invariably equates benevolentia with caritas sapientis. Without a certain kind of will, then, wise charity cannot serve as the heart of a justice which is more than sovereign-ordained law” (61). To prevent Hobbes from ruling the day, Leibniz must, as Riley correctly notes, devise a metaphysics which allows for freedom for both God and man.And here arises the one troubling aspect of Riley’s work. He addresses the problem of freedom in Leibniz’s metaphysics, but there is no discussion of the recent work done by such scholars as Robert Adams, whose book Leibniz: Determinist, Theist, Idealist makes significant contributions on exactly this topic. Regarding Leibniz’s serpentine defense of freedom, Riley does little more than bring up the problem and comment that Leibniz had a problem which, ultimately, he seemed unable to resolve. In fact, Riley shows little appreciation for the work done by mainstream scholars in the area of Leibniz’s metaphysics. If Riley’s work centered primarily on Leibniz’s political writings this might not matter, but given that the thrust of the first part of the book is to argue that Leibniz’s political theory is not merely compatible with his metaphysics but arises out of it, so that an understanding of Leibniz’s metaphysics is essential to grasping the logic of his political views, the absence of current scholarship on the metaphysics is troubling. References in footnotes confirm that Riley had read Adams’s book, as well as The Cambridge Companion to Leibniz, which contains David Blumenfeld’s excellent... (shrink)

This article examines the rift in Leibniz’s conception of determinism after being rebuffed by the Parisian theologian Antoine Arnauld in their correspondence of 1686. As, in addition, his study of surds infracted his confidence in the “complete concept,” Leibniz embarked on a new, dynamic doctrine of substance or “law of the series.” In the literature, this strategy has been widely understood as “tweaking” the system to allow some self-assertion of free will. But as this article will show, it amounts to (...) a revolutionary conception that culminates in the unmasking of determinism as an insupportable, indeed incoherent doctrine. As all forms of determinism are profoundly entangled with human self-perception, the Leibnizian Kehre invites us to a new engagement with human freedom and autonomy and the disentanglement from a philosophical position for which neither a metaphysical nor an empirical proof can be given. (shrink)

I have developed an informational interpretation of Leibniz’s metaphysics and dynamics, but in this paper I will concentrate on his theory of time. According to my interpretation, each monad is an incorporeal automaton programed by God, and likewise each organized group of monads is a cellular automaton governed by a single dominant monad. The activities of these produce phenomena, which must be “coded appearances” of these activities; God determines this coding. A crucially important point here is that we have to (...) distinguish the phenomena for a monad from its states. Both are a kind of representation: a state represents the whole world of monads, and phenomena for a monad “result” from the activities of monads. But the coding for each must be different; R for the first, Ph for the second, where W is a state of the monadic world. The reason for this is that no monadic state is in space and time, but phenomena occur in space and time. Now, the basis of the phenomenal time must be in the timeless realm of monads. This basis is the order of state-transition of each monads. All the changes of these states are given at once by God, and these do not presuppose time. The coded appearances of this order occur in time, and its metric must depend on God’s coding for phenomena. For humans, in particular, this metric time is derived from spatial distance via the laws of dynamics. Thus there may well be an interrelation between spatial and temporal metric. This means that the Leibnizian frame allows relativistic metric of space-time. I will show this after outlining Leibniz’s scenario. (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 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)

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)

While he was in the employ of the Elector of Mainz, between 1668 and 1671, Leibniz produced a series of important studies in natural law. One of these, dated between 1670 and 1671, is especially noteworthy since it contains Leibniz's earliest sustained attempt to develop an account of justice. Central to this account is the notion of what Leibniz would later come to call `disinterested love', a notion that remained essentially unchanged in Leibniz's work from this period to (...) the end of his life. Through his notion of disinterested love, Leibniz sought to resolve the supposed conflict between self- and other-regarding motives. For a variety of reasons, many commentators have failed to understand the basis of Leibniz's proposed resolution. My purpose in the present paper is to clarify the terms in which Leibniz effected this resolution, as well as to point out important developments in his later thought concerning the relation between pleasure, good, and happiness. (shrink)

Leibniz beschreibt sein philosophisches Anliegen oft als Versuch, bestimmte Formen, die von den modernen Philosophen verbannt waren, wieder herzustellen. Dieser Aufsatz erörtert den historischen Gang dieser Verbannung und Leibniz' Bemühen um eine Rehabilitierung der Begriffe Natur, Form und Kraft, wobei er jedoch okkulte, “barbarische” und überflüssige Zutaten zur Naturphilosophie vermeidet.

TheGenerales Inquisitiones de Analysi Notionum et Veritatumis Leibniz’s most substantive work in the area of logic. Leibniz’s central aim in this treatise is to develop a symbolic calculus of terms that is capable of underwriting all valid modes of syllogistic and propositional reasoning. The present paper provides a systematic reconstruction of the calculus developed by Leibniz in theGenerales Inquisitiones. We investigate the most significant logical features of this calculus and prove that it is both sound and complete with respect to (...) a simple class of enriched Boolean algebras which we call auto-Boolean algebras. Moreover, we show that Leibniz’s calculus can reproduce all the laws of classical propositional logic, thus allowing Leibniz to achieve his goal of reducing propositional reasoning to algebraic reasoning about terms. (shrink)