On its face, Leibniz's argument for primitive concepts seems to imply that unless we can analyze non-primitive concepts into their primitive constituents, we cannot grasp them. This implication, together with Leibniz's belief that we do conceive of some non-primitive concepts, entails that we can analyze some non-primitive concepts into their primitive components. However, Leibniz claims elsewhere that we are incapable of doing this. To resolve this inconsistency, I argue that, for Leibniz, grasping a concept is not an (...) all-or-nothing affair; instead we possess concepts in degrees. When reinterpreted in line with this, Leibniz's argument can avoid the inconsistency. (shrink)

This paper deals with Leibniz’s well-known reductio argument against the infinite number. I will show that while the argument is in itself valid, the assumption that Leibniz reduces to absurdity does not play a relevant role. The last paragraph of the paper reformulates the whole Leibnizian argument in plural terms to show that it is possible to derive the contradiction that Leibniz uses in his argument even in the absence of the premise that he refutes.

Leibniz’s short letter to the mathematician and physicist Ludovico Casati of 1689 is a short but interesting text on the Principle of Identity of Indiscernibles, to which it is entirely dedicated. Since there is no watermark in the paper of the letter, the letter is difficult to date, but it is likely that it was written during Leibniz’s stay in Rome, sometime between April and November of 1689 (A 2 2 287–8). When addressing the letter, Leibniz wrote ‘Casani’, but this (...) seems to be a mistake and the real addressee is thought to be Ludovico Casati, nephew of Paolo Casati, the Jesuit mathematician. The letter, reproduced in the Berlin’s Academy edition of Leibniz’s works, was first published by Gerhardt in the Archiv für Geschichte der Philosophie in 1892 (Gerhardt 1892: 53–54). It also appears in Robinet’s Iter Italicum (Robinet 1988: 134–35). But neither Gerhardt nor Robinet provide a philosophical discussion of the letter, and I am not aware of any other philosophical discussion of it. Furthermore, as far as I know, the letter has never been translated into any language. Thus I shall here provide a transcription (from A 2 2 288–89) and a translation of the letter into English, and a philosophical discussion of its treatment of the Identity of Indiscernibles. (shrink)

In Section 21 of his fifth letter to Clarke Leibniz attempts to derive the Identity of Indiscernibles from an application of the Principle of Sufficient Reason to God´s act of creation, namely that God has a reason to create the world he creates. In this paper I argue that this argument fails, not just because the Identity of Indiscernibles is false, but because there is a counterexample to one of the premises that Leibniz cannot satisfactorily rule out.

In this paper I reconstruct Leibniz's argument for the Identity of Indiscernibles in his *Primary Truths*. I criticise the alternative interpretation put forward by Cover and O'Leary-Hawthorne and defend my own interpretation, both on philosophical and hermeneutical grounds.

This paper develops a valid reconstruction in first-order predicate logic of Leibniz’s argument for his complete concept definition of substance in §8 of the Discours de Métaphysique. Following G. Rodriguez-Pereyra, it construes the argument as resting on two substantial premises, the “merely verbal” Aristotelian definition and Leibniz’s concept containment theory of truth, and it understands the resulting “real” definition as saying not that an entity is a substance iff its complete concept contains every predicate of that entity, but (...) iff its complete concept contains every predicate of any subject to which that concept is truly attributable. An account is suggested of why Leibniz criticises the Aristotelian definition as merely nominal and how he takes his own definition to overcome this shortcoming: while on the Aristotelian basis the predication relation could generate endless chains, so that substances as endpoints of predication would be impossible, Leibniz’s definition reveals lowest species as such endpoints, which he therefore identifies with individual substances. Since duplicate lowest species make no sense, the Identity of Indiscernibles for substances follows. The reading suggests a Platonist interpretation according to which substances do not so much have but are individual essences, natures or forms. (shrink)

Leibniz had a well-known argument against the existence of infinite wholes that is based on the part-whole axiom: the whole is greater than the part. The refutation of this argument by Russell and others is equally well known. In this note, I argue (against positions recently defended by Arthur, Breger, and Brown) for the following three claims: (1) Leibniz himself had all the means to devise and accept this refutation; (2) This refutation does not presuppose the consistency of (...) Cantorian set theory; (3) This refutation does not cast doubt on the part-whole axiom. Hence, should there be an obstacle to Gödel's wish to integrate Cantorian set theory within Leibniz' philosophy, it will not be this famous argument of Leibniz'. (shrink)

This essay proposes a new interpretation of a central, and yet overlooked, argument Leibniz offers against Descartes’s power-free ontology of the corporeal world. Appealing to considerations about the successiveness of motion, Leibniz attempts to show that the reality of motion requires force. It is often assumed that the argument is driven by concerns inspired by Zeno. Against such a reading, this essay contends that Leibniz’s argument is instead best understood against the background of an Aristotelian view of (...) the priority of real being over time. The essay also shows how this alternative interpretation can help to shed new light on the difference between Leibnizian forces and Aristotelian powers, as well as on Leibniz’s famous claim that accounting for force leads us beyond the mechanistic corporeal realm. (shrink)

This paper consists in a study of Leibniz’s argument for the infinite plurality of substances, versions of which recur throughout his mature corpus. It goes roughly as follows: since every body is actually divided into further bodies, it is therefore not a unity but an infinite aggregate; the reality of an aggregate, however, reduces to the reality of the unities it presupposes; the reality of body, therefore, entails an actual infinity of constituent unities everywhere in it. I argue that (...) this depends on a generalized notion of aggregation, according to which a thing may be an aggregate of its constituents if every one of its actual parts presupposes such constituents, but is not composed from them. One of the premises of this argument is the reality of bodies. If this premise is denied, Leibniz’s argument for the infinitude of substances, and even of their plurality, cannot go through. (shrink)

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

In a recent paper, Dennis Plaisted examines an important argument that Leibniz gives for the existence of primitive concepts. After sketching a natural reading of this argument, Plaisted observes that the argument appears to imply something clearly inconsistent with Leibniz’s other views. To save Leibniz from contradiction, Plaisted offers a revision. However, his account faces a number of serious difficulties and therefore does not successfully eliminate the inconsistency. We explain these difficulties and defend a more plausible alternative. (...) In the process, we call attention to the neglected topic of Leibniz’s views on the nature of conceiving, and reveal his commitment to the somewhat surprising thesis that one can conceive something through a concept even if one has no conscious grasp of that concept. (shrink)

Leibniz had a well-known argument against the existence of infinite wholes that is based on the part-whole axiom: the whole is greater than the part. The refutation of this argument by Russell and others is equally well known. In this note, I argue (against positions recently defended by Arthur, Breger, and Brown) for the following three claims: (1) Leibniz himself had all the means to devise and accept this refutation; (2) This refutation does not presuppose the consistency of (...) Cantorian set theory; (3) This refutation does not cast doubt on the part-whole axiom. Hence, should there be an obstacle to Gödel's wish to integrate Cantorian set theory within Leibniz' philosophy, it will not be this famous argument of Leibniz'. (shrink)

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

I argue that Leibniz’s well-known Argument from Unity is equally an argument from plurality. I detail two main claims about plurality that drive the argument, and I provide evidence that they structure Leibniz’s argument from the late 1670s onwards. First, there is what I call Mereological Nihilism (i.e., the claim that a plurality cannot be made into a true unity by any available means). Second, there is what I call the Plurality Thesis (i.e., the claim that (...) matter is a plurality in need of unity in the first place). I suggest that the Plurality Thesis offers a general analysis of materiality that, in some sense, is the most important aspect of Leibniz’s argument. Finally, I connect these claims about plurality to the common 17th & 18th century commitment known as the actual parts doctrine. (shrink)

In this article, I discuss Leibniz's interpretation of the cosmological argument for the existence of God. In particular, I consider whether Leibniz's position on this point was developed partly in reference to Spinoza's position. First, I analyze Leibniz's annotations from 1676 on Spinoza's Letter 12. The traditional cosmological argument, as found in Avicenna and Saint Thomas for example, relies on the Aristotelian assumption that an actual infinite is impossible and on the idea that there can (...) be no effect without a cause. From these premises, the argument concludes that God must be the uncaused first cause of all things. In Letter 12, Spinoza follows Chasdai Crescas and rejects this proof. Instead, he develops a variant of the cosmological argument which depicts God as the self-caused ground of all causes or things. In his annotations, Leibniz agrees with Spinoza about the inadequacy of the traditional argument, but remains ambiguous as to Spinoza's conception of God as a self-caused being. Next, I turn to Leibniz's comments from 1678 on Spinoza's Ethics. Here, Leibniz develops an original interpretation of the cosmological argument based entirely on the consideration of conceptual relations. Leibniz's argument depicts God as an uncaused being conceived through itself which is the condition of conceivability of all things. I argue that Leibniz developed this argument in deliberate opposition to Spinoza's conception of God as the self-caused ground of all causes or things. (shrink)

Section 17 of Leibniz’s Monadology contains a famous argument in which considerations of what it would be like to enter a machine that was as large as a mill are offered as reasons to reject materialism about the mental. In this paper, I provide a critical discussion of Leibniz’s mill argument, but, unlike most treatments, my discussion will focus on texts other than the Monadology in which considerations of the mill also appear. I provide a survey of three (...) previous interpretations of the argument and a partial defence of one of them, namely the one that Marc Bobro and I offered in Stepping Back Insider Leibniz's Mill (The Monist, 1998). However, I also argue that a fourth interpretation is necessary to account for the appearances of Leibniz’s mill in at least some of his writings. (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)

In a 1687 letter to Arnauld, Leibniz draws on an argument against mind-body causation that is reminiscent of one from Spinoza’s Ethics. According to this argument, mind-body causation is impossible because of the lack of proportion between thoughts and motions. This paper aims to shed light on Leibniz’s use of Spinoza’s argument by reconstructing both its internal structure and its development in Leibniz’s later works. In particular, the reconstruction focuses on the new version of this argument (...) that Leibniz adopts against Stahl’s vitalism as well as on the change that this new version reveals in Leibniz’s attitude towards occasionalism. The possible influence of Cordemoy is also taken into consideration. The epistemological and metaphysical issues surrounding this argument are an essential part of the history of Leibniz’s psycho-physical parallelism. (shrink)

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

In this article, I discuss Leibniz’s interpretation of the cosmological argument for the existence of God. In particular, I consider whether Leibniz’s position on this point was developed partly in reference to Spinoza’s position. First, I analyze Leibniz’s annotations from 1676 on Spinoza’s letter 12. The traditional cosmological argument, as found in Avicenna and Saint Thomas for example, relies on the Aristotelian assumption that an actual infinite is impossible and on the idea that there can be no effect (...) without a cause. From these premises, the argument concludes that God must be the uncaused first cause of all things. In letter 12, Spinoza follows Chasdai Crescas and rejects this proof. Instead, he develops a variant of the cosmological argument which depicts God as the self-caused ground of all causes or things. In his annotations, Leibniz agrees with Spinoza about the inadequacy of the traditional argument, but remains ambiguous as to Spinoza’s conception of God as a self-caus. (shrink)

Gonzalo Rodriguez-Pereyra presents an original study of the place and role of the Identity of Indiscernibles in Leibniz's philosophy. The Principle of the Identity of Indiscernibles rules out numerically distinct but perfectly similar things; Leibniz derived it from more basic principles and used it to establish important philosophical theses. Rodriguez-Pereyra aims to establish what Leibniz meant by the Principle of Identity of Indiscernibles, what his arguments for and from it were, and to assess those arguments and Leibniz's claims (...) about the Principle of Identity of Indiscernibles. He argues that Leibniz had a very strong version of the principle, according to which no possibilia are intrinsically perfectly similar, where this excludes things that differ in magnitude alone. The book discusses Leibniz's arguments for the Identity of Indiscernibles in the Meditation on the Principle of the Individual, the Discourse on Metaphysics, Notationes Generales, Primary Truths, the letter to Casati of 1689, the correspondence with Clarke, as well as the use of the Identity of Indiscernibles in Leibniz's arguments against the Cartesian conception of the material world, atoms, absolute space and time, the Lockean conception of the mind as a tabula rasa, and freedom of indifference. Rodriguez-Pereyra argues that the Identity of Indiscernibles was a central but inessential principle of Leibniz's philosophy. (shrink)

Schon in seinen frühen Jahren war Leibniz ein Gegner der Cartesischen Naturphilosophie, ca. 1697 zeigt sich in seinen Texten dann ein Argument gegen Descartes, das ich im folgenden behandle und als ,heterogeneity argument‘ bezeichnen möchte - eingangs wird hier dargestellt, wie Leibniz es im Paragraphen 13 seiner Schrift De ipsa natura expliziert, anschließend diskutiere ich zwei frühere Ansätze, die sich um das Thema drehen und die darin einig sind, daß Leibniz Descartes' Auffassung von der materiellen Welt aus a (...) priori - Gründen kritisiert, da sie intern inkonsistent bleibt: Ich versuche nachzuweisen, daß diese Interpretationen Leibniz nicht gerecht werden und plädiere für eine a posteriori - basierte Auslegung - Leibniz zieht Descartes' Ansatz in Zweifel, indem er sich auf ,contingentia‘ hinsichtlich der Art beruft, in der unsere Sinneswahrnehmung die materielle Welt repräsentiert. Zum Abschluß erörtere ich einige allgemeinere hermeneutische Probleme, die sich aus den Unterschieden zwischen früheren Interpretationen und meiner eigenen Deutung nun ergeben. (shrink)

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

J'attaque de front la notion d'un être nécessaire qui de par sa nécessité rend raison de sa propre existence. Une telle notion est entachée d'aporie. En plus elle confond la nécessité formelle, voire métaphysique avec la puissance réelle à un tel point qu'elle pousse Leibniz bel et bien vers le spinozisme. Le rejet d'une telle notion mène de sa part inéluctablement à une régression à l'infini de raisons raisonnantes d'où, bien entendu, Dieu est exclu, bien qu'il soutienne par son intellect (...) une telle régression en tant que celle-ci s'avère nécessaire. (shrink)

In the second edition of Hermann Cohen’s Kant’s Theory of Experience, he abandons the interpretation of Kant’s Anticipations of Perception that he gave in the first edition, in favourof a radically different one. On his early interpretation, the Anticipations is largely of psychological interest for its influence on, and continuing significance for, physiological psychology and psychophysics. But on his mature interpretation, it defends the superiority of a dynamic conception of nature over a mechanical conception. Further, on his early interpretation, Cohen (...) thought the Anticipations was not a central part of Kant’s critical theory of knowledge. But on his mature interpretation, he thinks it is absolutely central to that project. What is more, Cohen seems to have revised his interpretation in a relatively short period of time, in 1880-1. This paper argues that Cohen’s change in views about Kant’s Anticipations is explained by his reception of Leibniz in the very early 1880s, and specifically Cohen’s reception of Leibniz’s arguments against Descartes’ view that extension is the essence of matter. (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.

As Leibniz points out in the Méditation sur la notion commune de la jus tice, justice—defined as charity of the wise and universal benevolence—belongs “to the necessary and eternal truths about the nature of things, as numbers and proportions.” According to the interpretation of Patrick Riley, from this perspective the two manuscripts usually regarded as belonging to the Méditation should be seen as complementary parts of a unitary Platonizing work. According to Riley, the manuscript that now constitutes the first part (...) of the Méditation is concerned with definitions of ethical concepts viewed as “quasi-mathematical, demonstrable ‘eternal verities’”, whereas the manuscript that now constitutes the second part of the Méditation is concerned “with Platonic ‘ascent’, in the manner of Phaedrus and Symposium,” which recommends the transition from mere negative forbearance from harm to doing positive good. In formulating these claims, Riley uses scare quotes to indicate that he uses the terms “eternal verities” and “ascent” in an unusual way that diverges from the views of the historical Plato. According to his interpretation, Leibniz’s modifications of Platonism are restricted to peripheral parts such as the doctrine of the pre-existence of the soul or Pythagorean components such as the doctrine of metempsychosis. Therefore, Riley claims that when Leibniz is talking about knowing eternal truths, what he has in mind is literally the view that we know the same truths as the truths that the gods know and love but do not cause or change. (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.

Leibniz’s argument against Descartes’s conservation principle in the Brevis demonstratio (1686) has traditionally been read as passing from the premise that motive force must be conserved to the conclusion that motive force is not identical to quantity of motion and, finally, that quantity of motion is not conserved. In a lesser-known draft of the same year, Christiaan Huygens claimed that Descartes had in fact never held the view that Leibniz was attacking. Huygens is right as far as the traditional (...) reading is concerned. However, if the Brevis demonstratio is seen, as it should be, in the context of Leibniz’s attempt to ground mechanics in the foundational metaphysical axiom of the equivalence of full cause and entire effect, then Huygens’s objections can be answered. Leibniz may have committed Descartes to the foundational axiom because of the Traité de la méchanique, which was available to Leibniz at that time. Leibniz had used the equivalence of full cause and entire effect both in discovering the conservation of vis viva earlier and in various arguments for it later. Thus, the Brevis demonstratio should be viewed with Leibniz’s broader foundational mission in mind. (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)

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)

This book is a systematic reappraisal of Leibniz’s philosophy of mind. The main argument of this book is easy to state: Leibniz offers a fully natural theory of mind. In today’s philosophical climate, in which much effort has been put into discovering a naturalized theory of mind, Leibniz’s efforts to reach a similar goal 300 years earlier will provide a critical stance from which we can assess our own theories. But while the goals might be similar, the content of (...) Leibniz’s theory significantly diverges from the majority of today’s theories. Leibniz’s philosophy of mind meets the standards of what he would regard as a fully natural theory. Perhaps surprisingly, Leibniz’s theological commitments yield a thoroughgoing naturalizing methodology: the properties of an object are explicable in term of the object’s nature. This book argues that Leibniz pursued his philosophy of mind with this methodology in hand. If we keep this commitment to a naturalizing project in mind, then we will find in Leibniz a rich and interesting philosophy of mind. -/- This book provides an account of Leibniz’s naturalizing constraints and traces them through Leibniz’s philosophy of mind. It covers issues relating to mental representation, perception, sensation, consciousness, memory, and moral identity. (shrink)

In Western thinking, the tradition of the argument for the existence of God beganwith Plato and Aristotle. It was carried forward in medieval scholasticism,eminently in Aquinas‟s so-called quinque viae, and reached its peak in modernphilosophy. To date approximately 1850 different proofs for the existence of Godare known. The most frequently represented and well-known types of proofs arethe ontological, cosmological, teleological and the moral or deontological type,referring respectively to the arguments of Anselm, Aquinas , and Kant. In this paper I (...) will discuss the development of modernphilosophical proofs, from Descartes‟s and Spinoza‟s ontological arguments,through, Leibniz‟s cosmological argument to Swinburne‟s revision of Leibniz. (shrink)

In §18 of Principles of Nature and Grace, Based on Reason, Leibniz says: ”Thus our happiness will never consist, and must never consist, in complete joy, in which nothing is left to desire, and which would dull our mind, but must consist in a perpetual progress to new pleasures and new perfections.” -/- This passage is typical in Leibniz’s Nachlass. Universal perfection creates in us joy or pleasure of the mind and its source is our creator, God. When this joy (...) is constant, we reach happiness and wisdom which is a kind of standing state of virtue, readiness to practice charity in the best of all possible worlds. However, it also indicates that our knowledge is never perfect. Perfecting our knowledge is a never-ending process which gives us joy in itself and motivates us to act in imitation of God. In this way some passions advance our knowledge and we can create ourselves a passionate habit of knowing more about the world and its perfection. In this paper I try to see this process of self-perfection from a cognitive rather than ethical point of view. While it is clear that in the final stage of wisdom we act mostly on our volitions which are founded on clear and distinct perceptions, it is less clear what cognitive status is to be attributed to our initial perceptions of perfection, our emotions and finally, the intellectual emotions which lead us to perfection and God. I will also reflect the role of the minute perceptions in our struggle for happiness. My argument is that a central cognitive role in Leibniz’s views on self-perfection is held by clear, but confused perfections which are subjective, undemonstrable impressions, shades, feelings. Therefore our ethical action is largely founded on passing, minute feelings rather than on deliberated conscious volitions, although the goal in Leibniz’s moral theory is to change this fact. -/- My discussion is founded on several texts from Leibniz’s later philosophy, such as the discussion following from New System of the Nature and the Communication of Substances of 1695, Leibniz’s letter to Queen Sophie Charlotte of 1702 (also known as On What is Independent in Sense and Matter), New Essays on Human Understanding (1704), Theodicy (1710) and naturally Leibniz’s most important epistemological text, Meditations of Truth, Knowledge and Ideas (1684). (shrink)

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)

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)

It is often thought that, although Spinoza develops a bold and distinctive conception of God (the unique substance, or Natura Naturans, in which all else inheres and which possesses infinitely many attributes, including extension), the arguments that he offers which purport to prove God’s existence contribute nothing new to natural theology. Rather, he is seen as just another participant in the seventeenth century revival of the ontological argument initiated by Descartes and taken up by Malebranche and Leibniz among others. (...) That this is the case is both puzzling and unfortunate. It is puzzling because although Spinoza does offer an ontological proof for the existence of God, he also offers three other non‐ontological proofs. It is unfortunate because these other non‐ontological proofs are both more convincing and more interesting than his ontological proof. In this paper, I offer reconstructions and assessments of all of Spinoza’s arguments and argue that Spinoza’s metaphysical rationalism and his commitment to something like a Principle of Sufficient Reason are the driving force behind Spinoza’s non‐ontological arguments. (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.

Leibniz’s claim that it is possible for us to gain metaphysical knowledge through reflection on the self has intrigued many commentators, but it has also often been criticized as flawed or unintelligible. A similar fate has beset Leibniz’s arguments against materialism. In this paper, I explore one of Leibniz’s lesser-known arguments against materialism from his reply to Bayle’s new note L (1702), and argue that it provides us with an instance of a Leibnizian “argument from reflection”. This argument, (...) I further show, does not constitute a flawed appeal to mere introspection, but is in fact securely grounded in an important corollary of the Principle of Sufficient Reason: Leibniz’s Principle of Intelligibility. (shrink)

In this paper we argue for the robustness of Leibniz's commitment to the reality (but not substantiality) of body. We claim that a number of his most important metaphysical doctrines — among them, psychophysical parallelism, the harmony between efficient and final causes, the connection of all things, and the argument for the plurality of substances stemming from his solution to the continuum problem— make no sense if he is interpreted as giving an eliminative reduction of bodies to perceptions.

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.

This volume presents introductory chapters from internationally-renowned experts on eleven of Leibniz's key philosophical writings. Offering accessible accounts of the ideas and arguments of his work, along with information on their composition and context, this book is an invaluable companion to the study of Leibniz.

In the Discourse on Metaphysics Leibniz writes, 'Our perceptions are always true, it is our judgments that come from ourselves that deceive us' (section 14). Leroy Loemker in his 'Leibniz's Doctrine of Ideas' criticizes this account of error. His main worry can be presented in the form of the following syllogistic argument, which he derives from Leibniz's doctrine of ideas: (a) There cannot be a false perception; (b) All judgments are perceptions; and therefore (c) There cannot be (...) a false judgment. However, in this paper I argue that Leibniz can distinguish between a perception and a judgment in their semantic aspect. The sense in which a perception turns out to be false (or true) for Leibniz is different from the sense in which a judgment turns out to be false (or true). This is because, while a perception, understood in Leibniz's terms, lacks truth-conditions, a judgment, in being representational, has such conditions. Thus while a perception remains true always, a judgment can be false. Pointing to the equivocal use of 'false' in (a) and (c) above, I conclude that (c) does not follow from (a) and (b). (shrink)

As a lifelong Lutheran who resisted numerous attempts by Catholic acquaintances to convert him, one might reasonably expect Leibniz to have followedthe orthodox Lutheran line on disputed doctrinal issues, and thus held amongst other things that the doctrine of purgatory was false. Yet there is strong evidencethat Leibniz personally accepted the doctrine of purgatory. After examining this evidence, I determine how Leibniz sought to justify his endorsement of purgatory and explain how his endorsement sits alongside his frequent rehearsal of familiar (...) Protestant arguments against the doctrine. I then examine some of Leibniz’s other theological and philosophical commitments, including those on the afterlife, in order to tentatively tease out further details of the form of purgatory that wonhis approval. In considering these issues, I aim to make clear the extent to which Leibniz’s philosophical thinking underpins and shapes his theological beliefs. (shrink)

I present a formal framework historically faithful to Leibniz's analysis of relational sentences, which: (i) engrafts thematic roles and the non-truth-functional connective insofar as (quatenus) into the monadic fragment of first-order logic; (ii) suggests a plausible ontological picture of thematic roles and relational facts; (iii) supports argument deletion and related inferential patterns that are not taken into account by standard first-order logic.