Śrīgupta, a Buddhist philosopher in the Middle Way tradition, was born in Bengal in present-day India in the seventh century. He is best known for his Introduction to Reality with its accompanying auto-commentary,1 in which he presents the first Middle Way iteration of the influential "neither-one-nor-many argument."2 This antifoundationalist line of reasoning sets out to prove that nothing enjoys ontologically independent being.Gottfried Wilhelm Leibniz was born some one thousand years later, in the city of Leipzig, situated on the outskirts (...) of European learning and thought. He is best known today for having co-invented the infinitesimal calculus, for his... (shrink)

Leibniz argues that Cartesian extension lacks the unity required to be a substance. A key premise of Leibniz’s argument is that matter is a collection or aggregation. I consider an objection to this premise raised by Leibniz’s correspondent Burchard de Volder and consider a variety of ways that Leibniz might be able to respond to De Volder’s objection. I argue that it is not easy for Leibniz to provide a dialectically relevant response and, further, that the difficulty arises from Leibniz’s (...) commitment to part-whole priority in the case of material wholes, a commitment not shared by De Volder. One major implication is that Leibniz relies on a bottom-up conception of material things, which makes his argument vulnerable to objections stemming from certain types of monist positions. (shrink)

What is Leibniz’s argument for simple substances? I propose that it is an extension of his prior argument for incorporeal forms as principles of unity for individual corporeal substances. The extension involves seeing the hylomorphic analysis of corporeal substances as implying a resolution of matter into forms, and this seems to demand that forms, which are themselves simple, be the only elements of things. The argument for simples thus presupposes the existence of corporeal substances as a key premise. Yet a (...) theory of simple substances as the elements of things threatens to preclude the existence of corporeal substances for Leibniz, and the extension of the argument for forms into an argument for simples is not cogent. If nothing else rides on the simplicity of individual substances, then perhaps instead of being its most fundamental tenet, the doctrine of simples—the monadology—is something that over-extends and destabilizes Leibniz’s metaphysics. (shrink)

1. A substance is a being that is capable of action. It is either •simple, meaning that it has no parts, or •composite, meaning that it is a collection of simple substances or monads. (Monas is a Greek word meaning ‘unity’ or ‘oneness’.) Any composite thing—any body—is a multiplicity, ·a many, but simple substances are unities, ·or ones·. There must be simple substances everywhere, because without simples there would be no composites—·without ones there could not be manies·. And simple (...) substances are lives, souls, minds—·where there is a simple substance there is life·—and the world’s being full of such substances means that the whole of nature is full of life. (shrink)

In this paper I argue that what has been called Leibniz’s “aggregate argument” for unities in things in fact comprises three quite distinct lines of argument, with different concepts being advanced under the name ‘unity’ and meriting quite different conceptual treatment. Two of those arguments, what I call the Borrowed Reality Argument and the Multitude Argument, also appear in later writings to be further elaborated into arguments not just for unities but for simples. I consider the arguments in detail. (...) I suggest that one of the two, the Borrowed Reality Argument, is philosophically more promising and has the stronger evidence for being central in Leibniz’s thought as he argues for the existence of simple substances. (shrink)

1. A substance is a being that is capable of action. It is either •simple, meaning that it has no parts, or •composite, meaning that it is a collection of simple substances or monads. (Monas is a Greek word meaning ‘unity’ or ‘oneness’.) Any composite thing—any body—is a multiplicity, ·a many, but simple substances are unities, ·or ones·. There must be simple substances everywhere, because without simples there would be no composites—·without ones there could not be manies·. And simple (...) substances are lives, souls, minds—·where there is a simple substance there is life·—and the world’s being full of such substances means that the whole of nature is full of life. (shrink)

Mulla Sadra and Leibniz are two philosophers of the East and the West, and belong to two different worlds. Though they were unaware of ideas of each other, they share certain points that are comparable. Monads constitute the basis of Leibniz's thought and he refer to their features in his various works. Mulla Sadra's philosophy also is based on being and he tried to deal with its reality in his philosophy. Though Leibniz's monads are many and Mulla Sadras (...) class='Hi'>being is one, they use certain terms for monads and being which are very close to each other and are comparable from different points of view. Leibniz monads while being many are one as well. Similarly Mulla Sadra's philosophy too enjoys multiplicity in unity. Leibniz's monads enjoy perception and Mulla Sadra's being too coexist withknowledge. In this paper apart from comparing Leibniz's monads and Mulla Sadra's concept of being, their philosophies also have been compared and their common and different points have been unraveled. (shrink)

This monograph includes an analysis of the Commentary on the Introduction to Reality (Tattvāvatāravṛtti) by the Indian Madhyamaka Buddhist philosopher, Śrīgupta (7th/8th century), together with a Tibetan critical edition and annotated translation of this text, which has never before been available in English. In this work, Śrīgupta advances the “neither-one-nor-many argument,” which sets out to prove that all things lack ontological independence, and by implication, that everything depends for its existence on something else. I present a detailed reconstruction and analysis (...) of the argument, showing how Śrīgupta rejects the possibility of ontological independence by way of rejecting the possibility of mereological simples, both material and immaterial. Śrīgupta's other important philosophical contributions are brought to light, including his influential threefold criterion for conventional reality (saṃvṛtisatya) and his argument for the possibility of conceptual enlightened cognition (vikalpajñāna), which is standardly supposed to be non-conceptual. (shrink)

This paper submits the state-of-the-art review of the collection of remote articles of Hans Poser, the largest expert on philosophy Leibniz who has devoted to studying of his philosophy more half a century. Specifics of his position, as interpreter of philosophy of Leibniz, the author of this review sees in Poser’s justification of the fundamental character of Leibniz’s doctrine about modalities, signs and language. Underlining of reflexive and system forming character of modal concepts in the Leibniz’s philosophy and also relevance (...) of his doctrine about modal concepts both for modern modal logic, and for the modern theory of the proof and metamathematics is the central point of interpretation of Leibniz’s philosophy by H. Poser. Concerning a question of the relation of science and metaphysics, H. Poser speaks out in defense of metaphysics, pointing to impossibility of the solution of many problems without the appeal to metaphysics.24 articles presented in this collection give a complete look about all parties of many-sided thinking of Leibniz. The collection presents some kind of encyclopedia of Leibniz’s philosophy in which all last achievements of the modern Leibniz Research are accumulated and are presented in such systematic order that the collection by right can be considered as the monography and to serve as the reference book for everyone who wants to gain a complete and competent view about Leibniz’s philosophy. (shrink)

According to Madhyamaka Buddhist philosophers, everything depends for its existence on something else. But what would a world devoid of fundamentalia look like? In this paper, I argue that the anti-foundationalist “neither-one-nor-many argument” of the Indian Mādhyamika Śrīgupta commits him to a position I call “metaphysical indefinitism.” I demonstrate how this view follows from Śrīgupta’s rejection of mereological simples and ontologically independent being, when understood in light of his account of conventional reality. Contra recent claims in the secondary literature, (...) I clarify how the Madhyamaka metaphysical dependence structure is not a straightforward infinitism since it does not honor strict asymmetry or transitivity. Instead, its dependence relations are irreflexive and extendable, admitting of dependence chains of indefinite (though not actually infinite) length and dependence loops of non-zero length. Yet, the flexible ontology of Śrīgupta's Madhyamaka can accommodate a contextualist account of asymmetry and support a revisable theory of conventional truth, delivering significant payoffs for the view, including the capacity to accommodate developments in scientific explanation. (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)

This work presents Leibniz's view of infinity and the central role it plays in his theory of living beings. Nachtomy argues that Leibniz employs three degrees of infinity: absolute infinity, which applies to God; maximum or infinite in kind, which applies to created, living beings; and mathematical infinity.

In the correspondence with Arnauld, Leibniz contends that each corporeal substance has a substantial form. In support he argues that to be real a corporeal substance must be one and indivisible, a true unity. I will show how this argument precludes a tempting interpretation of corporeal substances as composite unities. Rather it mandates the interpretation that each corporeal substance is a single monad.

Leibniz denies that the actual world possesses the per se unity of a substance. Instead, he seems to hold, the world is limited to the mind-dependent unity of an aggregate. Against this answer, criticized by Kant in his Inaugural Dissertation, I argue that for Leibniz the unity of the actual world is not grounded simply in God’s perception of relations among created substances but in the common dependence of those substances on a unitary cause. First, the actual world is one (...) because every created substance is continuously dependent on God for its perfection. Without being the soul of the world, God is an emanative cause through which the created world is unified. Second, every substance is a unique “concentration” of an ideal world that is God’s model for creation. Consequently, while extensionally many, created substances are versions of the same one world chosen by God for creation. (shrink)

In this paper, I argue that it is in the fourteenth century that the problem of the compatibility or unity of efficient and final causality emerges. William Ockham and John Buridan start to flirt with a mechanized view of nature solely explainable by efficient causality, and they hence push final causality into the human mind and use it to explain for example action, morality and the good. Their argumentation introduces the problem of how to give a unified account of the (...) world, that is, how are nature and freedom compatible. In the paper, I set up the discussion by going through some of the problems associated with final causality in the seventeenth century and show that Ockham and Buridan's problems are similar. I then argue using a formulation from Leibniz's Monadology that the problems here traced should be seen as versions of the mind/body problem. (shrink)

In the early modern period one can find unity of consciousness arguments in the writings of Rene Descartes and G. W. Leibniz, and in the recent literature they have been defended by David Barnett, William Hasker, and Richard Swinburne (among others). Descartes's unity of consciousness argument for dualism is to be found in the sixth of his Meditations on First Philosophy. Descartes claims that his unity of consciousness argument was itself sufficient to establish substance dualism. Swinburne's central line of argument (...) involves deploying a number of puzzle cases. He argues that our intuitions about these cases can be accommodated only by adopting a “further fact” view of the self, according to which the continued existence of a person over time consists in the continued existence of a mental substance, and “it is metaphysically possible that the substance acquires a totally new body, totally new apparent memories, and character”. (shrink)

ne of the leading problems for Cartesian dualism is to provide an account of the union of mind and body. This problem is often construed to be one of explaining how thinking things and extended things can causally interact. That is, it needs to be explained how thoughts in the mind can produce motions in the body and how motions in the body can produce sensations, appetites, and emotions in the mind. The conclusion often drawn, as it was by three (...) of Descartes's illustrious successors, Malebranche, Spinoza, and Leibniz, is that mind and body cannot causally interact.' I mention this problem of the interaction between thinking things and extended things only to distinguish it from the problem concerning the union of mind and body which I wish to discuss. Some commentators, such as Daisie Radner, maintain that the.. (shrink)

Leibniz can be counted among the remote, but still significant, sources of Sellars's philosophy. Such thesis, however, is meaningless unless its conceptual relevance is displayed. Therefore, it will be immediately added that Sellars's relation with Leibniz is focused on three main fundamental issues, which respectively concern (1) the concept of nature, (2) the concept of truth and (3) the concept itself of nominalism. Besides, there are other seemingly minor topics, which actually refers to the definition of abstract entities, of predicates, (...) of proper names and to the datum/factum distinction. Another challenge the paper is faced with, regards the fact that Sellars does not consider Leibniz only in himself, given that he very often positions him in a close relation to Kant: it is as though there were multifaceted issues brought forward by Leibniz and Kant together forming a complex theoretical unity (over and above their differences). According to Sellars, in fact, they both undermine some of the most solid epistemological principles of the early modern times (mainly founded upon the subject- object lexicon and the idea of veritas as adaequatio rei et intellectus) and they both reshape the meaning of expressions such as “being actual” or “being true”. (shrink)

In the correspondence with Arnauld, Leibniz contends that each corporeal substance has a substantial form. In support he argues that to be real a corporeal substance must be one and indivisible, a true unity. I will show how this argument precludes a tempting interpretation of corporeal substances as composite unities. Rather it mandates the interpretation that each corporeal substance is a single monad.

Any interesting philosopher’s thoughts contain many prima facie mutually contradicting ideas. Especially if a thinker philosophizes intensely on an extremely wide area of enquiry over a long period, as is the case with Leibniz, advancing many views on each problem, often shifting his position, especially in the context of exchanges of opinions in letters, developing his views without necessarily tying up loose ends, and if in addition the thinker only publishes a minute portion of what he has written, it would (...) be strange, even grotesque, if his writings did not contain conflicting and contradictory strands. What is philosophically interesting, is not so much tracing the exact time of the changes, worthy and difficult as the detective work of historical scholarship involved may be, but realising, through such investigation, the depth and multiple facets of the issue that troubled the philosopher and led him to assert or hold on to those contradictory pairs or groups of ideas. We are sometimes made to realize that the issues throw light on problems that still puzzle us today. (shrink)

The author has taken an important subject, one which has pervaded the thinking of scientists, philosophers, and historians, and with impeccable scholarship and great clarity has concerned himself with a specific aspect of it: the way in which the determination of how the unity of the sciences is to be conceived presented itself to philosophers as a specifically philosophical or logical problem. The study is not, therefore, an essay in the history of ideas showing the idea of unity at work (...) in many cultural contexts, or in the history of the classification fo the sciences; nor does it discuss philosophers who suppose a unity but do not discuss it. Rather it is an exposition of what is directly said on the subject of unity by a number of philosphers who view it in their different ways as a problem for solving. Those chosen for discussion belong to the classical period of modern philosophy, the seventeenth and eighteenth centuries, and chapters take up the contributions of Bacon, Descartes, Leibniz, Condillac, Diderot and D'Alembert, and Kant. This will be an important book for students and teachers in the history of philosophy, of science, of ideas; and will also be useful to students of English and French literature in the period it covers. (shrink)

Leibniz took pride in the Pre-established Harmony as an account of mind-body union. On the other hand, he sometimes claimed that he did not have a good account of such a union. I explain the tension by distinguishing between two importantly different issues that concern the union: body-soul interaction and the per se unity of the composite. Leibniz's positive evaluation concerns the issue of interaction rather than per se unity, R.M. Adams proposed that Leibniz did have the philosophical resources to (...) account for a per se unity of the body-soul composite, in the form of Aristotelian scholastic solutions to that problem. I argue, by contrast, that Leibniz's notions of body and soul were too far removed from their scholastic predecessors for him to be able to deploy those resources in a compelling way. (shrink)

Leibniz claims that God acts in the best possible way, and that this includes creating exactly one world. But worlds are aggregates, and aggregates have a low degree of reality or metaphysical perfection, perhaps none at all. This is Leibniz’s tendency toward acosmism, or the view that there this no such thing as creation-as-a-whole. Many interpreters reconcile Leibniz’s acosmist tendency with the high value of worlds by proposing that God sums the value of each substance created, so that the best (...) world is just the world with the most substances. I call this way of determining the value of a world the Additive Theory of Value (ATV), and argue that it leads to the current and insoluble form of the problem of incompossibility. To avoid the problem, I read “possible worlds” in “God chooses the best of all possible worlds” as referring to God’s ideas of worlds. These ideas, though built up from essences, are themselves unities and so well suited to be the value bearers that Leibniz’s theodicy requires. They have their own value, thanks to their unity, and that unity is not preserved when more essences are added. (shrink)

This essay examines the relationship between monads and space in Kant’s early pre-critical work, with special attention devoted to the question of ubeity, a Scholastic doctrine that Leibniz describes as “ways of being somewhere”. By focusing attention on this concept, evidence will be put forward that supports the claim, held by various scholars, that the monad-space relationship in Kant is closer to Leibniz’ original conception than the hypotheses typically offered by the later Leibniz-Wolff school. In addition, Kant’s monadology, in (...) conjunction with God’s role, also helps to shed light on further aspects of his system that are broadly Leibnizian, such as monadic activity and the unity of space. (shrink)

Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz’s argument against the world soul relies on his rejection of infinite number, and, as such, (...) Leibniz cannot assert that any body has a soul without also accepting infinite number, since any body has infinitely many parts. Previous attempts to address this concern have misunderstood the character of Leibniz’s rejection of infinite number. I argue that Leibniz draws an important distinction between ‘wholes’– collections of parts that can be thought of as a single thing – and ‘fictional wholes’ – collections of parts that cannot be thought of as a single thing, which allows us to make sense of his rejection of infinite number in a way that does not conflict either with his view that the world is actually infinite or that the bodies of substances have infinitely many parts. (shrink)

This is the most up-to-date and comprehensive interpretation of the philosophy of Gottfried Wilhelm Leibniz. Amongst its other virtues, it makes considerable use of unpublished manuscript sources. The book seeks to demonstrate the systematic unity of Leibniz's thought, in which theodicy, ethics, metaphysics and natural philosophy cohere. The key, underlying idea of the system is the conception of nature as an order designed by God to maximise the opportunities for the exercise of reason. From this idea emerges the view that (...) this world is the best of all possible worlds, and an ethical ideal in which the well-being of human beings is promoted through the gradual extension of intellectual enlightenment. (shrink)

Heidegger holds that our age is dominated by the ambition of reason to possess the world. And he sees in Leibniz the man who formulated the theorem of our modern age: nothing happens without a reason. He calls this attitude `calculating thought' and opposes to it a kind of thought aimed at preserving the essence of things, which he calls `meditating thought'. Cristin's book ascribes great importance to this polarity of thinking for the future of contemporary philosophy, and thus compares (...) the basic ideas of the two thinkers. Leibniz announces the conquest of reason; Heidegger denounces the dangers of reason. Their diversity becomes manifest in the difference between the idea of reason and the image of the path. But is Leibniz's thought really only `calculating'? And do we not perhaps also encounter the traces of reason along Heidegger's path? With these questions in mind we may begin to redefine the relation between the two thinkers and between two different conceptions of reason and philosophy. The hypothesis is advanced that Heidegger's harsh judgment of Leibniz may be mitigated, but it also becomes clear that Heidegger's rewriting of the code of reason is an integral part of our age, in which many signs point to new loci of rationality. With his original interpretation, aware of the risks he is taking, Renato Cristin offers a new guide to the understanding of reason: he shows forth Leibniz as one who defends the thought of being in the unity of monadology, and Heidegger as a thinker who preserves the sign of reason in his meditating thought. (shrink)

I argue that Leibniz consistently subscribes to the view that phenomena (thus bodies) have their being in perceiving substances. I then argue that this mentalistic conception of phenomenon coheres with three of his doctrines of body: (1) that bodies presuppose the unities or simple substances on which they are founded; (2) that bodies are aggregates of those substances; and (3) that bodies derive or borrow their reality from their simple constituents.

Nothing is as complex as the world – but soon we must master this complexity to be able to live in it. Our means to do so are the languages. However, they are so manifold and so differently in vocabulary, structure and in the way linked with the world that it is difficult to ascribe to them a common relation. Noam Chomsky’s empirical search for a deep structure grammar had no success. For Leibniz our actual world is infinitely complex, beginning (...) with the monad and its subordinated “worlds in the worlds”. Thus exactly our problem constellation of today can already be found there–namely how to master infinite complexity by languages. But what connects these languages? This will be discussed from (1) the representational function of signs concerning the connection between res / signum / notio / idea, via (2) the Ars characteristica and its formal-linguistic sign systems; the next step counts (3) for the natural languages and their functions, marked above all by an adaptation to new problems. The last step deals with the functions of languages, finally leading to the unity of reason. (shrink)

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

In the Monadology Leibniz has us imagine a thinking machine the size of a mill in order to show that matter can’t think. The argument is often thought to rely on the unity of consciousness and the notion of simplicity. Leibniz himself did not see matters this way. For him the argument relies on the view that the qualities of a substance must be intimately connected to its nature by being modifications, limitations of its nature. Leibniz thinks perception is (...) not a modification of matter because it is active and matter is passive. At the same time, there are traces in Leibniz of a different argument that relies on the notion of internal action, which may involve the notion of simplicity. Critics have sometimes charged that the Mill Argument is an argument from ignorance, but Leibniz was aware of this problem and made clear that he did not make that mistake. (shrink)

Leibniz was probably the last universal scholar in modern times who made original and innovative achievements in all the essential fields of knowledge of his time: as a reform-oriented lawyer, a multilateral thinking diplomat, as a mathematician of infinitesimal calculus, as the inventor of a calculating machine and in the mining of horizontal wind power, as an organizer of science and as one of the first historians who strived for source-critical methodical objectivity. However, this baroque diversity can only be understood (...) from the center of a monadological philosophy, which wants to establish the unity of scientific worldview and metaphysical concept of the world. It is distorted in the classical reception because only Leibniz the Theodicy was known. The topicality of Leibniz today consists in re-exposing the original basic idea of unity in diversity and asking how it can be made fruitful for philosophical and political thought in the 21st century. This book is a translation of the original German 1st edition Leibniz und die Folgen by Jörg Zimmer, published by J.B. Metzler, imprint of Springer-Verlag GmbH, part of Springer Nature in 2018. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors. (shrink)

One of the most intriguing – and arguably counter-intuitive – doctrines defended by environmental philosophers is that of positive aesthetics, the thesis that all of nature is beautiful. The doctrine has attained philosophical respectability only comparatively recently, thanks in no small part to the work of Allen Carlson, one of its foremost defenders. In this paper, we argue that the doctrine can be found much earlier in the work of Gottfried Wilhelm Leibniz who devised and defended a version of positive (...) aesthetics in the early modern period, grounded in a conception of the world as a world of monads, each of which individually fulfils the rationalist aesthetic criteria of multiplicity-in-unity and that taken together ensure that the world as a whole is a harmoniously ordered system of multiple and diverse individuals, whose intelligible order and variety is made known to us through natural scientific endeavour. In showing this, we advance two further theses: first, that Leibniz's vers.. (shrink)

I maintain that Leibniz's distinction between 'organic machines of nature' and the artificial machine that we produce cannot be adequately understood simply in terms of differing orders of structural complexity. It is not simply that natural machines, having been made by God, are infinitely more complex than the products of our own artifice. Instead, Leibniz's distinction is a thoroughly metaphysical one, having its root in his belief that every natural machine is a corporeal substance, the unity and identity conditions of (...) which derive ultimately from its substantial form. Natural machines are thus true unities, while artificial machines are mere aggregates of substances and are therefore only accidental unities. I briefly explore this connection between Leibniz's distinction between natural and artificial machines and his views about individuality. I conclude on a polemical note, in which it is suggested that these results undermine the currently popular view that Leibniz renounced corporeal substances toward the end of his life. (shrink)

abstract: The notion of force is at the heart of Leibniz’s metaphysics. One of his central theses is that powers are to be reconceived as forces. Connectedly, he maintains that force is essential to the very account of substance. The paper contends that these claims have not been well understood due to an inadequate understanding of the notion of force itself. Against a common reading, I argue that Leibnizian force is not fundamentally dispositional, but an activity. Taking seriously this idea (...) means reconsidering not only the nature and function of powers, but also the basic character of Leibniz’s metaphysics—including his view of substances as soul-like and as causally independent. This paves the way for a novel interpretation of the unity of physical and metaphysical forces. (shrink)

Gottfried Wilhelm Leibniz was a man of extraordinary intellectual creativity who lived an exceptionally rich and varied intellectual life in troubled times. More than anything else, he was a man who wanted to improve the life of his fellow human beings through the advancement of all the sciences and the establishment of a stable and just political order. In this Very Short Introduction Maria Rosa Antognazza outlines the central features of Leibniz's philosophy in the context of his overarching intellectual vision (...) and aspirations. Against the backdrop of Leibniz's encompassing scientific ambitions, she introduces the fundamental principles of Leibniz's thought, as well as his theory of truth and theory of knowledge. Exploring Leibniz's contributions to logic, mathematics, physics, and metaphysics, she considers how his theories sat alongside his concerns with politics, diplomacy, and a broad range of practical reforms: juridical, economic, administrative, technological, medical, and ecclesiastical. Discussing Leinbniz's theories of possible worlds, she concludes by looking at what is ultimately real in this actual world that we experience, the good and evil there is in it, and Leibniz's response to the problem of evil through his theodicy. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. (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)

For Leibniz, it was a requirement upon the `fundamentally real' to have a `principle of unity'. What does this mean?One general point is that Substance cannot be understood as pure extension. But there is a particular point about cohesion: a real thing had to have some means by which its parts were stuck together. But Leibniz' insistence on `unity' is also an insistence on indivisibility. Under this head there is first the point that there appears to be a contradiction between (...) extension and being incapable of being cut in two. Second, Leibniz uses the notion of `indivisibility' to mark the following distinction among things made up of parts: those which cannot be split without being destroyed; and the rest . To be `indivisible' is to be of the first type. Leibniz' insistence that the truly real must be `indivisible' is then his insistence that the truly real, if it is made up of parts, must be a thing with `integrity', i.e. not an aggregate.What does Leibniz think of as the connection between what is truly real and the possession of `integrity'? He took from Scholasticism the doctrine that action is necessarily attributed to a substance having `integrity', contructing what was in effect a theory of action with two parts: only self-subsistent substances can act; and an action is an origination of change. Leibniz thus insists that self-subsistent substances must be indivisible, in the sense that they cannot be mere aggregates. Aggregates cannot act, and self-subsistence in effect is the capacity for action. This is the most fundamental reason Leibniz had for insisting that the truly real must have a `principle of unity'.It is misleading to speak of Leibniz reintroducing the Scholastic form-and-matter conception of substance for the following reasons: the Scholastic `form' precisely lacked a `principle of action'; and during the period when it is suggested that Leibniz' conception was essentially Scholastic he was defending the view that what his `form' informed was not matter at all but what he called a `metaphysical point'. (shrink)

The correspondence between Leibniz and Arnauld was judged by Leibniz himself to be very useful for understanding his philosophy. Historians have concurred in this judgment. Leibniz did not find any philosophy of independent interest in the letters Arnauld sent him. Historians have, for the most part, also concurred in this finding. I shall argue that on one set of issues at least — modal metaphysics and free will — Arnauld accomplished more than facilitating Leibnizian elucidations. He held his own in (...) this dispute. Indeed, were it not for the general sophistication and superior handling of such issues as identity, unity, and the nature of body enjoyed by the Leibnizian system, the Cartesian position on modal metaphysics and free will espoused by Arnauld might have won the day in the eyes of later philosophers. A proper appreciation of the Cartesian framework should also make it of considerable interest to philosophers presently at work on the metaphysics of modality. I shall argue that Descartes and some Cartesians like Arnauld espoused a strongly actualist doctrine. This means they thought that all philosophically interesting uses of possibles were analyzable into facts about actually existing things. (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)

As an idealist, Gottfried Wilhelm Leibniz could not recognize anything corporeal as substantial. However, under the influence of Cartesian terminology, he devoted considerable effort to analysing the corporeal world, while not recognizing its real substantiality of course. Leibniz took the concept of substance from Plato, Aristotle and the scholastics, but developed it in two ways. It is a well-known fact that Leibniz introduced the term ‘corporeal substance’ in his letter to Antoine Arnauld dated to October 1687. In the letter, Leibniz (...) understands an object of nature, like an animal or a plant, as ‘corporeal substance’. In the very same letter, Leibniz introduces the terms ‘indivisibility’ and ‘phenomenon’. Every corporeal substance can be real only as a unity, i.e. by being indivisible. Such entity must have a soul or at least an entelechy. In an opposite case, that entity would not be a real unity but just a phenomenon. No corporeal entity is indivisible and therefore not a substance. The paper aims at introducing Leibniz’s distinction between substances and phenomena and taking a closer look at the historicalphilosophical influences Leibniz experienced while developing his views of the corporeal world. Aristotle and Descartes will receive most of the attention, of course, as the concepts of ‘entelechy’ and ‘hylomorphism’ were introduced by the former, and the understanding of corporeal substance as determined by extension alone is part of the latter. The core of the original critique by Leibniz takes off from the properties of the continuum as well as the nature of shape, motion and extension. The case of continuum will receive special attention. It is analysed with the help of the novel approaches by Samuel Levey and Vassil Vidinsky. Leibniz was critical about our poor understanding of the continuum but his own interpretation of it was not fully consistent either. Although the new developments enable us to take a fresh look that has not been possible so far, the issue remains open for further study. (shrink)

This chapter explores the relationship between the views of Leibniz and Berkeley on the fundamental nature of the created universe. It argues that Leibniz concurs with Berkeley on three key points: that in the final analysis there are only perceivers and their contents (subjective idealism), that there are strictly speaking no material or corporeal substances, and that bodies or sensible things reduce to the contents of perceivers (phenomenalism). It then reconstructs his central argument for phenomenalism, which rests on his belief (...) in the infinite division of matter, his doctrine of the ideality of relations, and the traditional principle of the convertibility of being and unity. Finally, it explores Leibniz’s belief that a body having its being in one perceiver can be “founded” on other perceivers, and considers Berkeley’s reasons for opposing such a view. (shrink)

Leibniz famously argues that there must be simple substances, since there are composites, and a composite is nothing but a collection of simples. I reconstruct Leibniz’s argument, showing that it relies on a commitment to mereological nihilism (i.e., the view that composites cannot be true beings). I show further that Leibniz endorses mereological nihilism as early as the 1680s and offers both direct and indirect support for this commitment: indirect support via the notion of unity and direct support via the (...) notion of persistence. I then assess the alignment of Leibniz’s mereological nihilism with his other commitments during the 1680s, including his potential commitment to corporeal substances. I argue that any viable interpretation of Leibniz’s commitment to corporeal substances is compatible with mereological nihilism, which provides a new perspective both on Leibniz’s developing theory of substance and on his mature theory of simple substance. (shrink)

In this dissertation it is argued that Kant's critique of Leibniz as found in the amphiboly chapter of the Critique of Pure Reason derives from his theory of reflection. It is argued further that this unfocused and fragmentary amphiboly chapter, which contains the Leibniz-critique, can be seen to have a previously unsuspected unity to it. The keys to perceiving this unity are the appendix's purpose, structure and mosaic composition. ;The primary purpose of the appendix is not to present Kant's criticisms (...) of Leibniz as is commonly thought, but rather it is to sketch his theory of reflection. Not only is this attested to by Kant himself , it is also made evident by the structure of the appendix. Structurally, the appendix is built around an introduction to the operation of transcendental reflection and a discussion of the concepts of reflection, this being the structure of each of the first three sections. By means of each pair of concepts of reflection Kant claims to summarize the basic tenets and origin of Leibniz's philosophy. Kant also claims that Leibnizls whole philosophy rests on one seminal error, which will be shown to be the omission of the operation of transcendental reflection. To be sure, Kant claims Leibniz made a number of other errors, but these various errors all derive from the omission of transcendental reflection. ;While this omission can be used to explain the other more well-known epistemological mistakes with which Kant charges Leibniz, it is undeniable that there are certain textual difficulties with the appendix. These can be dealt with by the hypothesis that the different sections were composed at different times and than pieced together without detailed revisions. If such a mosaic composition is granted, then some allowance can be made for the noticeable incongruities between these sections and for occasional problematic passages. This does not, however, warrant the claim that the appendix is not properly placed or unimportant. On the contrary, supplemented by clearer statements of Kant's theory of reflection and of his Leibniz-critique, the following interpretation shows that the appendix is properly placed and integral to the primary aims of the Critique of Pure Reason. (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 and the Rational Order of Nature is intended to offer a broad panorama on Leibniz’s philosophy. Although necessarily selective in its focus, it aspires to a comprehensive understanding of how the different parts of Leibniz’s philosophy — theodicy, ethics, metaphysics, natural philosophy — fit together in a coherent and compelling fashion. In the book, I indicate some of the places where tensions threaten the unity of this scheme. My primary goal, however, is to reconstruct a system that would be (...) recognizable to Leibniz himself. Within this system, primacy is assigned to the doctrine of theodicy. Although many topics vied for Leibniz’s philosophical attention, none was more firmly embedded in his consciousness than the problem of comprehending the existence and nature of the world in a way consistent with its creation by a supremely wise and good God. One of the central theses of the book is that it is only against the background of this project that we can properly understand the details of Leibniz’s complex metaphysics. (shrink)

In his Essays on the Intellectual Powers of Man Thomas Reid draws an analogy between his notion of the self and Leibniz’s notion of a monad. Reid formulates this analogy in order to highlight what he considers to be the essential feature of the self: its unified and indivisible structure. This paper considers Reid’s analogy in the specific context of the diachronic aspect of substantial unity. Its focus is specifically on the role that the idea of continuity plays in establishing (...) the unity and indivisibility of the entities in question (viz., the self and the monad). As part of the ongoing debate over Leibniz’s mature metaphysics of substance, this paper highlights the positive implication of Reid’s analysis of the self (usually viewed as a critical reaction to Locke and Hume) and its place within the early modern debate over the nature of substantial unity. (shrink)

The objective of this paper is to show the unity of leibniz's philosophical system. the connection between his inesse-principle and the idea that our world is the best of all possible worlds is this: the individual 'concept' of alexander may be defined as containing his whole biography, but the existence of an 'individual' falling under this concept can be deduced a priori only on the basis of the principle of sufficient reason, the application of which takes into account not only (...) god's intellect but also his goodness. (shrink)

Die Suche nach historischen Quellen für die Leibniz’sche Philosophie scheint zunächst unerschöpflich. Durch alle in diesem Band versammelten Arbeiten wird der Einfluss der Philosophie des Aristoteles auf das Leibniz’sche Denken näher umrissen. Ein wesentliches Ziel ist es hierbei, einen Beitrag zur Analyse dieser philosophischen Beziehung zu leisten und zu zeigen, dass auch Aristoteles’ Philosophie nach Ansicht unserer Autoren entscheidend zum Verständnis des Leibniz’schen Denkens beiträgt. Die Texte befassen sich mit wesentlichen Themen der Leibniz’schen Logik und Metaphysik, z. B. mit den (...) Grundbegriffen „Monade“ (und deren „Körperhaftigkeit“), „Entelechie“, „Nous“, mit dem Problem der Individuation (Individuum, Atomismus, Einheit), mit den substanziellen Formen, mit der Wissenschaft im Allgemeinen und der Technik, mit der Transformation der Logik, mit den Prinzipien (nämlich denjenigen des zureichenden Grundes, der Individuation und der Notwendigkeit), mit Zukunft und Kontingenz sowie Vergänglichkeit, mit der Theorie der syllogistischen Folgerung, usw. Diese Themen werden stets in der Gegenüberstellung von Leibniz und Aristoteles behandelt – sie zeigen daher, wie Leibniz aristotelische Thesen übernahm, veränderte oder kritisierte. The search for the historical sources of Leibniz’s philosphy initially seems to be unending. All the essays in this volume outline more clearly the influence of Aristotle’s philosophy on Leibniz’s thought. In this context a fundamental aim is to contribute to the analysis of this philosophical relationship and to demonstrate that Aristotle’s philosophy, in the opinion of our authors, plays a decisive role in the understanding of Leibniz’s thought. The texts address fundamental themes of Leibniz’s logic and metaphysics, e.g. the basic concepts of ‘monads’ (and their ‘corporality’), ‘entelechy’ and ‘nous; the problem of individuation (individual, atomism, unity); substantial forms; knowledge in general, and technology; the transformation of logic; principles (namely those of sufficient grounds, of individuation and of necesssity); future and contingency and transientness; the theory of syllogistic deduction, etc. These themes are regularly considered in the comparison between Leibniz and Aristotle – they demonstrate how Leibniz took over, treated or criticised Aristotelian theses. (shrink)

We argue in this paper that Leibniz’s characterization of a substance as “un être” in his correspondence with Arnauld stresses the per se unity of substance rather than oneness in number. We employ two central lines of reasoning. The first is a response to Mogens Lærke’s claim that one can mark the difference between Spinoza and Leibniz by observing that, while Spinoza’s notion of substance is essentially non-numerical, Leibniz’s view of substance is numerical. We argue that Leibniz, like Spinoza, qualifies (...) the substance as “one” primarily in a non-numerical sense, where non-numerical means per se unity or qualitative uniqueness. The second line of reasoning suggests that the term “one” should be understood as a-unity-presupposed-by-multiplicity in two senses: a) externally, in the sense of being presupposed by higher complex structures, such as aggregates, and, b) internally, in the sense of having itself a complex structure. We develop an analogy along these lines between the role the notion of a fundamental unity plays in Leibniz’s view of numbers and his view of substance. In other words, we suggest that looking at the role units play in Leibniz’s view of mathematics can shed some light on the role they play in his metaphysics. (shrink)