Beta integrals for several non-integer values of the exponents were calculated by Leonhard Euler in 1730, when he was trying to find the general term for the factorial function by means of an algebraic expression. Nevertheless, 70 years before, Pietro Mengoli (1626–1686) had computed such integrals for natural and half-integer exponents in his Geometriae Speciosae Elementa (1659) and Circolo(1672) and displayed the results in triangular tables. In particular, his new arithmetic–algebraic method allowed him to compute the quadrature of the circle. (...) The aim of this article is to show how Mengoli calculated the values of these integrals as well as how he analysed the relation between these values and the exponents inside the integrals. This analysis provides new insights into Mengoli’s view of his algorithmic computation of quadratures. (shrink)

The introduction of a new analytical method, due fundamentally to François Viète and René Descartes and the later dissemination of their works, resulted in a profound change in the way of thinking and doing mathematics. This change, known as process of algebrization, occurred during the seventeenth and early eighteenth centuries and led to a great transformation in mathematics. Among many other consequences, this process gave rise to the treatment of the results in the classic treatises with the new analytical method, (...) which allowed new visions of such treatises and the obtaining of new results. Among those treatises is the Arithmetic of Diophantus of Alexandria which was written, using the new algebraic language, by the French mathematician Jacques Ozanam, who in addition to profusely increasing the original problems of Diophantus, solved them in a general way, thus obtaining many geometric consequences. The work is handwritten, it has never been published, it has been lost for almost 300 years, and the known references show its importance. We will show that Ozanam’s manuscript was quoted as an important work on several occasions by others mathematicians of the time, among whom G. W. Leibniz stands out. Once the manuscript has been located, our aim in this article is to show and analyze this work of Ozanam, its content, its notation and its structure and how, through the new algebraic method, he not only solved and expanded the questions proposed by Diophantus, but also introduced a connection between the algebraic solutions and what he called geometric determinations by obtaining loci from the solutions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.1 (2003) 131-132 [Access article in PDF] Christia Mercer. Leibniz's Metaphysics: Its Origins and Development. New York: Cambridge University Press, 2001. Pp. xiii + 528. Cloth, $80.00. Christia Mercer's massive study is aimed at unearthing the hidden roots of Leibniz's metaphysics by placing the German philosopher back in the intellectual context within which his thought first took shape. In so doing she stresses (...) the fundamental importance of Leibniz's early years for the development of his philosophy. In particular she convincingly argues for the key role played by Leibniz's early exposure to the thought of eclectic thinkers (including his teachers) who were trying to build a new philosophical synthesis centered around the key tenets of Christian theology and combining elements of Aristotelianism, Platonism, and (in at least some cases) the new mechanical philosophy of nature.One of Mercer's central theses is that the methodological and metaphysical commitments that Leibniz developed during his youth formed the bedrock of his mature philosophy (23). More precisely, her bold claim is that Leibniz's core metaphysics (including the complete concept account of substance) was constructed in 1668-71, re-examined and slightly developed in 1672-79, and then used for the rest of his long philosophical career (18, 470). The key inspirational forces driving the development of Leibniz's philosophy, in her view, had even earlier origins. In the mid-1660s Leibniz did not yet have a fully formulated metaphysics; but he already possessed very definite philosophical objectives which were to guide the development of his metaphysics and form the unstated assumptions underlying his mature thought (40). Mercer identifies these unstated assumptions as a "Metaphysics of Method," a "Metaphysics of Substance," and a "Metaphysics of Divinity," all of which she finds fully developed in his early thought (468-9).According to Leibniz's "Metaphysics of Method" (examined in part I), there exists a truth beneath the prominent philosophical schools which can and ought to be discovered. This conciliatory methodology was Leibniz's answer to the political, religious, and philosophical chaos around him. He was deeply convinced that his brilliantly original eclectic metaphysics would provide the foundation of philosophical, theological, and even political peace. Leibniz's "Metaphysics of Substance," Mercer argues in part II, melded an Aristotelian approach to substance with a mechanical physics and originated at the very outset of his intellectual carrier in an attempt to solve specific theological problems (e.g., those of the incarnation and resurrection). Platonism in turn offered the material for Leibniz's "Metaphysics of Divinity" (explored in part III), that is, for his conception of the relationship between God and creatures. The fourth and final part of Mercer's book takes her analysis of Leibniz's writings up to 1679 and describes the laying of the foundations of his mature metaphysics. She concludes not only that Leibniz proposed the doctrine of pre-established harmony prior to his departure for Paris in March 1672, but also, more generally, that the other tenets of Leibniz's mature thought, including his theory of truth, grew naturally out of his early metaphysics (see, in particular, 2, 15-8, 47, 52, 169-70, 250-2, 300-1, 472).Throughout the book Mercer describes her interpretation as "startling," "unfamiliar," "dramatic," and "surprising," and fears that "readers may balk" at her conclusions since "so much of Leibniz's thought has escaped us for so long" (see, for instance, 1, 9, 471). Some readers may feel, on the contrary, that she has underestimated the extent to which several of her central theses—such as the importance of the earliest stages of Leibniz's philosophical development in general and of eclecticism, theological problems, and Platonism, as well as Aristotelianism within that development in particular—are already reflected in the [End Page 131] best recent traditions of international Leibniz scholarship. But her book undoubtedly breaks new ground and remains an important contribution to an exciting field which cannot and will not be ignored. While international Leibniz scholarship may not absorb some of this book's more... (shrink)

This paper advances the view that the history of philosophy is both a kind of history and a kind of philosophy. Through a discussion of some examples from epistemology, metaphysics, and the historiography of philosophy, it explores the benefit to philosophy of a deep and broad engagement with its history. It comes to the conclusion that doing history of philosophy is a way to think outside the box of the current philosophical orthodoxies. Somewhat paradoxically, far from imprisoning its students in (...) outdated and crystallized views, the history of philosophy trains the mind to think differently and alternatively about the fundamental problems of philosophy. It keeps us alert to the fact that latest is not always best, and that a genuinely new perspective often means embracing and developing an old insight. The upshot is that the study of the history of philosophy has an innovative and subversive potential, and that philosophy has a great deal to gain from a long, broad, and deep conversation with its history. (shrink)

Drawing inspiration from a well-attested historical tradition, I propose an account of cognition according to which knowledge is not only prior to belief; it is also, and crucially, not a kind of belief. Believing, in turn, is not some sort of botched knowing, but a mental state fundamentally different from knowing, with its own distinctive and complementary role in our cognitive life. I conclude that the main battle-line in the history of epistemology is drawn between the affirmation of a natural (...) mental state in which there is a contact between ‘mind’ and ‘reality’ and the rejection of such a natural mental state. For the former position, there is a mental state which is different in kind from belief, and which is constituted by the presence of the object of cognition to the cognitive subject, with no gap between them. For the latter position, all our cognition is belief, and the question becomes how and when belief is permissible. (shrink)

Of all the thinkers of the century of genius that inaugurated modern philosophy, none lived an intellectual life more rich and varied than Gottfried Wilhelm Leibniz. Maria Rosa Antognazza's pioneering biography provides a unified portrait of this unique thinker and the world from which he came. At the centre of the huge range of Leibniz's apparently miscellaneous endeavours, Antognazza reveals a single master project lending unity to his extraordinarily multifaceted life's work. Throughout the vicissitudes of his long life, (...) Leibniz tenaciously pursued the dream of a systematic reform and advancement of all the sciences. As well as tracing the threads of continuity that bound these theoretical and practical activities to this all-embracing plan, this illuminating study also traces these threads back into the intellectual traditions of the Holy Roman Empire in which Leibniz lived and throughout the broader intellectual networks that linked him to patrons in countries as distant as Russia and to correspondents as far afield as China. (shrink)

This paper aims to show that a proper understanding of what Leibniz meant by “hypercategorematic infinite” sheds light on some fundamental aspects of his conceptions of God and of the relationship between God and created simple substances or monads. After revisiting Leibniz’s distinction between (i) syncategorematic infinite, (ii) categorematic infinite, and (iii) actual infinite, I examine his claim that the hypercategorematic infinite is “God himself” in conjunction with other key statements about God. I then discuss the issue of whether the (...) hypercategorematic infinite is a “whole”, comparing the four kinds of infinite outlined by Leibniz in 1706 with the three degrees of infinity outlined in 1676. In the last section, I discuss the relationship between the hypercategorematic infinite and created simple substances. I conclude that, for Leibniz, only a being beyond all determinations but eminently embracing all determinations can enjoy the pure positivity of what is truly infinite while constituting the ontological grounding of all things. (shrink)

Throughout his long intellectual life, Leibniz penned his reflections on Christian theology, yet this wealth of material has never been systematically gathered or studied. This book addresses an important and central aspect of these neglected materials—Leibniz’s writings on two mysteries central to Christian thought, the Trinity and the Incarnation. -/- From Antognazza’s study emerges a portrait of a thinker surprisingly receptive to traditional Christian theology and profoundly committed to defending the legitimacy of truths beyond the full grasp of human reason. (...) This view of Leibniz differs strikingly from traditional perceptions of the philosopher as a “hard” rationalist and quasi-deist. Antognazza also sets Leibniz’s writings in the context of the important theological controversies of his day. (shrink)

What are intuitions? Do they exist as distinctive mental states? Do they have an epistemic function? Can we discern specific features that characterize intuitions? Questions like these are widely d...

In this paper I argue that, in Leibniz’s mature metaphysics, primary matter is not a positive constituent which must be added to the form in order to have a substance. Primary matter is merely a way to express the negation of some further perfection. It does not have a positive ontological status and merely indicates the limitation or imperfection of a substance. To be sure, Leibniz is less than explicit on this point, and in many texts he writes as if (...) primary matter were a positive constituent of a substance. It seems to me, however, that the view most in keeping with the thrust of his mature philosophical system is that captured by a striking remark of 1695: “Materia rerum est nihilum: id est limitatio [The matter of things is nothing: that is, limitation].” This becomes especially apparent in texts showing that Leibniz’s conception of primary matter corresponds to his conception of creaturely limitation. I start by discussing the notion of primary matter in the scholastic tradition. I then show that although Leibniz places the scholastic terminology of primary matter at a crucial juncture of his metaphysics, he thinks of primary matter in a way which significantly deviates from earlier scholastic views. I conclude that despite his adoption of distinctive terminology of Aristotelian scholasticism, instead of holding a broadly Aristotelian concept of primary matter as the ultimate subject of inherence, Leibniz thinks of primary matter according to a Neoplatonic blue-print in which matter is non-being, privation, mere absence of perfection. (shrink)

This contribution discusses Leibniz’s conception of the Christian church, his life-long ecumenical efforts, and his stance toward religious toleration. Leibniz’s regarded the main Christian denominations as particular churches constituting the only one truly catholic or universal church, whose authority went back to apostolic times, and whose theology was to be traced back to the entire ecclesiastical tradition. This is the ecclesiology which underpins his ecumenism. The main phases and features of his work toward reunification of Protestants and Roman Catholics, and (...) unification of Protestant churches are briefly explored, before turning to the issue of religious toleration. It is argued that a remarkably inclusive conception of toleration can be gleaned from a broad sample of Leibniz’s writings and correspondence. It is thanks to the philosophical and theological grounds of this conception that toleration can in principle be extended, for Leibniz, to all men and women of good will, including non-Christians, pagans, and atheists. (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)

As one might expect, throughout his life Leibniz assumed an attitude of religious toleration both ad intra (that is, toward Christians of other confessions) and ad extra (that is, toward non-Christians, notably Muslims). The aim of this paper is to uncover the philosophical and theological foundations of Leibniz’s views on this subject. Focusing in particular on his epistolary exchange with the French Catholic convert Paul Pellisson-Fontanier, I argue that neither toleration ad intra nor toleration ad extra is grounded for Leibniz (...) in indifference toward the content of revealed religion. On the contrary, Leibniz remained convinced of the objective truth of the Christian religion as it is handed down by the millennia-old tradition of the truly universal church. In his view, reasons internal to the very nature of salvation and to the conception of God and man explicitly contained in or, at least, in accord with this tradition present religious toleration as the only justifiable answer to the differences among religions. (shrink)

This contribution discusses Leibniz’s conception of faith and its relation to reason. It shows that, for Leibniz, faith embraces both cognitive and non-cognitive dimensions: although it must be grounded in reason, it is not merely reasonable belief. Moreover, for Leibniz, a truth of faith (like any truth) can never be contrary to reason but can be above the limits of comprehension of human reason. The latter is the epistemic status of the Christian mysteries. This view raises the problem of how (...) it can be determined whether a doctrine above the full grasp of human reason does or does not imply contradiction. The notion of ‘presumption’ and the ‘strategy of defence’ are presented and discussed as Leibniz’s way to tackle this issue. Finally, the article explores the ‘motives of credibility’ which, according to Leibniz, can and should be produced to uphold the credibility of a putative divine revelation, including his account of miracles. (shrink)

"This handbook is currently in development, with individual articles publishing online in advance of print publication. At this time, we cannot add information about unpublished articles in this handbook, however the table of contents will continue to grow as additional articles pass through the review process and are added to the site. Please note that the online publication date for this handbook is the date that the first article in the title was published online. For more information, please read the (...) site FAQs." -- website. (shrink)

This paper explores the question of Leibniz’s contribution to the rise of modern ‘science’. To be sure, it is now generally agreed that the modern category of ‘science’ did not exist in the early modern period. At the same time, this period witnessed a very important stage in the process from which modern science eventually emerged. My discussion will be aimed at uncovering the new enterprise, and the new distinctions which were taking shape in the early modern period under the (...) banner of the old Aristotelian terminology. I will argue that Leibniz begins to theorize a distinction between physics and metaphysics that tracks our distinction between the autonomous enterprise of science in its modern meaning, and the enterprise of philosophy. I will try to show that, for Leibniz, physics proper is the study of natural phenomena in mathematical and mechanical terms without recourse for its explanations to metaphysical notions. This autonomy, however, does not imply for Leibniz that physics can say on its own all that there is to be said about the natural world. Quite the opposite. Leibniz inherits from the Aristotelian tradition the view that physics needs metaphysical roots or a metaphysical grounding. For Leibniz, what is ultimately real is reached by metaphysics, not by physics. This is, in my view, Leibniz’s chief insight: the new mathematical physics is an autonomous enterprise which offers its own kind of explanations but does not exhaust what can (and should) be said about the natural world. (shrink)

ABSTRACT This paper explores some key features of Medieval accounts of intuition, focusing on Thomas Aquinas (1224/5–1274), on the one hand, and on Duns Scotus (c. 1266-1308), Peter Auriol (c. 1280–1322), and William Ockham (c. 1287-1347), on the other hand. The first section is devoted to the type of intuitive cognition which is accepted by all these authors, namely, the immediate and direct grasp of some present material object by the senses. It is from this basic sensory intuition – they (...) agree – that human cognition starts. The second section turns to intuitive intellectual cognition and to the much greater disagreements which divide these philosophers. Notwithstanding these important differences, the paper’s conclusion draws attention to the similarities in the conception of intuition which cut across the otherwise significantly different accounts of the authors discussed. I end with an invitation to recover their older way of thinking of intuition. (shrink)

Over the past decades a number of scholars have identified Johann Heinrich Bisterfeld as one of the most decisive early influences on Leibniz. In particular, the impressive similarity between their conceptions of universal harmony has been stressed. Since the issue of relations is at the heart of both Bisterfeld and Leibniz’s doctrines of universal harmony, the extent of the similarity between their doctrines will depend, however, on Bisterfeld and Leibniz’s respective theories of relations, and especially on their ontologies of relations. (...) This paper attempts to determine in more detail whether Bisterfeld’s ontology of relations contains at least the germ of the defining features of the ontology of relations later developed by Leibniz. It comes to the conclusion that, although Bisterfeld’s theory of relations is not as fully developed and explicit as that of Leibniz, it does contain all the key “ingredients” of it. (shrink)

Revolução e Terror andaram sempre de braços dados? Uma parcela significativa do que foi outrora a esquerda acredita que sim e propõe o fortalecimento da democracia como alternativa à revolução, vista como fonte do totalitarismo. Este artigo procura contribuir para esse debate, mostrando a alternativa revolucionária e democrática apresentada por Rosa Luxemburg. Para ela, a democracia não é um valor universal abstrato, mas justamente o resultado de um processo revolucionário em que as massas proletárias, atuando com irrestrita liberdade, lançam (...) os fundamentos de uma "nova época". Entretanto, a revolução alemã, em que Rosa Luxemburg e Karl Liebknecht tiveram um papel central, fracassa e ambos são assassinados. Derrota que traça, de certa forma, o destino da Alemanha contemporânea.Y aurait-il un lien indissoluble entre révolution et terreur? De nos jours, une partie de ce qui a été autrefois la gauche y croit Contre l'idée de révolution, saisie corne la source du totalitarisme, on propose le renforcement de la démocratie. Cet article a l'intention de contribuer à ce débat en montrant l'alternative révolutionnaire et démocratique présentée par Rosa Luxemburg. Pour elle la démocratie n'est pas une valeur universelle abstraite mais justement le résultat d'un processus révolutionnaire où les masses prolétariennes, agissant dans la plus large liberté, lancent les fondements d'une "nouvelle époque". Néanmoins la révolution allemande où Rosa Luxemburg et Karl Liebknecht ont eu un rôle de premier plan avorte et ils sont assassinés. Cette défaite trace, d'une certaine manière, le destin de l'Allemagne contemporaine. (shrink)

In this paper I will discuss certain aspects of Leibniz's theory and practice of 'soft reasoning' as exemplified by his defence of two central mysteries of the Christian revelation: the Trinity and the Incarnation. By theory and practice of 'soft' or 'broad' reasoning, I mean the development of rational strategies which can successefully be applied to the many areas of human understanding which escape strict demonstration, that is, the 'hard' or 'narrow' reasoning typical of mathematical argumentation. These strategies disclose an (...) 'other' reason, i.e. a complementary set of arguments and methods developed by Leibniz in order to deal with crucial issues such as the 'weighting' of probabilities and truths of fact. I will argue that one of the most compelling examples of the importance and fertility of Leibniz's 'other' reason is provided by his solution to the problems posed by the unique epistemological status of theological mysteries. (shrink)

The category of metaphysical evil introduced by Leibniz appears to cast a sinister shadow over the goodness of creation. It seems to imply that creatures, simply in virtue of not being gods, are to some degree intrinsically and inescapably evil. After briefly unpacking this difficulty and outlining a recent attempt to deal with it, this paper returns to the texts to propose a novel and multilayered understanding of Leibniz’s category of metaphysical evil by reading it against the backdrop of the (...) traditional typologies of evil with which he was unquestionably familiar. It comes to the conclusion that metaphysical evil plays two key roles for Leibniz. First, it captures what Aquinas and especially Suarez meant by ‘natural evil’. Contrary to the common assumption that it is Leibniz’s category of physical evil that holds the place of natural evil, the paper shows that Leibniz’s physical evil corresponds to Augustine’s category of evil of punishment for sin whereas natural evil – intended as a kind of evil which is not related to moral responsibility -- is subsumed under metaphysical evil. Secondly, the category of metaphysical evil covers also the notion of original creaturely imperfection. In classifying creaturely limitation as a kind of evil Leibniz breaks from the Augustinian-Thomist-Scholastic tradition and its distinction between negatio and privatio. On the other hand, notwithstanding this important break, Leibniz’s notion of metaphysical evil is intended to account for something which is firmly within the broadly Augustinian-Scholastic tradition, namely the ascription to all creatures of a limitation that stems from their being created ex nihilo. Finally, the paper returns a verdict of non-guilty to the charge that Leibniz’s metaphysical evil implies that creatures qua creatures are to some extent necessarily intrinsically evil. More generally, in typical Leibnizian fashion, the notion of metaphysical evil will appear to be a complex mix of indebtedness to tradition and bending of received doctrines into something significantly different. (shrink)

This article tries to show that focusing on why and how subject and object are distinct is of key importance for understanding the nature of knowledge itself. It argues that: 1) cognition starts with an aliud which is present to a felt self in a way fundamentally different from one’s own modes of being; 2) individual human knowledge in its paradigmatic form is essentially first-personal, that is, its object-directedness requires a built-in, implicit awareness of a ‘self’ that provides the unifying (...) perspective from which the aliud is apprehended; 3) this is a first-order awareness which is crucially distinct from the second-order awareness which requires a reflexive cognitive act – a distinction which the author proposes to cash out in terms of ‘first-person knowledge’ versus ‘self-knowledge. (shrink)

The issue discussed in this paper is as topical today as it was in the early modern period. The Reformation presented with heightened urgency the question of how to relate the system of beliefs and values regarded as fundamental by an established political community to alternative beliefs and values introduced by new groups and individuals. Through a discussion of the views on toleration advanced by some key early modern thinkers, this paper will revisit different ways of addressing this problem, focusing (...) on the relationship between truth and toleration. The comparison between different proposals in their historical and political contexts, will reveal a variety of understandings of toleration and of models for its promotion. These understandings will be shown to be grounded in different conceptions of religious belief, of its relation to truth, and of human reason’s ability to reach it. They will provide a map of possible models for addressing conflict in a pluralist world from which lessons of enduring relevance can be learnt. The upshot of the paper is that, from a theoretical point of view, the culprit in intolerance is not in itself belief in some objective truth. Some of the common assumptions about the denial of religious truth or the reduction of religious truth to a minimal creed as the best paths to universal toleration will be challenged. Likewise, the narrative centred on England and France which has led to the celebration of the heroes of a supposedly ‘universal’ toleration that still manages to exclude millions of people will be shown to be in need of significant revision. After discussing approaches based on the rights of the individual conscience and on the unknowability of religious truths above human reason, the paper will finally investigate whether grounds for a general and principled theory of toleration can be found in religious truth itself and, following the tradition of natural law, in some universal truth discoverable by natural reason. (shrink)

This contribution discusses Leibniz’s views on key Christian doctrines which were surrounded, in the early modern period, by particularly lively debates. The first section delves into his defence of the Trinity and the Incarnation against the charge of contradiction, and his exploration of metaphysical models capacious enough to accommodate these mysteries. The second section focuses on the resurrection and the Eucharist with special regard to their connections with Leibniz’s metaphysics of bodies. The third section investigates Leibniz’s position on predestination, grace, (...) salvation, and damnation. It comes to the conclusion that salvation, for Leibniz, does not ultimately depend on believing a set of true doctrines, but on a practical attitude: the love of God above all things. Leibniz’s theology is thus fundamentally a theology of love which is ultimately practical, and tries to be both universalist and Christian. (shrink)

Over the past decades a number of scholars have identified Johann Heinrich Bisterfeld as one of the most decisive early influences on Leibniz. In particular, the impressive similarity between their conceptions of universal harmony has been stressed. Since the issue of relations is at the heart of both Bisterfeld and Leibniz’s doctrines of universal harmony, the extent of the similarity between their doctrines will depend, however, on Bisterfeld and Leibniz’s respective theories of relations, and especially on their ontologies of relations. (...) This paper attempts to determine in more detail whether Bisterfeld’s ontology of relations contains at least the germ of the defining features of the ontology of relations later developed by Leibniz. It comes to the conclusion that, although Bisterfeld’s theory of relations is not as fully developed and explicit as that of Leibniz, it does contain all the key “ingredients” of it. (shrink)

This paper explores the development of Leibniz’s metaphysics of the Incarnation in the context of his philosophy. In particular it asks to what extent Leibniz’s repeated endorsement of the traditional analogy between the union in humankind of soul (mind) and body, and the union in Christ of divine and human natures, could be accommodated by his more general metaphysical doctrines. Such an investigation highlights some of the deepest commitments in Leibniz’s theory of substance as well as detect in it some (...) unresolved tensions. The paper comes to the conclusion that puzzling points of Leibniz’s metaphysics of the Incarnation, rather than being problems specific to his theology, uncover tensions in his theory of substance as such – tensions converging on the vexed question of whether there can or cannot be genuine corporeal substances in Leibniz’s mature philosophy. (shrink)

Leibniz is not commonly numbered amongst canonical writers on toleration. One obvious reason is that, unlike Locke, he wrote no treatise specifically devoted to that doctrine. Another is the enormous amount of energy which he famously devoted to ecclesiastical reunification. Promoting the reunification of Christian churches is an objective quite different from promoting the toleration of different religious faiths – so different, in fact, that they are sometimes even construed as mutually exclusive. Ecclesiastical reunification aims to find agreement at least (...) on the most important doctrines. Religious toleration involves accepting and respecting disagreement even on the most important doctrines. If one regards these two projects as alternative rather than complementary strategies for dealing with religious diversity, Leibniz might more readily be characterised as an ecumenist rather than a tolerationist. Such appears to be the conclusion, at any rate, implicit in the balance of critical literature on these topics: whereas a steady stream of studies has discussed Leibniz’s project of ecclesiastical reunification, only a meager trickle has been devoted to his views on toleration; and some of these studies go so far as to conclude that Leibniz had no doctrine of toleration at all. This paper will attempt to show, on the contrary, that a robust, many-layered, and unusually inclusive doctrine of toleration can be gleaned from Leibniz’s writings. This doctrine operated at least at three different levels: philosophical, theological, and pragmatic. As this implies, the doctrine of religious toleration, rather than being in collision with Leibniz’s core project of ecclesiastical reunification, was an essential element of that very project: it should be seen, in other words, not as a competing goal, but as a necessary first step toward ecclesiastical reunification. Yet at the same time it will also emerge that Leibniz’s doctrine of toleration was no mere function of this intra-Christian project of reunification: rather it was a still more fundamental principle which extended beyond the ecumenical project as well. It had the resources for accepting and respecting irreducible religious diversity and disagreement on points of importance not only between Christian communities, but also between Christians and non-Christians, including, in principle, even the atheists. These points will emerge from a discussion of statements on the philosophical, theological, and pragmatic justifications of religious toleration scattered throughout Leibniz’s sprawling corpus of writings. (shrink)

Over the past decades a number of scholars have identified Johann Heinrich Bisterfeld as one of the most decisive early influences on Leibniz. In particular, the impressive similarity between their conceptions of universal harmony has been stressed. Since the issue of relations is at the heart of both Bisterfeld and Leibniz’s doctrines of universal harmony, the extent of the similarity between their doctrines will depend, however, on Bisterfeld and Leibniz’s respective theories of relations, and especially on their ontologies of relations. (...) This paper attempts to determine in more detail whether Bisterfeld’s ontology of relations contains at least the germ of the defining features of the ontology of relations later developed by Leibniz. It comes to the conclusion that, although Bisterfeld’s theory of relations is not as fully developed and explicit as that of Leibniz, it does contain all the key “ingredients” of it. (shrink)

Introductions to epistemology routinely define knowledge as a kind of belief which meets certain criteria. In the first two sections of this article, I discuss this account and its application to religious epistemology by the influential movement known as Reformed Epistemology. In the last section, I argue that the controversial consequences drawn from this account by Reformed Epistemology offer one of the best illustrations of the untenability of a conception of knowledge as a kind of belief. I conclude by sketching (...) an alternative account of cognition which also provides a different framework for religious epistemology. (shrink)

This paper employs the revised conception of Leibniz emerging from recent research to reassess critically the ‘radical spiritual revolution’ which, according to Alexandre Koyré’s landmark book, From the closed world to the infinite universe was precipitated in the seventeenth century by the revolutions in physics, astronomy, and cosmology. While conceding that the cosmological revolution necessitated a reassessment of the place of value-concepts within cosmology, it argues that this reassessment did not entail a spiritual revolution of the kind assumed by Koyré, (...) in which ‘value-concepts, such as perfection, harmony, meaning and aim’ were shed from the conception of the structure of the universe altogether. On the contrary, thanks to his pioneering intuition of the distinction between physical and metaphysical levels of explanation, Leibniz saw with great clarity that a scientific explanation of the universe which rejected the ‘closed world’ typical of Aristotelian cosmology did not necessarily require the abandonment of key metaphysical doctrines underlying the Aristotelian conception of the universe. Indeed the canon of value-concepts mentioned by Koyré—meaning, aim, perfection and harmony—reads like a list of the most important concepts underlying the Leibnizian conception of the metaphysical structure of the universe. Moreover, Leibniz’s universe, far from being a universe without God—because, as Clarke insinuated, it does not need intervention from God—is a universe which in its deepest ontological fabric is interwoven with the presence of God.Author Keywords: Leibniz; Koyré; Clarke; Universe; Cosmology; Harmony. (shrink)

This chapter examines the moral philosophy of four early modern thinkers – Descartes, Malebranche, Leibniz, and Spinoza – who affirm in different ways the Platonic intuition of the priority of the perfect or infinite over the limited beings of which we have experience. In making this affirmation, Descartes, Malebranche, and Leibniz share the framework of a substantially traditional conception of God. Spinoza, on the other hand, challenges the Christianized Platonism of the other three while stretching to the extreme some features (...) of Platonism. (shrink)

Este trabajo trata de las aguas termales explotadas en dos contextos nacionales diferentes: en la ciudad argentina de Nueva Federación y en el municipio catarinense de Santo Amaro da Imperatriz, dialogando con una amplia literatura sobre este tema, y destacando sus múltiples usos, centrados para la salud, para actividades de ocio y religiosas. Además, estas aguas son asumidas como patrimonio natural y cultural, como fuente de identificación y referencia simbólica, y como el centro de las disputas en "campos sociales de (...) conflicto", relativos al poder de su uso y su apropiación. También se destacan, más allá de la similitud en la forma en que las aguas termales son explotadas y pensadas en los referidos contextos, las especificidades que marcan ambos balnearios. Por último, se subraya la importancia del termalismo tanto para la Provincia de Entre Ríos como para el Estado de Santa Catarina. (shrink)

This essential historical introduction to the main themes of the book starts with a close, sympathetic, and significantly novel analysis of a famous argument in Plato’s Republic in which Plato draws a distinction of kind between knowledge and belief, and between their objects. It is then demonstrated that the distinction, broadly so understood, remained a dominant force, in one form or another, in all non-sceptical branches of the European philosophical tradition, including empiricism, until the eighteenth century. It is argued that (...) there is much to learn from this history, and specific features of the traditional distinction are identified as deserving the further, sympathetic consideration given, in effect, in later chapters. (shrink)

This paper re-assesses the place of theology in Leibniz’s thought focusing on the relationship between theory and praxis. It takes as its point of departure a general conclusion established in previous work, namely that Leibniz’s key formulations of his overarching plan for the reform and advancement of all the sciences, are devoted to a set of objectives which is both shaped by broadly theological concerns and ultimately practical. Against this backdrop, the discussion will then turn to an exploration of how (...) Leibniz thought of theology as such. I argue that Leibniz was committed to the elaboration of a robust Christian dogmatic which was rationally defensible, and that this commitment resulted in a genuine engagement with Christian theology which took very seriously its theoretical content. The key additional thesis argued for in this paper is that this theoretical engagement was in the service of a science which he conceived as ultimately practical. For Leibniz, the ultimate aim of theology was to lead to the love of God above all things and, in so doing, to salvation and eternal happiness. It is in the light of this practical end that his theological pragmatism should be evaluated. When this is done, it becomes apparent that, beneath Leibniz’s efforts at theological reconciliation in the context of his Kirchenpolitik, there lies a deeper, fundamental and properly theological emphasis on praxis, grounded in Leibniz’s epistemology and driven by his conception of salvation as ultimately dependent on a practical attitude – the love of God above all things. Leibniz’s theological pragmatism was remarkably -- perhaps even surprisingly -- close to the family of prudential approaches to religious belief proposed by Pascal and later authors such as William James. The paper concludes that Leibniz’s conception of theology as ultimately practical is very much in line with the whole thrust of Leibniz’s intellectual programme as expressed in the over-arching plans discussed in the first section. These plans too were driven by a practical end: the promotion of the common good and of human happiness as the celebration of the glory of God in his creation. At the same time, the end of happiness – whether worldly or eternal -- should not be regarded as competing with Leibniz’s theoretical endeavours – whether in the sciences or in theology -- but as directly supported by them. (shrink)

This chapter argues that the outbreak of the Protestant Reformation undermined the Christian consensus that unaided human reason could prove God’s existence. As a consequence the issue of the provability of God in principle gained new prominence and had to be addressed in the first instance before entering the discussion of specific proofs of His existence. On the basis of the answers given to the preliminary question of the provability of God’s existence, the chapter discusses eighteenth-century reformulations of a priori (...) and a posteriori arguments for the existence of God, as well as new directions taken by natural theology in the late eighteenth century. (shrink)

Leibniz's repeated interventions in the Trinitarian polemics widespread throughout Europe in the seventeenth and eighteenth centuries cannot merely be read as scholastic exercises or concessions to the conventions of his time. On the contrary, they involved reflection on issues fundamental to Leibniz's philosophical doctrines: issues such as the relationship between faith and reason, the limitations of the human intellect and the various grades of human knowledge, and the significance of the ' analogia Trinitatis' reconsidered in light of the concept of (...) harmony. This paper concentrates on the writings of the young Leibniz before his visit to Paris and aims to examine the role played by contemporary discussions concerning the Trinity and the Incarnation in the formation of Leibniz's thought. (shrink)