Leibniz's Concept Research Articles

On the Unviability of Interpreting Leibniz's Infinitesimals through Non-standard analysis

Non-standard analysis has often been presented as the proper framework for expressing rigorously Leibniz's conception of infinitesimals. This paper intends to study this interpretation from an historical point of view and to dispel a series of misunderstandings on which it rests. In order to do so, we propose to go back to Leibniz's conception of quantity, number and magnitude, an approach which has not been developed yet in the literature.

Час і простір у філософії Ляйбніца. Частина І

Arina Oriekhova's interview with Professor Serhii Secundant, devoted to Leibniz's concept of time and space, the peculiarities of Michael Fatch's interpretation of this concept, and various historico-philosophical approaches to understanding Leibniz's philosophy as a whole.

God Can Do Otherwise

Abstract This paper locates a source of contingency1 for Leibniz in the fact that God can do otherwise, absolutely speaking.23 This interpretative line has been previously thought to be a dead-end because it appears inconsistent with Leibniz's own conception of God, as the ens perfectissimum, or the most perfect being (Adams 1994). This paper points out that the best argument on offer which seeks to demonstrate this inconsistency fails. The paper then argues that the supposition that God does otherwise implies for Leibniz (at least) that God would not be praiseworthy, which is an absurd implication—or a violation of the principle of sufficient reason (PSR)—but that this is not, strictly speaking, an inconsistency—or a violation of the principle of contradiction (POC).4 While praiseworthiness is a perfection—and is compossible with God's other perfections—and so God must in some sense instantiate it, this paper argues that, given the nature of praiseworthiness for Leibniz, it in fact makes sense to say that praiseworthiness is merely a contingent perfection of God.5

Leibniz’s Philosophical Dream of Rational and Intuitive Enlightenment

This paper is a new translation and interpretation of the essay by Leibniz which has come to be known as “Leibniz’s Philosophical Dream.” Leibniz used many different literary styles throughout his career, but “Leibniz’s Philosophical Dream” is unique insofar as it combines apparent autobiography with a dreamscape. The content is also somewhat surprising. The essay is reminiscent of Plato, insofar as Leibniz describes a transition from existence in a cave to a more enlightened mode of being outside of it. But, in contrast with the usual identification of Leibniz as a “rationalist,” the mode of being that is valorised involves cognition that is intuitive and supra-rational. The paper begins with the translation followed by an interpretation of the essay. I conclude by considering the ramifications of my interpretation for our conception of Leibniz’s philosophy.

Concept of Personal Identity

Leibniz's concept of monads had of great importance for the development of the idealistic conception. Through Kant and his "Physical Monadology" she infiltrated into modern German philosophy. However, not only modern idealists referred to the concept of monads. Especially, that many scientific disciplines, which emanated from philosophy, related to the scope of idealistic notions, for example: psychology or sociology. German psychology and its creators have many often referred to monads theory. Freud, Fromm and Jung presented even their own point of views on this topic. Later theories, such as Lowe's theory, also refer to the concept of monads. These relations and the historical connections between monad theory and modern German psycho-philosophy are shown in this work.

The Old/New Enlightenment: From the Compossible to the Complex

There has been considerable debate as of late concerning the need for a new Enlightenment. The “old” Enlightenment was considered inadequate to contemporary challenges, having failed in achieving genuine reform. Arguments for and against a “new” Enlightenment have come from a range of disciplines: the history of ideas, political science, philosophy, socio‐economic history, and literary studies. The cause for a perceived need for a new approach to Enlightenment concepts is multivalent. Most immediate is the radical questioning of the value of the humanities in general and literature in particular, the corporatization of higher education, a misreading of the historical epoch itself, and a shift to right‐wing ideologies in Western societies. This essay reviews reasons behind the perceived need for a reevaluation, but argues that only reclamation of its essential values is necessary. The guiding concepts here are Leibniz's concept of compossibility and the recognition of motion as integral to everything.

Buried layers: On the origins, rise, and fall of stratification theories.

This article presents a historical analysis of the origins, rise, and demise of theories of stratification (Schichtentheorien). Following their roots in the ancient metaphysical idea of the "great chain of being," Aristotle's scala naturae, the medieval "Jacob's ladder," and Leibniz's concept of the lex continua, I argue that theories of stratification represent the modern heir to the ancient cosmological idea of a harmonious, hierarchical, and unified universe. Theories of stratification reached their heyday during the interwar period within German academia, proliferating over a vast number of disciplines and rising to special prominence within personality psychology, feeding the hope for a unitary image of the world and of human beings, their biological and mental development, their social organization and cultural creations. This article focuses on the role of visuality as a distinct mode of scientific knowledge within theories of stratification as well as the cultural context that provided the fertile ground for their flowering in the Weimar Republic. Finally, the rapid demise of theories of stratification during the 1950s is discussed, and some reasons for their downfall during the second half of the 20th century are explored. (PsycINFO Database Record

Medieval Romance: The Aesthetics of Possibility ed. by James F. Knapp and Peggy A. Knapp

Reviewed by: Medieval Romance: The Aesthetics of Possibility ed. by James F. Knapp and Peggy A. Knapp Daniel Reeve James F. Knapp and Peggy A. Knapp. Medieval Romance: The Aesthetics of Possibility Toronto: University of Toronto Press, 2018. Pp. 264. $75.00. The authors of this intriguing book regard medieval romance as a "deeply philosophical" (3) kind of writing whose speculative force lies in its exploration of possible worlds and its resistance to conceptualization. In order to explain the continuing "immediacy" (ix) of romance for its readers today, the authors draw upon Kantian aesthetics, since, in such a system, aesthetic judgments are universal, not historically contingent (22–23). Accordingly, the book devotes much space to arguing that the texts it discusses are beautiful in the Kantian sense. This commitment to arguing for the transhistorical appeal of romance surfaces in several other aspects of the book's structure. The core readings of medieval romances are supplemented at various points with discussions of postmedieval analogues and adaptations. This practice is justified using a theory of bidirectional intertextuality derived from Leibniz's concept of apperception. Texts contain a multiplicity of [End Page 488] detail, and our knowledge of other texts determines which details are perceived as important; the simple presence of intertexts thus exerts a force on our interpretation (12–14). The sections in which later adaptations are discussed generally follow this gentle logic of juxtaposition, rather than insisting on rigid connections. The Leibnizian notion of "folded time" is another key component of the book's methodology. Time is not a "smooth historical progression" but contains "mysterious deep connections" along different axes (9). On the face of it, this would seem to be queer temporality stripped of any non-normative politics, and while the similarity with Carolyn Dinshaw's work is briefly noted (9), the absence of any detailed comparison of these two theoretical frameworks is regrettable. Each of the book's six chapters focuses on case studies that "have echoed across culture with particular vitality and which reflect internally on romance itself" (6). Chapter 1, on the Lais of Marie de France, takes an initial cue from the Prologue's famous metapoetic reflection on the interpretation of difficult texts: Marie's term surplus de sen is used to describe an excess "within the text itself, an excess of tiny detail always available to new perception" (31). In a reading of Eliduc alongside John Fowles's The Ebony Tower, the concept of possible worlds allows for a deft account of the consequences of changing the lai's name (as Marie's narrator suggests) from Eliduc to Guildeluëc and Guilliadun: "the tale suddenly becomes two tales … both told at the same time, through the same events … obscuring untroubled perception of either" (36). The reading of Lanval draws upon the Leibnizian idea of compossibility (the capacity of objects to exist together in a given world without logical contradiction) to show how the lai uses Lanval's love for a fairy from another world to express the irreconcilability of love and feudal obligation. The chapter's final reading, of Yonec, makes a distinction between two types of possible world, metaphysical and epistemic, in order to explore what might be at stake in the imaginative work of fiction for the construction of possible futures. Chapter 2, on Sir Orfeo, takes the Middle English poem as a point in the intertextual web of the Orpheus legend, between ancient and more recent versions: Virgil's Georgics, Marcel Camus's Black Orpheus, and Salman Rushdie's The Ground beneath Her Feet. The poem's intertextual affiliations are taken as analogous to a narrative scheme in which "the past is not restored, but strangely folded into Orfeo's present" (54). The reading thus teases out the poem's awareness of its own legendary past [End Page 489] and narrative future, reflecting on the ways in which traveling through time and between worlds demarcates the essential and contingent aspects of personal identity. Chapter 3 discusses Chaucer's Troilus and Criseyde, arguing that the poem oscillates between a "realistic mode" and a "tendency towards allegory" (85). This refusal of either schematic allegory or simplistic realism allows Troilus and...

Leibniz on determinateness and possible worlds

AbstractLeibniz argues that God doesn't create everything possible because not all possible things are compossible, that is, compatible with each other. Much recent debate has focused on Leibniz's conception of compossibility. One important aspect of this debate, which has not been examined directly, is the distinction between possible worlds and possible creations: the notion of possible world is more robust than simply whatever God can create. Many commentators have relied on this distinction without a clear formulation of it.I develop the distinction between possible worlds and possible creations by looking at how Leibniz characterizes what God is capable of creating. I argue that possible creations must be both logically consistent and determinate. Possible creations differ from possible worlds insofar as possible creations fail to be either maximal or harmonious. I conclude, therefore, that focusing on the notion of determinateness offers a new approach to answering the question why doesn't God create everything possible?

The Force that Is but Does Not Act: Ruyer, Leibniz and Deleuze

In What Is Philosophy?, Deleuze and Guattari attribute to Leibniz and Raymond Ruyer a vitalism of ‘a force that is but does not act’. This is a judicious characterisation of Leibniz's vitalism, but not Ruyer's. In The Fold, Deleuze presents Ruyer as a disciple of Leibniz, but if Leibniz's monads have no doors or windows, Ruyer's are nothing but doors and windows, nothing but liaisons actively forming themselves. For Ruyer, there is only one force, a consciousness-force, matter-form in sustained, non-localisable self-formation. In Deleuze's reading of Leibniz's concept of the vinculum substantiale, Deleuze comes close to presenting a notion of force like that of Ruyer's, in that the vinculum inextricably interfolds monads and bodies, but ultimately the separation of the forces of monads from those of bodies prevails in a fashion incompatible with Ruyer's conception of force. Deleuze and Guattari make use of Ruyer's understanding of consciousness and the brain as the auto-overflight of an absolute surface in their concluding remarks on philosophy and the arts in What Is Philosophy?, but they depart from Ruyer in their characterisation of the relation of force to those two domains, ultimately because they reject Ruyer's advocacy of a universal, goal-directed finalism.

Metaphysics of the principle of least action

Despite the importance of the variational principles of physics, there have been relatively few attempts to consider them for a realistic framework. In addition to the old teleological question, this paper continues the recent discussion regarding the modal involvement of the principle of least action and its relations with the Humean view of the laws of nature. The reality of possible paths in the principle of least action is examined from the perspectives of the contemporary metaphysics of modality and Leibniz's concept of essences or possibles striving for existence. I elaborate a modal interpretation of the principle of least action that replaces a classical representation of a system's motion along a single history in the actual modality by simultaneous motions along an infinite set of all possible histories in the possible modality. This model is based on an intuition that deep ontological connections exist between the possible paths in the principle of least action and possible quantum histories in the Feynman path integral. I interpret the action as a physical measure of the essence of every possible history. Therefore only one actual history has the highest degree of the essence and minimal action. To address the issue of necessity, I assume that the principle of least action has a general physical necessity and lies between the laws of motion with a limited physical necessity and certain laws with a metaphysical necessity.

Concrete curves: architectural curvilinearity, Descartes’ Géométrie, Leibniz's calculus and Eero Saarinen's TWA terminal

ABSTRACTSince the 1990s, analyses of architectural curvilinearity have drawn upon Gilles Deleuze's The Fold, a philosophical consideration of the Baroque in terms of Gottfried Wilhelm von Leibniz's calculus and theory of matter. Deleuze's analogy between a curvilinear aesthetic and Leibniz's conception of curvature and matter as forces has influenced investigations of both Baroque and contemporary architecture. I argue that architectural curvilinearity can also be understood in terms of another mathematical conception of curves – namely, René Descartes’ geometric representation of curvature. Like Leibniz, Descartes’ understanding of mathematical curvature resembles his theory of matter. I examine how Eero Saarinen's TWA terminal, a Baroque-inspired building, can be considered in terms of Leibniz's notion of curves and matter as forces as well as Descartes’ conception of curves and matter as extensions in space. This paper offers a new understanding of how Deleuze's ideas in The Fold are applicable to investigations of architecture.

On Kant’s Knowledge of Leibniz’ Metaphysics—a Reply to Garber

Daniel Garber has put forward an argument that aims to show that Kant’s understanding of Leibniz’ metaphysics should be discounted because he could only have had access to a small and narrow sample of Leibniz’ works from around 1710–1714. In particular, Garber argues that as Kant could not have read Leibniz’ correspondence with Arnauld or his correspondence with Des Bosses he could not have had an adequate conception of Leibniz’ understanding of the relation between substance and body. I will show that Kant could have read some of the Arnauld correspondence and practically all of the Des Bosses correspondence, as well as a number of other related texts that are important for understanding Leibniz’ metaphysics, over a decade before writing the Critique of Pure Reason. Garber’s historical-textual argument for dismissing Kant’s account of Leibniz’ metaphysics is therefore seriously misleading.

Heidegger on the Being of Monads: Lessons in Leibniz and in the Practice of Reading the History of Philosophy

This paper is a discussion of the treatment of Leibniz's conception of substance in Heidegger's The Metaphysical Foundations of Logic. I explain Heidegger's account, consider its relation to recent interpretations of Leibniz in the Anglophone secondary literature, and reflect on the ways in which Heidegger's methodology may illuminate what it is to read Leibniz and other figures in the history of philosophy.

Four: A Reflection on the Wholeness of Nature, Part III

In this third part of my reflection on the wholeness of nature I return to the period of the Enlightenment and provide some of the main steps that led to the disappearance of the Aristotelian concept of the soul. The mechanical paradigm rapidly dethroned the ancient wisdom based on the principle of life. For Gottfried Wilhelm Leibniz, one of the pioneers of the Scientific Revolution, the reform had been carried too far and lacked great ideas on the majesty of nature. In particular, the new science lacked an ontological principle upon which to ground reality, which he found in the principle of harmony. I illustrate Leibniz's conception of the monad, or soul, with personal dreams that helped me understand it, and show that the soul is intimately related to harmony and the dimension of time. This illustration further refines the idea of a physoid nature, introduced in this series of articles. Finally, I interpret a third dream in the series on the symbol of the number four, which is at the basis of this reflection, in the light of the physoid nature of the soul.

Leibniz's Concept of Substance and his Reception of John Calvin's Doctrine of the Eucharist

Leibniz saw the question of the eucharist as a crucial stumbling block to the agreement between Lutherans and Calvinists. Mandated together with Daniel Ernst Jablonsky to prepare working documents for the negotiations between Hanover and Brandenburg in 1697, Leibniz carefully read through the Calvinist Confessions of faith and the works of Calvin in their 1671 edition. He made an extensive collection of excerpts from the Confessions of faith and from Calvin's Institutes all intended to show that Calvinists admitted the substantial presence of Christ's body in the eucharist. (This collection of excerpts is analysed here for the first time and compared with another little-known document, the Unvorgreiffliches Bedencken). L. had argued previously in 1691/92 that, contrary to the assertions of Pellisson-Fontanier, his own conception of substance and of Christ's presence in the eucharist was completely different from Calvin's. However, by 1697, it was clear to Leibniz that Calvin's concept of substance, which was broadly speaking Aristotelian, was never defined clearly by the reformer, and could be made to coincide with Leibniz's own notion of substance as force rather than substance in its dimensional sense. At the same time L. dissociated Ubiquitarianism (doctrine characteristic of late sixteenth century Lutheranism, which defended the dimensional presence of Christ's body in heaven and in the eucharist, by arguing that Christ in his divine nature could cause his physical body to be present in several places at the same time) from Lutheranism. He also drove a wedge between the doctrines of Zwingli and Calvin. L. thus attempted to find religious union on a common ontology and he might well have succeeded if it were not for complex political circumstances, which ultimately caused the failure of the negotiations.

Disentangling Leibniz's Views on Relations and Extrinsic Denominations

Disentangling Leibniz's Views on Relations and Extrinsic Denominations Anja Jauernig (bio) 1. Introduction Most commentators agree that Leibniz advocates some version of a doctrine of the ideality or reducibility of relations, but there is considerable disagreement on the question of what exactly this doctrine is supposed to amount to. This question is pressing because of the central place that Leibniz's theory of relations occupies in his philosophy. How one understands Leibniz's views on relations will influence how one understands Leibniz's complete concept doctrine, his (super)essentialism, the principle of the identity of indiscernibles, his account of compossibility, and his theory of space and time, to name just a few examples.1 [End Page 171] The most divisive question in this context is whether Leibniz is what I will call a "reductionist," i.e., whether he advocates some form of "reductionism" about relations. There are several ways in which this question could be understood, depending on how the term 'reductionism' is explicated. A reductionist about relations could be said to hold that all there is in the world are individuals and their intrinsic properties, or that a complete description of the world is possible in purely non-relational terms, or that all relations and extrinsic properties (strongly) supervene on intrinsic properties—which are popular ways in which Leibniz's views on relations and extrinsic denominations have been interpreted. The question of whether Leibniz is a reductionist splits commentators into two camps: those who answer the question in the affirmative,2 and those who answer it in the negative.3 Despite much good work on this topic, the proponents of the two camps have been talking past each other to a considerable extent. One of the main factors [End Page 172] hampering the discussion is the widespread, if only implicit, assumption that there must be one unified thesis, or, at most, a small number of closely related theses, that Leibniz is trying to articulate in his various pronouncements on relations and extrinsic denominations. On my view, this assumption is clearly false.4 Another obstacle to exegetical progress is the frequent inadequate appreciation of Leibniz's division of reality into different ontological levels. The failure to take this level distinction into account tends to obscure the complex and multi-faceted nature of Leibniz's views on relations and extrinsic denominations. Once Leibniz's various theses about relations and extrinsic properties have been sorted out, it becomes clear that both camps of commentators are correct about some aspects of Leibniz's views, even though the overall flavor of Leibniz's position on relations remains non-reductionist. The argument of this paper will proceed as follows. Section 2 covers some preliminaries and background material, including a sketch of Leibniz's tiered ontology. In section 3, I discuss Leibniz's thesis of the ideality of abstract relations. Section 4 explicates the sense in which all phenomenal extrinsic properties can be reduced to the perceptions of monads, and addresses the question of whether monads have irreducibly extrinsic properties. In section 5, I analyze Leibniz's notorious claims that there are no purely extrinsic denominations and that every extrinsic denomination has a foundation in the thing denominated, which I take to be concerned primarily with the phenomenal level of reality. I argue that these claims do not commit Leibniz to reductionism, but they warrant ascribing to him five other weaker theses about extrinsic denominations and their relation to intrinsic denominations. In the sixth and final section, I revisit Leibniz's much discussed project of reformulating relational sentences into non-relational ones, and identify two more Leibnizian theses about relations and extrinsic properties. 2. Preliminaries and Background The main focus of this paper is on Leibniz's views on relations and extrinsic properties in his mature philosophy, which I take to have been in place by the mid-1680s, at least as far as its main doctrines and principles are concerned, several changes in emphasis and presentation style notwithstanding.5 An important step toward disentangling these views is a careful appreciation of Leibniz's division of reality into several ontological levels. This level-distinction is widely acknowledged in the literature, but there are different views...

The Epistemological Roots of the Dispute over Time and Freedom in the Leibniz-Clarke Correspondence

Historians and philosophers of science commonly ignore the epistemological disagreement about the theoretical limits of rationality that underlies the disputes over the absoluteness or relationality of time and the true nature of divine freedom in the Leibniz-Clarke Correspondence. Accordingly, I explore both the logical interconnectedness and the deeper philosophical roots of these disputes, with a view to evaluating the contrast in Leibniz's and Clarke's underlying notions of the limits of rationality. In tracing this contrast, I attempt to show first that Clarke's position can be used to demonstrate successfully that Leibniz's concept of divine freedom, and his use of the Principle of Sufficient Reason to justify it, involves a contradiction. Second, I attempt to demonstrate that the concept of the limits of rationality underlying Clarke's conception of divine freedom can be successfully defended against Leibniz's attacks.

Guerre et paix selon Leibniz

AbstractThis article deals with Leibniz's dynamic conception of political order. Leibniz reduces the sovereignty of States to the monopoly of coercion by setting apart jurisdictional monopoly and sovereignty. With this new definition of sovereignty however, war becomes the core of international relations. The sovereigns' ability to make war is the condition to take part in law of nations, whose precise aim is to prevent wars. Peace can only exist if there is a balance between opposite forces of similar magnitude that cancel each other.

Leibniz on Final Causes

In this paper, I investigate Leibniz's conception of final causation. I focus especially on the role that Leibnizian final causes play in intentional action, and I argue that for Leibniz, final causes are a species of efficient causation. It is the intentional nature of final causation that distinguishes it from mechanical efficient causation. I conclude by highlighting some of the implications of Leibniz's conception of final causation for his views on human freedom, and on the unconscious activity of substances.