Leibniz’s Network

Leibniz’s network is a major subject of study in its own right, exemplifying the centrality of the ‘republic of letters’ to the intellectual history of early modern Europe. Yet the primary reason for discussing it here is that understanding Leibniz’s network is also indispensable for understanding his thought. Leibniz’s thought is not a fixed product, immortalized in a small number of polished publications. Its content and expression evolved constantly in a long series of fragmentary statements, many penned in dialogue with contemporaries. To understand these fragments, we must understand the hundreds of people with whom Leibniz was interacting, and the networks and communities for which they spoke. Grasping the complexity of these interactions surpasses the limitations of print technology. Obtaining a synoptic understanding of Leibniz’s network therefore requires a new generation of digital infrastructure capable of assembling and exploring the relevant data in a highly collaborative and interactive fashion.

Leibniz as Historian

The aim of this chapter is to provide a first impression of Leibniz’s long and deep engagement with history and historiography, in the hope of stimulating a more thorough investigation of this poorly studied aspect of his oeuvre. After a brief account of Leibniz’s work as an historian, the second section of the chapter explores Leibniz’s conception of history, which is shown to be profoundly embedded in his philosophical thought. The last section focuses on epistemological issues, namely, on Leibniz’s view of testimony as the epistemological ground of historical reconstruction, on the problem of historical credibility and scepticism, and on the role of sources in historiography.

The Calculus

This chapter discusses the history of Leibniz's work on infinitesimal calculus of which a considerable part is still unknown. His new method, emerging from studies in the summing of infinite number series and the quadrature of curves, combines two procedures with opposite orientation, differentiation and integration. These two procedures are united in a common formalism introducing in 1675 the symbols d and ∫ for differentiation and integration. Subsequently, Leibniz and his followers developed new rules and solution methods, and applied the calculus to physics. During Leibniz’s lifetime the public success of his calculus was overshadowed by discussions over the foundations of his methods and the priority dispute with Newton. While infinitesimals were eliminated from the calculus during the 19th century, non-standard analysis reinstated them again. The status of infinitesimals in Leibniz’s own philosophy of mathematics is still disputed.

Freedom and Contingency

This chapter attempts to clarify Leibniz’s theories of freedom and contingency by viewing them against the backdrop of his efforts to reengineer important philosophical concepts. In developing a concept of freedom, Leibniz is above all concerned to preserve divine and human responsibility (Section 1). His account of freedom requires him to reject necessitarianism, that is, the view that all things are absolutely necessary (Section 2). Leibniz therefore carves out two concepts of contingency. The first is centered on the thought that something may be contingent considered by itself – that is, per se – even if it is necessary in light of God’s goodness or will (Section 3). The second is centered on the thought that it may be possible to draw a distinction between contingent and necessary propositions in terms of logic alone (Section 4).

Calculating Machine

This chapter sketches the challenges Leibniz faced in building a calculating machine for arithmetic, especially his struggle to coordinate with skilled artisans, surveys his philosophical remarks about such machines and the practical knowledge needed to make them, and recounts the eighteenth-century legacy of his failure to produce a machine understood to be adequately functional.

Force and Dynamics

Leibniz’s mature physics is most noted for the centrality of the notion of force and the development of the dynamics, the science of force. This chapter examines the development and challenges of this “dynamics project,” active from 1676–c. 1700, from its initial motivations and methodological maturation to its important convergence with the systematic metaphysics of his later writings. The chapter begins with Leibniz’s early approach to physical questions and his development in Paris (1672–76), then turns to the emerging theory of power or force from the late 1670s to the late 1680s. In 1689, Leibniz coined the term “dynamica” and composed the two most significant texts of the project. Finally, during the period after 1690, Leibniz not only developed the internal structure of the dynamics but also employed its results toward a convergence between his scientific work and his systematic metaphysics of substantial forms.

Body and Corporeal Substance

This chapter discusses Leibniz’s conception of body and the closely related concept of corporeal substance. Leibniz saw problems with Descartes’s and Hobbes’s view and introduced a new conception of body based on a metaphysical argument that multiplicity presupposes unities, leading Leibniz to the view that extended bodies are made up of corporeal substances, genuine unities on the model of living animals, and a physical argument that the proper laws of nature require forces, active and passive in bodies; thus, that extended bodies are to be understood in terms of corporeal substances considered as unities of form (active force) and matter (passive force). The chapter traces the development of this view of body as Leibniz introduces monads as metaphysically more fundamental than corporeal substances and struggles to integrate them into the world of nonextended monads.

Ecclesiology, Ecumenism, and Toleration

This chapter discusses Leibniz’s conception of the Christian church, his life-long ecumenical efforts, and his stance toward religious toleration. Leibniz 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 traceable back to the entire ecclesiastical tradition. This is the ecclesiology that 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, for Leibniz, toleration can be extended in principle to all men and women of good will, including non-Christians, pagans, and atheists.

Early Physics

This chapter discusses Leibniz’s earliest work on physical questions. It begins with how his discovery of contemporary publications on the laws of motion prompted him to investigate the topic for himself, leading him to make a fundamental distinction between pure theory and natural phenomena. From this distinction emerged his two tracts Theoria motus abstracti and Hypothesis physica nova, the latter of which played an important role in his admission to the fellowship of the Royal Society in 1673. Salient parts of these two tracts are outlined, as are some of the more important physical ideas Leibniz developed from them during his stay in Paris.

Faith and Reason

This chapter discusses Leibniz’s conception of faith and its relation to reason. It shows that, for Leibniz, faith embraces both cognitive and noncognitive dimensions: although faith 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 defense” are discussed as Leibniz’s way to tackle this issue. Finally, the chapter explores the “motives of credibility” that, according to Leibniz, can and should be produced to uphold the credibility of a putative divine revelation, including his account of miracles.