What I plan to do in this paper is to provide a survey of the ways in which Spinoza’s philosophy has been deployed in relation to early modern thought, in the history of ideas and in a number of different domains of contemporary philosophy, and to offer an account of how some of this research has developed. The past decade of research in Spinoza studies has been characterized by a number of tendencies; however, it is possible to identify four main (...) domains that characterize these different lines of research: studies of Spinoza’s individual works, of its problematic concepts, from the point of view of the history of ideas, and comparative studies of Spinoza’s ideas. (shrink)

In the chapter of Difference and Repetition entitled ‘Ideas and the synthesis of difference,’ Deleuze mobilizes mathematics to develop a ‘calculus of problems’ that is based on the mathematical philosophy of Albert Lautman. Deleuze explicates this process by referring to the operation of certain conceptual couples in the field of contemporary mathematics: most notably the continuous and the discontinuous, the infinite and the finite, and the global and the local. The two mathematical theories that Deleuze draws upon for this purpose (...) are the differential calculus and the theory of dynamical systems, and Galois’ theory of polynomial equations. For the purposes of this paper I will only treat the first of these, which is based on the idea that the singularities of vector fields determine the local trajectories of solution curves, or their ‘topological behaviour’. These singularities can be described in terms of the given mathematical problematic, that is for example, how to solve two divergent series in the same field, and in terms of the solutions, as the trajectories of the solution curves to the problem. What actually counts as a solution to a problem is determined by the specific characteristics of the problem itself, typically by the singularities of this problem and the way in which they are distributed in a system. Deleuze understands the differential calculus essentially as a ‘calculus of problems’, and the theory of dynamical systems as the qualitative and topological theory of problems, which, when connected together, are determinative of the complex logic of different/ciation. (DR 209). Deleuze develops the concept of a problematic idea from the differential calculus, and following Lautman considers the concept of genesis in mathematics to ‘play the role of model ... with respect to all other domains of incarnation’. While Lautman explicated the philosophical logic of the actualization of ideas within the framework of mathematics, Deleuze (along with Guattari) follows Lautman’s suggestion and explicates the operation of this logic within the framework of a multiplicity of domains, including for example philosophy, science and art in What is Philosophy?, and the variety of domains which characterise the plateaus in A Thousand Plateaus. While for Lautman, a mathematical problem is resolved by the development of a new mathematical theory, for Deleuze, it is the construction of a concept that offers a solution to a philosophical problem; even if this newly constructed concept is characteristic of, or modelled on the new mathematical theory. (shrink)

To make sense of what Gilles Deleuze understands by a mathematical concept requires unpacking what he considers to be the conceptualizable character of a mathematical theory. For Deleuze, the mathematical problems to which theories are solutions retain their relevance to the theories not only as the conditions that govern their development, but also insofar as they can contribute to determining the conceptualizable character of those theories. Deleuze presents two examples of mathematical problems that operate in this way, which he considers (...) to be characteristic of a more general theory of mathematical problems. By providing an account of the historical development of this more general theory, which he traces drawing upon the work of Weierstrass, Poincaré, Riemann, and Weyl, and of its significance to the work of Deleuze, an account of what a mathematical concept is for Deleuze will be developed. (shrink)

The aim of this chapter is to test the degree to which Deleuze’s philosophy can be reconciled with the subject naturalist approach to pragmatism put forward by Macarthur and Price.

Much has been made of Deleuze’s Neo-Leibnizianism,3 however not very much detailed work has been done on the specific nature of Deleuze’s critique of Leibniz that positions his work within the broader framework of Deleuze’s own philo- sophical project. The present chapter undertakes to redress this oversight by providing an account of the reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold. Deleuze provides a systematic account of the structure of Leibniz’s metaphys- ics in terms of its mathematical underpinnings. (...) However, in doing so, Deleuze draws upon not only the mathematics developed by Leibniz – including the law of continuity as reflected in the calculus of infinite series and the infinitesimal calculus – but also the developments in mathematics made by a number of Leibniz’s contemporaries – including Newton’s method of fluxions – and a number of subsequent developments in mathematics, the rudiments of which can be more or less located in Leibniz’s own work – including the theory of functions and singularities, the theory of continuity and Poincaré’s theory of automorphic functions. Deleuze then retrospectively maps these developments back onto the structure of Leibniz’s metaphysics. While the theory of continuity serves to clarify Leibniz’s work, Poincaré’s theory of automorphic functions offers a solution to overcome and extend the limits that Deleuze identifies in Leibniz’s metaphysics. Deleuze brings this elaborate conjunction of material together in order to set up a mathematical idealization of the system that he considers to be implicit in Leibniz’s work. The result is a thoroughly mathematical explication of the structure of Leibniz’s metaphysics. What is provided in this chapter is an exposition of the very mathematical underpinnings of this Deleuzian account of the structure of Leibniz’s metaphysics, which, I maintain, subtends the entire text of The Fold. (shrink)

The theme of the conflict between the different interpretations of Spinoza’s philosophy in French scholarship, introduced by Christopher Norris in this volume and expanded on by Alain Badiou, is also central to the argument presented in this chapter. Indeed, this chapter will be preoccupied with distinguishing the interpretations of Spinoza by two of the figures introduced by Badiou. The interpretation of Spinoza offered by Gilles Deleuze in Expressionism in Philosophy provides an account of the dynamic changes or transformations of the (...) characteristic relations of a Spinozist finite existing mode, or human being. This account has been criticized more or less explicitly by a number of commentators, including Charles Ramond. Rather than providing a defence of Deleuze on this specific point, which I have done elsewhere, what I propose to do in this chapter is provide an account of the role played by “joyful passive a affections” in these dynamic changes or transformations by distinguishing Deleuze’s account of this role from that offered by one of his more explicit critics on this issue, Pierre Macherey. An appreciation of the role played by “joyful passive affections” in this context is crucial to understanding how Deleuze’s interpretation of Spinoza is implicated in his broader philosophical project of constructing a philosophy of difference. The outcome is a position that, like Badiou in the previous chapter, rules out “intellect in potentiality” but maintains a role for the joyful passive affects in the development of adequate ideas. (shrink)

Michael Hunter, The Boyle Papers: Understanding the Manuscripts of Robert Boyle. With contributions by Edward B. Davis, Harriet Knight, Charles Littleton and Lawrence M. Principe. Aldershot, England; Burlington, VT: Ashgate, 2007. Pp. xiii + 674. US$139.95/£70.00 HB. -/- The publication by Michael Hunter of this revised edition of the catalogue of the Boyle Papers contributes admirably to the renaissance in Boyle studies which has taken place over the past decade and a half. Robert Boyle (1627–91), arguably the most influential British (...) scientist of the late seventeenth century, was a pioneering experimenter, profound thinker, and figure-head of the new science in its early years of development. This volume brings together the materials necessary for understanding the Boyle archive, one of the most important archives from this period, which has been at the Royal Society since 1769. (shrink)

Michiel Wielema: The March of the Libertines. Spinozists and the Dutch Reformed Church (1660–1750). ReLiC: Studies in Dutch Religious History. Hilversum: Uitgeverij Verloren, 2004; pp. 221. The Dutch Republic of the seventeenth century is famous for having cultivated an extraordinary climate of toleration and religious pluralism — the Union of Utrecht supported religious freedom, or “freedom of conscience”, and expressly forbade reli- gious inquisition. However, despite membership in the state sponsored Calvinist Dutch Reformed Church not being compulsory, the freedom to (...) gather and worship, or “to air anti-Christian or atheistic opinions” was little tolerated “within” the organized structure of the church, which functioned more as “an exclusive organisation for those willing to submit freely to certain confessional canons and to the disciplinary author- ity of the church’s governing bodies” (10): the consistories, classes, and synods. Those not prepared to submit to Reformed doctrine were free to leave the church without fear of any legal or political repercussions. However, for those not prepared to leave for reasons of personal belief, matters turned out to be quite different. Because the Reformed Church enjoyed full State protection, matters of doctrinal conflict could well evolve into political affairs. And, contrary to the Union of Utrecht, religious inquisition was in some cases actually applied with political approval for “heretics” within the Reformed Church. The main focus of The March of the Libertines is an investigation of this obvious tension. (shrink)