Simon Duffy

Spinoza Today: The Current State of Spinoza Scholarship

Taylor and Francis Ltd RIHR_A_372467.sgm 10.1080/174969 0902722973 Inte lectual History Review 749-6977 p n /1749-6985 online Original Article 2 0rnational So ety for Intellectual History 9 0 0002009 Simo D ffy si o .d ff @arts.usyd.edu.au The history of Spinoza scholarship is marked by a number of renaissances in the reception of his work: from the polemics on atheism during Spinoza’s lifetime,1 to the pantheism debate [Pantheismusstreit], which was a prelude to German idealism;2 from the debate between neo-Kantians and post-Hegelians during the second half of the nineteenth century,3 to the late twentieth-century Marxist-inspired French and Italian Spinozisms.4 Spinoza has had a marked impact on each of these developments in the tradition of philosophy. It is the open and contestable nature of his philosophy that has contributed to the repeated renewal of its importance. The most recent renaissance in Spinoza studies in the 1970s is represented by the major works of Martial Gueroult, Alexandre Matheron and Bernard Rousset,5 which aimed to bring out the full richness and diversity of Spinoza’s work by means of its internal structural analysis. Their methods were based on determining the order of reasons in Spinoza’s work or the architecture of the Spinozist system. The work of Gilles Deleuze and Robert Misrahi6 should also be included as representative of the resurgence of interest in Spinoza at the time. There has, however, been a decided shift away from employing the methods that characterized the work of the 1970s. The research of the last two decades of the twentieth century largely contributed to a better understanding of the texts and sources of the tradition. The continued interest in Spinoza during the past decade has profited from this research and contributed to it in a number of different ways. The philosophy of Spinoza is increasingly recognized as holding a position of crucial importance and influence in early modern thought, and in recent years it has been the focus of a rich and growing body of scholarship. While still closely following the rich contours of his work, investigations conducted over the past decade have also demonstrated a willingness to relocate engagements with Spinoza within the discipline of the history of ideas and to engage with his thought from the point of view of contemporary philosophy. 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

The differential point of view of the infinitesimal calculus in Spinoza, Leibniz and Deleuze

In Hegel ou Spinoza, Pierre Macherey challenges the influence of Hegel’s reading of Spinoza by stressing the degree to which Spinoza eludes the grasp of the Hegelian dialectical progression of the history of philosophy. He argues that Hegel provides a defensive misreading of Spinoza, and that he had to “misread him” in order to maintain his subjective idealism. The suggestion being that Spinoza’s philosophy represents, not a moment that can simply be sublated and subsumed within the dialectical progression of the history of philosophy, but rather an alternative point of view for the development of a philosophy that overcomes Hegelian idealism. Gilles Deleuze also considers Spinoza’s philosophy to resist the totalising effects of the dialectic. Indeed, Deleuze demonstrates, by means of Spinoza, that a more complex philosophy antedates Hegel’s, which cannot be supplanted by it. Spinoza therefore becomes a significant figure in Deleuze’s project of tracing an alternative lineage in the history of philosophy, which, by distancing itself from Hegelian idealism, culminates in the construction of a philosophy of difference. It is Spinoza’s role in this project that will be demonstrated in this paper by differentiating Deleuze’s interpretation of the geometrical example of Spinoza’s Letter XII (on the problem of the infinite) in Expressionism in Philosophy, Spinoza, from that which Hegel presents in the Science of Logic. Both Hegel and Deleuze each position the geometrical example at different stages in the early development of the differential calculus. By demonstrating the relation between “the differential point of view of the infinitesimal calculus” and the differential calculus of contemporary mathematics, Deleuze effectively bypasses the methods of the differential calculus which Hegel uses to support the development of the dialectical logic.

Maimon’s Theory of Differentials As The Elements of Intuitions

Abstract Maimon’s theory of the differential has proved to be a rather enigmatic aspect of his philosophy. By drawing upon mathematical developments that had occurred earlier in the century and that, by virtue of the arguments presented in the Essay and comments elsewhere in his writing, I suggest Maimon would have been aware of, what I propose to offer in this paper is a study of the differential and the role that it plays in the Essay on Transcendental Philosophy (1790). In order to do so, this paper focuses upon Maimon’s criticism of the role played by mathematics in Kant’s philosophy, to which Maimon offers a Leibnizian solution based on the infinitesimal calculus. The main difficulties that Maimon has with Kant’s system, the second of which will be the focus of this paper, include the presumption of the existence of synthetic a priori judgments, i.e. the question quid facti, and the question of whether the fact of our use of a priori concepts in experience is justified, i.e. the question quid juris. Maimon deploys mathematics, specifically arithmetic, against Kant to show how it is possible to understand objects as having been constituted by the very relations between them, and he proposes an alternative solution to the question quid juris, which relies on the concept of the differential. However, despite these arguments, Maimon remains sceptical with respect to the question quid facti.

Deleuze, Leibniz and Projective Geometry in the Fold

Explications of the reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold: Leibniz and the Baroque focus predominantly on the role of the infinitesimal calculus developed by Leibniz. While not underestimating the importance of the infinitesimal calculus and the law of continuity as reflected in the calculus of infinite series to any understanding of Leibniz’s metaphysics and to Deleuze’s reconstruction of it in The Fold, what I propose to examine in this paper is the role played by other developments in mathematics that Deleuze draws upon, including those made by a number of Leibniz’s near contemporaries – the projective geometry that has its roots in the work of Desargues (1591–1661) and the ‘‘proto-topology’’ that appears in the work of Dürer (1471– 1528) – and a number of the subsequent developments in these fields of mathematics. 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 paper 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. Deleuze’s project in The Fold is predominantly oriented by Leibniz’s insistence on the metaphysical importance of mathematical speculation. What this suggests is that mathematics functions as an important heuristic in the development of Leibniz’s metaphysical theories. Deleuze puts this insistence to good use by bringing together the different aspects of Leibniz’s metaphysics with the variety of mathematical themes that run throughout his work. Those aspects of Leibniz’s metaphysics that Deleuze undertakes to clarify in this way, and upon which this paper will focus, include: (1) the definition of a monad; (2) the theory of compossibility; (3) the difference between perception and apperception; and (4) the range and meaning of the pre-established harmony. However, before providing the details of Deleuze’s reconstruction of the structure of Leibniz’s metaphysics, it will be necessary to give an introduction to Leibniz’s infinitesimal calculus and to some of the other developments in mathematics associated with it. simon duffy

The Logic of Expression in Deleuze's Expressionism in Philosophy: Spinoza: A Strategy of Engagement

According to the reading of Spinoza that Gilles Deleuze presents in Expressionism in Philosophy: Spinoza, Spinozas philosophy should not be represented as a moment that can be simply subsumed and sublated within the dialectical progression of the history of philosophy, as it is figured by Hegel in the Science of Logic, but rather should be considered as providing an alternative point of view for the development of a philosophy that overcomes Hegelian idealism. Indeed, Deleuze demonstrates, by means of Spinoza, that a more complex philosophy antedates Hegels which cannot be supplanted by it. Spinoza therefore becomes a significant figure in Deleuzes project of tracing an alternative lineage in the history of philosophy, which, by distancing itself from Hegelian idealism, culminates in the construction of a philosophy of difference. Deleuze presents Spinozas metaphysics as determined according to a ‘logic of expression’, which, insofar as it contributes to the determination of a philosophy of difference, functions as an alternative to the Hegelian dialectical logic. Deleuzes project in Expressionism in Philosophy is therefore to redeploy Spinoza in order to mobilize his philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic.

Leibniz, Mathematics and the Monad

The reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold provides a systematic account of the structure of Leibniz’s metaphysics in terms of its mathematical foundations. However, in doing so, Deleuze draws not only upon the mathematics developed by Leibniz — including the law of continuity as reflected in the calculus of infinite series and the infinitesimal calculus — but also upon developments in mathematics made by a number of Leibniz’s contemporaries — including Newton’s method of fluxions. He also draws upon 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 Weierstrassian theory of analytic continuity, and Poincare’s theory of automorphic functions. Deleuze then retrospectively maps these developments back onto the structure of Leibniz’s metaphysics. While the Weierstrassian theory of analytic continuity serves to clarify Leibniz’s work, Poincare’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 idealisation 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. This essay 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.

LAUTMAN ON PROBLEMS AS THE CONDITIONS OF EXISTENCE OF SOLUTIONS

Abstract Albert Lautman (1908–44) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that “in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe” (Mathematics, Ideas and the Physical Real (London: Bloomsbury, 2011) 87). He goes on to characterise this reality as an “ideal reality” that “governs” the development of mathematics. The relation between mathematical problems as they arise in the historical development of mathematics and the solutions that are provided to these problems by mathematicians, in the form of new mathematical theories, definitions or axioms, are governed by what Lautman characterises as a dialectics of mathematics. The aim of this paper is to give an account of this Lautmanian dialectic and of how it can be understood to govern the development of solutions to mathematical problems.

Deleuze, Spinoza and the Question of Reincarnation in the Mahāyāna Tradition

In the spirit of the Dalai Lama’s interest to provide an account of a secular foundation to ethics in Beyond Religion (2011, p. xiv), on the basis that everyone wants to avoid suffering, what I aim to develop in this paper is a secular foundation to the concept of reincarnation that is consistent with the different ways in which this concept is understood across a number of Buddhist traditions, drawing in particular upon the doctrinal understanding of reincarnation in the Mahāyāna or Madhyamaka tradition as presented in the work of Śāntideva and Nāgārjuna.

The Role of Mathematics in Deleuze’s Critical Engagement with Hegel

Abstract The role of mathematics in the development of Gilles Deleuze’s (1925–95) philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic is demonstrated in this paper by differentiating Deleuze’s interpretation of the problem of the infinitesimal in Difference and Repetition from that which G. W. F Hegel (1770–1831) presents in the Science of Logic. Each deploys the operation of integration as conceived at different stages in the development of the infinitesimal calculus in his treatment of the problem of the infinitesimal. Against the role that Hegel assigns to integration as the inverse transformation of differentiation in the development of his dialectical logic, Deleuze strategically redeploys Leibniz’s account of integration as a method of summation in the form of a series in the development of his philosophy of difference. By demonstrating the relation between the differential point of view of the Leibnizian infinitesimal calculus and the differential calculus of contemporary mathematics, I argue that Deleuze effectively bypasses the methods of the differential calculus which Hegel uses to support the development of the dialectical logic, and by doing so, sets up the critical perspective from which to construct an alternative logic of relations characteristic of a philosophy of difference. The mode of operation of this logic is then demonstrated by drawing upon the mathematical philosophy of Albert Lautman (1908–44), which plays a significant role in Deleuze’s project of constructing a philosophy of difference. Indeed, the logic of relations that Deleuze constructs is dialectical in the Lautmanian sense.