•  658
    According to the reading of Spinoza that Gilles Deleuze presents in Expressionism in Philosophy: Spinoza, Spinoza's 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 m…Read more
  •  244
    Spinoza today: the current state of Spinoza scholarship
    Intellectual History Review 19 (1): 111-132. 2009.
    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 …Read more
  •  230
    The differential point of view of the infinitesimal calculus in Spinoza, Leibniz and Deleuze
    Journal of the British Society for Phenomenology 37 (3): 286-307. 2006.
    In Hegel ou Spinoza,1 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…Read more
  •  215
    Angelaki 9 (3). 2004.
    In the paper “Math Anxiety,” Aden Evens explores the manner by means of which concepts are implicated in the problematic Idea according to the philosophy of Gilles Deleuze. The example that Evens draws from Difference and Repetition in order to demonstrate this relation is a mathematics problem, the elements of which are the differentials of the differential calculus. What I would like to offer in the present paper is an historical account of the mathematical problematic that Deleuze deploys in …Read more
  •  194
    Deleuze, Leibniz and Projective Geometry in the Fold
    Angelaki 15 (2): 129-147. 2010.
    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.1 While not underestimat- ing 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 r…Read more
  •  180
    Virtual Mathematics: the logic of difference (edited book)
    Clinamen. 2006.
    Of all twentieth century philosophers, it is Gilles Deleuze whose work agitates most forcefully for a worldview privileging becoming over being, difference over sameness; the world as a complex, open set of multiplicities. Nevertheless, Deleuze remains singular in enlisting mathematical resources to underpin and inform such a position, refusing the hackneyed opposition between ‘static’ mathematical logic versus ‘dynamic’ physical world. This is an international collection of work commissioned f…Read more
  •  180
    Maimon’s Theory of Differentials As The Elements of Intuitions
    International Journal of Philosophical Studies 22 (2): 1-20. 2014.
    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 f…Read more
  •  149
    The Role of Mathematics in Deleuze’s Critical Engagement with Hegel
    International Journal of Philosophical Studies 17 (4). 2009.
    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 o…Read more
  •  141
    This article examines the seventeenth-century debate between the Dutch philosopher Benedict de Spinoza and the British scientist Robert Boyle, with a view to explicating what the twentieth-century French philosopher Gilles Deleuze considers to be the difference between science and philosophy. The two main themes that are usually drawn from the correspondence of Boyle and Spinoza, and used to polarize the exchange, are the different views on scientific methodology and on the nature of matter that…Read more
  •  56
    Gilles Deleuze’s engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems – for example, the problem of individuation – and to develop new concepts in response to them. The highly original research presented in this bo…Read more
  •  50
    The question of Deleuze’s Neo-Leibnizianism
    In Patricia Pisters & Rosi Braidotti (eds.), Down by Law: Revisiting Normativity with Deleuze, Bloomsbury Academic. 2012.
    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 …Read more
  •  38
    In Difference and Repetition, Deleuze explores the manner by means of which concepts are implicated in the problematic Idea by using a mathematics problem as an example, the elements of which are the differentials of the differential calculus. What I would like to offer in the present paper is a historical account of the mathematical problematic that Deleuze deploys in his philosophy, and an introduction to the role played by this problematic in the development of his philosophy of difference. O…Read more
  •  36
    The first English collection of the work of Albert Lautman, a major figure in philosophy of mathematics and a key influence on Badiou and Deleuze.
  •  32
    The role of joyful passions in Spinoza’s theory of relations
    In Dimitris Vardoulakis (ed.), Spinoza Now, Minnesota University Press. 2011.
    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…Read more
  •  29
    It is possible today to observe in hindsight the epistemological landscape of the twentieth century, and the work of Albert Lautman in mathematical philosophy appears as a profound turning point, opening to a true under- standing of creativity in mathematics and its relation with the real. Little understood in its time or even today, Lautman’s work explores the difficult but exciting intersection where modern mathematics, advanced mathe- matical invention, the structural or unitary relations of …Read more
  •  28
    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), …Read more
  •  28
    If the allusive stratagems can claim to define a new type of systematicity, it is because they give access to a space where the singularity, the diagram and the metaphor may interlace, to penetrate further into the physico-mathematic intuition and the discipline of the gestures which precede and accompany ‘formalisation’. This interlacing is an operation where each component backs up the others: without the diagram, the metaphor would only be a short-lived fulguration because it would be unable …Read more
  •  28
    Badiou’s Platonism: The Mathematical Ideas of Post-Cantorian Set-Theory
    In Sean Bowden & Simon B. Duffy (eds.), Badiou and Philosophy, Edinburgh University Press. 2012.
    Plato’s philosophy is important to Badiou for a number of reasons, chief among which is that Badiou considered Plato to have recognised that mathematics provides the only sound or adequate basis for ontology. The mathematical basis of ontology is central to Badiou’s philosophy, and his engagement with Plato is instrumental in determining how he positions his philosophy in relation to those approaches to the philosophy of mathematics that endorse an orthodox Platonic realism, i.e. the independent…Read more
  •  28
    The collection Virtual Mathematics: the logic of difference brings together a range of new philosophical engagements with mathematics, using the work of French philosopher Gilles Deleuze as its focus. Deleuze’s engagements with mathematics rely upon the construction of alternative lineages in the history of mathematics in order to reconfigure particular philosophical problems and to develop new concepts. These alternative conceptual histories also challenge some of the self-imposed limits of the…Read more
  •  26
    Deleuze and the Mathematical Philosophy of Albert Lautman
    In Jon Roffe & Graham Jones (eds.), Deleuze’s Philosophical Lineage, Edinburgh University Press. 2009.
    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 t…Read more
  •  23
    Leibniz, Mathematics and the Monad
    In Sjoerd van Tuinen & Niamh McDonnell (eds.), Deleuze and the Fold: A Critical Reader, Palgrave-macmillan. pp. 89--111. 2010.
    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 me…Read more
  •  21
    Spinoza, according to common opinion, could only have written lamentable platitudes on sexual love, narrowly inspired by the prejudices of his time and without serious philosophical foundation: that for which, in the past, he has been congratulated,1 he is now reproached; or, at best, excused. He would even have, some believe to be able to add, increased the pervading puritanism: sexuality, as such, would give rise in him to a deep repulsion and women would horrify him. The second of these two a…Read more
  •  19
    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.
  •  17
    Badiou and Philosophy (edited book)
    Edinburgh University Press. 2012.
    A reassessment of Badiou's work which demonstrates its critical importance for contemporary philosophy. This collection of thirteen essays engages directly with the work of Alain Badiou, focusing specifically on the philosophical content of his work and the various connections he established with both his contemporaries and his philosophical heritage. You’ll find in-depth critical readings of his oeuvre through the lens of a number of important philosophical thinkers and themes, ranging from Can…Read more
  •  17
    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 …Read more
  •  16
    Albert Lautman (b. 1908–1944) 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’ (Lautman 2011, 87). He…Read more
  •  15
    In October 1984, Bruno Huisman stated with regards to Jean Cavaillès, ‘Let us be honest, or at least realistic: today, one can be a professor of philosophy without ever having read a single line of Cavaillès. Often invoked, sometimes quoted, the oeuvre of Cavaillès is little attended for itself’ (Huisman 1984). As for Albert Lautman, it would seem that the situation is even more extreme. In 1994, the publisher Hermann, under the impetus of Bruno Huisman and George Canguilhem, collected almost th…Read more
  •  14
    Deleuze and the pragmatist priority of subject naturalism
    In Sean Bowden & Simone Bignall (eds.), Deleuze and Pragmatism, Routledge. pp. 199-215. 2015.
    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.
  •  13
    Models, Mathematics and Deleuze's Philosophy: A Reply to Williams
    Deleuze and Guatarri Studies 11 (3): 481-489. 2017.
    Rather than defend each instance of problem suggested by Williams, what I propose to do is to respond by making two clarificatory points: first, I rule out two ways of understanding mathematical problems that might be clouding the water; and then, second, I further characterise how Deleuze thinks some mathematical problems, two in particular, are not just examples of mathematical problems, but provide mathematical models for what a mathematical problem in general can be understood to be. This is…Read more
  •  13
    The Ethical View of Spinoza’s theory of relations
    In B. Bolt, F. Coleman, G. Jones & A. Woodward (eds.), Sensorium: Aesthetics, Art, Life, Cambridge Scholars Press. 2007.
    Gilles Deleuze maintains that an individual’s power to act is open to “metaphysical” or ontological changes. An individual for Deleuze is limited by the passive affections that it experiences in its interactions with other more composite bodies, which, at any given moment, have the potential to limit its further integration, and, therefore, the further development of its power to act, and by consequence, its actual existence. This limit determines the margin of variation of the expression of the…Read more