
The transformation of relations in Spinoza's metaphysicsIn Jack Stetter & Charles Ramond (eds.), Spinoza in TwentyFirstCentury American and French Philosophy: Metaphysics, Philosophy of Mind, Moral and Political Philosophy, Bloomsbury Academic. 2019.

IndexIn Sean Bowden & Simon Duffy (eds.), Badiou and Philosophy, Edinburgh University Press. pp. 271276. 2012.

BibliographyIn Sean Bowden & Simon Duffy (eds.), Badiou and Philosophy, Edinburgh University Press. pp. 262270. 2012.

20Engaging with the challenging and controversial reading of Spinoza presented by Gilles Deleuze in Expressionism in Philosophy (1968), this book focuses on Deleuze's redeployment of Spinozist concepts within the context of his own philosophical project of constructing a philosophy of difference as an alternative to the Hegelian dialectical philosophy. Duffy demonstrates that a thorough understanding of Deleuze's Spinozism is necessary in order to fully engage with Deleuze's philosophy of differe…Read more

9Proportion as a barometer of the affective life in SpinozaIn Beth Lord (ed.), Spinoza’s Philosophy of Ratio, Edinburgh University Press. pp. 111133. 2018.In this paper, two different ways of thinking about individuality in Spinoza are presented to draw out what is at stake in trying to make sense of what could be described as a double point of view of the degree of the power to act of a singular thing in Spinoza’s Ethics: sometimes it seems to be fixed to a precisely determined degree; sometimes it seems to admit a certain degree of variation. The problem of resolving this apparent contradiction has been responsible for a variety of interpretatio…Read more

33Lautman on problems as the conditions of existence of solutionsAngelaki 23 (2): 7993. 2018.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

229Deleuze and the conceptualizable character of mathematical theoriesIn Nathalie Sinclair & Alf Coles Elizabeth de Freitas (ed.), What is a Mathematical Concept?, Cambridge University Press. 2017.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 proble…Read more

33Models, Mathematics and Deleuze's Philosophy: A Reply to WilliamsDeleuze and Guatarri Studies 11 (3): 481489. 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

102Deleuze and the pragmatist priority of subject naturalismIn Sean Bowden & Simone Bignall (eds.), Deleuze and Pragmatism, Routledge. pp. 199215. 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.

46Deleuze, Spinoza and the Question of Reincarnation in the Mahāyāna TraditionIn Tony See (ed.), Deleuze and Buddhism, Palgrave Macmillan. pp. 3349. 2016.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.

218Interlacing the singularity, the diagram and the metaphor. Translated by Simon B. DuffyIn Simon B. Duffy (ed.), Virtual Mathematics: the logic of difference, Clinamen. 2006.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 physicomathematic 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 shortlived fulguration because it would be unable …Read more

347The Role of Mathematics in Deleuze’s Critical Engagement with HegelInternational Journal of Philosophical Studies 17 (4). 2009.The role of mathematics in the development of Gilles Deleuze's (192595) 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 (17701831) presents in the Science of Logic . Each deploys the operation of integration as conceived at different stages in the development o…Read more

243Leibniz, Mathematics and the MonadIn Sjoerd van Tuinen & Niamh McDonnell (eds.), Deleuze and the Fold: A Critical Reader, Palgravemacmillan. pp. 89111. 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

47The first English collection of the work of Albert Lautman, a major figure in philosophy of mathematics and a key influence on Badiou and Deleuze.

293Deleuze and the Mathematical Philosophy of Albert LautmanIn 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

535The difference between science and philosophy: the SpinozaBoyle controversy revisitedParagraph 29 (2): 115138. 2006.This article examines the seventeenthcentury debate between the Dutch philosopher Benedict de Spinoza and the British scientist Robert Boyle, with a view to explicating what the twentiethcentury 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

51. Badiou’s Philosophical HeritageIn Sean Bowden & Simon Duffy (eds.), Badiou and Philosophy, Edinburgh University Press. pp. 115. 2012.In the wake of the numerous translations of Badiou’s works that have appeared in recent years, including the translation of the second volume of his major work, Logic of Worlds: Being and Event II, there has been a marked increase in interest in the philo sophical underpinnings of his oeuvre. The papers brought together in this volume provide a range of incisive and critical engagements with Badiou’s philosophical heritage and the philosophical prob lems his work engages, both directly and ind…Read more

20The Ethical View of Spinoza’s theory of relationsIn 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

2034. Badiou’s Platonism: The Mathematical Ideas of PostCantorian Set TheoryIn Sean Bowden & Simon Duffy (eds.), Badiou and Philosophy, Edinburgh University Press. pp. 5978. 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

997Virtual 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

710Maimon’s Theory of Differentials As The Elements of IntuitionsInternational Journal of Philosophical Studies 22 (2): 120. 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

40Spinoza and sexuality. Translated by Simon B. Duffy and Paul PattonIn Moira Gatens (ed.), Feminist Interpretations of Benedict Spinoza, Pennsylvania State University Press. 2009.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

21French and Italian SpinozismIn Rosi Braidotti & Alan D. Schrift (eds.), After Poststructuralism  Transitions and Transformations. The History of Continental Philosopy, Acumen; Chicago University Press. 2010.A renaissance in Spinoza studies took place in France at the end of the 1960s, which gave new impetus to the study of Spinoza’s work and continues to have a marked effect on the direction of research in the field today. The effect of this renewed interest and direction did not remain isolated to France but quickly spread across the continent. Although certain of the figures involved in this event have become rather well known in some academic circles, and their work widely read, the details of t…Read more

1712The logic of expression in Deleuze's expressionism in philosophy: Spinoza: A strategy of engagementInternational Journal of Philosophical Studies 12 (1). 2004.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

562Deleuze, Leibniz and Projective Geometry in the FoldAngelaki 15 (2): 129147. 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

68In 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

62Deleuze and MathematicsIn Virtual Mathematics: the logic of difference, Clinamen. 2006.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 selfimposed limits of the…Read more

463Schizo‐MathAngelaki 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

60It 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

195Review of Michael Hunter, The Boyle Papers: Understanding the Manuscripts of Robert Boyle (Ashgate, 2007) (review)Reviews in the Enlightenment 1. 2008.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
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