Simon B. Duffy

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.

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 assertions, if one sticks to the manifest content of the texts, actually rests on nothing; if one calls upon their latent content, it would require, to be established with a minimum of rigor, a study of which we will not dispute the theoretical possibility, but which, in fact, has not yet been undertaken. The first, on the other hand, has all the appearance of the obvious: that men love women for their beauty and do not support their attachment to someone else,2 that they desire them more the more admirers they have,3 that the jealousy of the male is exacerbated by the representation of the pudenda and of the excrementa of his rival,4 that sensual attachment is unstable and conflictual,5 that it often turns to obsession,6 that Adam loved Eve because of their similarity of nature,7 that he who remains insensitive to the generosity of a courtesan does not offend by ingratitude,8 that only free men and free women can marry one another and only if they want children,9 well, it seems, that isn’t anything sensational; now these eight passages, if the two definitions of the libido are added to them,10 are the only, if I’m not mistaken, that Spinoza expressly devoted to the question! He would therefore, apparently, only have drawn up a report of deficiency.

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 these developments and the specific texts that contributed to and sustained this new direction in research have remained largely unknown in the English-speaking world. The aim of this essay, therefore, is to provide a survey of this event, to review the background to these developments, to introduce the main protagonists – along with some of the lesser known but equally important figures – and to single out and asses the key texts, their specific focus and their contribution to the new direction in research.

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 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. Deleuze presents Spinoza's 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. Deleuze's 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.

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 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 Du ̈rer (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.

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. One of the points of departure that I will take from the history of mathematics is the theme of ‘power series’ (Deleuze 1994, 114), which will involve a detailed elaboration of the mechanism by means of which power series operate in the differential calculus deployed by Deleuze in Difference and Repetition. Deleuze actually constructs an alternative history of mathematics that establishes a historical continuity between the differential point of view of the infinitesimal calculus and modern theories of the differential calculus. It is in relation to this differential point of view that Deleuze determines a differential logic which he deploys, in the form of a logic of different/ciation, in the development of his project of constructing a philosophy of difference.