ABSTRACT
The Letter on the Infinite Having utilized the geometrical example of Spinoza’s Letter XII in chapter 1 to distinguish the respective interpretations of Spinoza by Hegel and Macherey, Deleuze’s reading of Spinoza will be distinguished from that of Hegel and Macherey insofar as it too offers an alternative reading of what Deleuze describes as the ‘very bizarre, curious’1 geometrical example. By implicating Leibniz’s understanding of the early form of the infinitesimal calculus in his reading of the geometrical example, Deleuze argues that it is able to be characterized as an example of what had already been established of the infinitesimal calculus. He thereby traces an alternative lineage between Leibniz and Spinoza to that determined by Hegel in the development of the dialectical logic. It is therefore by means of Deleuze’s reading of Letter XII that the investigation into the logic that is mobilized in his reading of Spinoza in Expressionism in Philosophy, as an alternative to the dialectical logic, will be developed, and it is Gueroult’s reading of Letter XII which provides the point of departure for this investigation. In ‘Spinoza’s Letter on the Infinite’, Gueroult suggests that the meaning of the geometrical example is ‘generally wrongly understood’, and that it has been ‘vitiated in its principle through errors in translation’.2 Macherey continues this argument in Hegel ou Spinoza when he writes that ‘the example as reproduced by Hegel is not the same as that given in the text of Spinoza’.3 He argues that the same example is exploited by each commentator ‘in markedly different ways’.4 Macherey corrects Hegel’s error of ascribing to the ‘inequalities of space’ only ‘unequal distances’ with the more accurate ‘differences in distance’, thus realigning the concept of the maximum and minimum limits, which Hegel incorrectly ascribes solely to the circumferences of the greater and smaller circles rather than also to the maximum and minimum orthogonal distances, which
1 Deleuze, ‘sur Spinoza’, 20 January 1981, trans. S. Duffy. 2 Gueroult, ‘Spinoza’s Letter on the Infinite’, p. 206.
