The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze, by Simon Duffy

If the import of a book can be assessed by the problem it takes on, how that problem unfolds, and the extent of the problem’s fruitfulness for further exploration and experimentation, then Duffy has produced a text worthy of much close attention. Duffy constructs an encounter between Deleuze’s creation of a concept of difference in Difference and Repetition (DR) and Deleuze’s reading of Spinoza in Expressionism in Philosophy: Spinoza (EP). It is surprising that such an encounter has not already been explored, at least not to this extent and in this much detail. Since the two works were written simultaneously, as Deleuze’s primary and secondary dissertations, it is to be expected that there is much to learn from their interaction. Duffy proceeds by explicating, in terms of the differential calculus, a logic of what Deleuze in DR calls different/ciation, and then maps this onto Deleuze’s account of modal expression in EP. While Hegel’s name appears in the title and Hegel’s thought is discussed early in the book, Duffy’s treatment of Hegel serves mostly as a foil for establishing a great distance between the dialectical logic, founded on negation, and the logic of difference elaborated in DR in relation to the differential calculus which Duffy uses to explicate the logic of expression Deleuze finds in Spinoza. Duffy argues that Hegel forces Spinoza’s understanding of determinateness into the pattern of the dialectic logic by distorting Spinoza’s text and neglecting its complexity. Hegel’s assertion that for Spinoza all determination is negation abstracts the determination of finite modes from their causes and thereby from the expressive order of nature in which finite modes are differentiated positively rather than by reciprocal limitation. Duffy, then, arranges a series of readings of Spinoza’s difficult and obscure Letter XII, on the infinite, to explore the significance of Spinoza’s geometric diagram of the extreme orthogonal distances between two nested non-concentric circles. These readings chart a great distance between Hegel’s crude misreading of the letter and Deleuze’s understanding of the letter as an early anticipation of the differential calculus. Spinoza claims this diagram illustrates something infinite included between a maximum and minimum which cannot be expressed by any number. The readings differ regarding which infinite the diagram is supposed to illustrate. For Hegel, this infinite consists of the sum of the distances between the circles; this forms an algebraic sum of finite quantities. However, this reading fails to give any significance to Spinoza’s description of the circles as nonconcentric and his reference to the maximum and minimum orthogonal distances. Deleuze (along with Guéroult) instead, argues that the infinite in question is an infinite sum of the successive differences between the orthogonal distances, a geometrical infinite sum of differentials, and so a precursor of the differential calculus. It is this turn to the differential, to the infinitesimal difference between consecutive values, that Duffy extracts from these readings which shows how Deleuze exploits 17thand 18th-century interpretations of the calculus (what Duffy following Carl Boyer calls ‘the infinitesimal calculus from the differential point of view’) in developing a Reviews 341