Florian Vermeiren

This paper offers a fresh interpretation of Leibniz’s theory of relations. I argue that we should take seriously Leibniz’s idea of non-ideal relations inhering in one subject. Such single-inhering relations should not be understood in terms of non-relational, absolute properties, but in terms of perspectival relations. Through the notion of perspective, we can understand how a relation between two relata inheres in only one of those relata. For example, my perception of you involves my point of view. Therefore, it is individual to me. My perception of you is not equal to your perception of me. However, it does relate me to you. Perspective can thus explain how relations only inhere in one subject while nevertheless really relating one thing to another. This leads to a novel understanding of the rejection of purely extrinsic denominations and the supposed isolation of substances. Published on 2023-03-22 10:43:18.

This paper examines the role of the notion of structure in Leibniz’s mathematical thought. I show (i) how Leibniz’s structuralist understanding of truth and reason conditions his methodological formalism; (ii) how Leibniz’s prioritization of arithmetic over geometry is founded on his relational and structural conception of number; (iii) how his mathematics of infinity, i. e. his calculus, relies on the structural traits of infinity; and lastly, (iv) how the concept of structure is the indispensable partner of the concept of expression that Leibniz considers universal and metaphysically fundamental. I conclude that the power and innovative character of his mathematical thought stems from a mathematical structuralism that is supported by a structural conception of truth and reason, and an even more fundamental metaphysical structuralism.

RésuméCet article examine la distinction essence-existence dans la théorie des modes de Spinoza. Cette distinction est généralement faite de deux manières. Premièrement, l'essence et exis-tence sont séparées par leur cause. Les essences découlent verticalement de l'essence de Dieu, tandis que l'existence découle horizontalement d'autres modes. Je présente des arguments textuels et systématiques contre une telle bifurcation causale. Deuxièmement, l'essence et l'existence se distinguent par leur nature temporelle. L'essence est éternelle. L'existence dure. Cependant, dans plusieurs passages, Spinoza écrit que l’éternité et la durée constituent deux manières de comprendre la nature plutôt que deux aspects réellement distincts de la nature.

Why does Deleuze rely so heavily on Spinoza and Leibniz? At first glance, his critique of representation and the traditional ‘image of thought’ seems to oppose him to rationalism. However, Deleuze says that when the ‘cry of rationalism’ is pursued until the end, rationalism becomes ‘delirious’. In such a state, it undermines the model of representation. This delirium is found in Spinoza and Leibniz's critique of generality and their conflation of essence and existence, through which they ruin the traditional mediation of difference by identity and generality. However, for this rationalism to completely break with representationalism it must undergo some Deleuzian corrections.

The Extensive Continuum is most often seen as an empty form that awaits the accommodation of actuality. Contrary to this popular interpretation, I argue that extension is completely immanent to actual occasions and their prehensive relations. Whitehead's doctrine of internal relations entails that extension cannot be separated from actual occasions, just as actual occasions cannot be separated from extension. To prehend is to extend. Furthermore, any strict separation of form and actuality is shown to bifurcate nature into publicity and privacy. Only with the immanence of extension is nature truly one.

This paper examines the Leibnizian influence in Deleuze's theory of the spatium. Leibniz's critique of Cartesian extension and Newtonian space leads him to a conception of space in terms of internal determination and internal difference. Space is thus understood as a structure of individual relations internal to substances. Making some Nietzschean corrections to Leibniz, Deleuze understands the spatium in terms of individuating differences instead of individual relations. Leibnizian space is thus transformed into a genetic space producing both extension (quantity) and quality

In What Is Philosophy? Deleuze and Guattari understand concepts in a very unconventional way. One of the central aspects of their theory is that concepts are self-referential and should not be understood in terms of any form of reference or representation. Instead, concepts are complex “assemblages” interacting on a “plane of immanence.” I argue that we can best understand this theory through the philosophy of Spinoza. The latter understands thought and ideas through the model of physical bodies. Spinoza’s theory of thought is, as François Zourabichvili says, a “physics of thought.” I do not only call upon Spinoza to elucidate the general approach of Deleuze and Guattari; I also use Spinoza’s notions of modal essence and existence, interpreted by Deleuze in terms of intensity and extensity, to expound the details of their distinction between concepts and propositions.

ABSTRACT This article examines Bergson’s critique of intensive magnitude in Time and Free Will. I demonstrate how his rejection of a different kind of quantity that is ordinal and does not allow measurement, and the underlying strict dualism of quantity and quality, is inconsistent with both the letter and the spirit of his later philosophy. I dismantle two main strategies for explaining these inconsistencies. Furthermore, I argue that Bergson’s simplistic conception of quantity in terms of homogeneous multiplicity, which is operative in his rejection of an alternative conception of quantity, lacks justification in the face of the transformations that the concept of quantity underwent in the history of mathematics and physics.

Salomon Maïmon argues that the formal determination of experience in Kant’s first Kritik insufficiently answers the question ‘quid juris?’. As an alternative to Kant’s theory, he develops a genetic transcendentalism in which experience is completely determined a priori. Discussing this genetic approach, I focus on how the spatiotemporal determinations of conscious experience are traced back to pure ideal relations. Relying on Leibniz and his theory of space and time, I explain how the extensive magnitudes of consciousness are founded in intensive magnitudes of what Maïmon calls ‘pure thought’. As the latter is the transcendental ground for both sensibility and the understanding, Maïmon’s theory contains a radical form of immanence, much like the philosophy of Spinoza and Gilles Deleuze.

This paper aims to show that Deleuze’s ideas on space and extension are heavily in debt to Leibniz. The focus is on chapter five, ‘the Asymmetrical Synthesis of the Sensible’, of Difference and Repetition. Concepts such as ‘intensive magnitude’, ‘distance’, ‘order’ and most importantly ‘spatium’ are shown to have their origin in Leibniz’s philosophy. In order to do so, the article starts with Leibniz’s critique on Cartesian mechanics and how this leads Leibniz to a conception of space that goes beyond the Cartesian concept of extension. The latter lacks difference, potentiality and individuality. Leibniz argues that the Cartesian homogeneous plenum should therefore be grounded in a deeper more substantial space: the spatium. Understood as such, space is not an absolute substance but a structure of relations between substances. Although Leibniz’s texts offer enough to understand this spatium, they do not explain how the genesis of extension out of space should be understood. It is on this point that Deleuze offers a fruitful interpretation of Leibniz by conceptualizing such a genesis in terms of difference. Extension is understood as a homogenization and externalization of the internal and pure differences in space. In the end, Leibniz helps us to understand Deleuze’s theory, while Deleuze offers us an enriching interpretation of Leibniz that succeeds where authors such as Yvon Belaval and Martial Gueroult have failed.