Papers by Florian Vermeiren
Studia Leibnitiana, 2023
This paper challenges Mugnai's conceptualist reading of Leibniz's theory of relations. I specific... more This paper challenges Mugnai's conceptualist reading of Leibniz's theory of relations. I specifically question his idea that relational accidents are mental additions to absolute foundations. I examine some of the evidence on which he relies. Most importantly, I question his interpretation of Leibniz's rejection of purely extrinsic denominations (abbreviated "NPED") as stating that relations result from non-relational foundations. Mugnai thereby understands Leibniz's notion of 'extrinsic' as 'relational' or 'relative'. Such a reading contradicts both Leibniz's definition of 'extrinsic denominations' and the scholastic meaning of this notion. Furthermore, Leibniz's use of NPED shows that some relations are intrinsic denominations. Additionally, I argue that conceptual relations cannot do all the work in Leibniz's metaphysics. Fundamental notions such as expression, order and, most importantly, coexistence rely on non-conceptual relations.
Dialogue: Canadian Philosophical Review, 2022
This article examines the essence-existence distinction in Spinoza's theory of modes. This distin... more This article examines the essence-existence distinction in Spinoza's theory of modes. This distinction is commonly made in two ways. First, essence and existence are separated by cause. Essences are understood to follow vertically from the essence of God, while existence follows horizontally from other modes. I present textual and systematic arguments against such a causal bifurcation. Second, essence and existence are distinguished by their temporal nature. Essence is eternal. Existence is durational. However, in several passages, Spinoza writes that eternity and duration constitute two ways of understanding nature rather than two really distinct aspects of nature.
Journal of Modern Philosophy, 2023
This paper offers a fresh interpretation of Leibniz's theory of relations. I argue that we should... more 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.
Pli: Warwick Journal of Philosophy, Apr 12, 2018
Studia Leibnitiana, 2019
This paper examines the role of the notion of structure in Leibniz's mathematical thought. I show... more 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.
Journal of the British Society for Phenomenology , 2021
In "Reconstructing Bergson's Critique of Intensive Magnitude" (abbreviated as "JB") John Bagby de... more In "Reconstructing Bergson's Critique of Intensive Magnitude" (abbreviated as "JB") John Bagby defends Bergson against the criticism that I develop in "Bergson and Intensive Magnitude: Dismantling his Critique". I thank him for his insightful commentary and would like to offer a reply.
Journal of the British Society for Phenomenology, 2021
Bergson’s critique of intensive magnitude in Time and Free Will mainly targets Kant’s “Anticipati... more Bergson’s critique of intensive magnitude in Time and Free Will mainly targets Kant’s “Anticipations of Perception”, in which the Kantian distinction between matter and form is lowered. Bergson praises precisely this distinction for safeguarding sensation as something extra-intellectual. As the concept of intensity is the main tool of neo-Kantian intellectualism, in which the whole of reality is determined by the intellect, younger Bergson forcefully rejects intensive magnitude. However, his relation towards Kant changes. In Creative Evolution, Bergson proposes a genetic correction to Kantianism in which the distinction between matter and form is weakened. By comparing Bergson’s theory with the genetic Kantianism of Salomon Maïmon, who heavily relies on the concept of intensity, I argue that the concept fits his later project of renewing the Kantian theory. I thus demonstrate how the critique of intensive magnitude merely belongs to a provisional stage of Bergson’s relation to Kant.
Deleuze and Guattari Studies, 2021
Why does Deleuze rely so heavily on Spinoza and Leibniz? At first glance his critique of represen... more Why does Deleuze rely so heavily on Spinoza and Leibniz? At first glance his critique of representation and the 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.
Deleuze and Guattari Studies, 2021
This paper examines the Leibnizian influence in Deleuze's theory of the spatium. Leibniz's critiq... more 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 Nietzschian 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.
Process Studies, 2021
In this article I argue that Whitehead's doctrine of internal relations necessitates an immanent ... more In this article I argue that Whitehead's doctrine of internal relations necessitates an immanent and genetic conception of extension. I thereby criticize interpretations taking the Extensive Continuum as an empty form external to the occasions that occupy it. My argumentation starts from an examination of the doctrine of internal relations in the first section. I argue that the internality of relations is fundamental to Whitehead’s metaphysics and that the rejection of external relations entails a rejection of empty form and external determination. In the second section, I defend the identification of the Extensive Continuum with the realm of eternal objects in Science and the Modern World. The division of the Extensive Continuum is thereby understood in terms of the development of complex eternal objects out of the uniform ‘realm of possibility’. The third section, argues that this division of extension, equated with the limitation of the realm of eternal objects, results in actual occasions and not in mere forms. In other words, the development of structure from the uniform ‘scheme of relatedness’ results in actual togetherness, not in mere forms of togetherness. Furthermore, I widen the scope and consider the immanent and genetic conception of form and potentiality in general to better understand the Extensive Continuum as the ‘realm of potentiality’. The final section connects this immanent understanding of extension to a broader reading of Whitehead’s metaphysics in terms of immanence. I argue that the conception of extension as an empty form stems from a broader separation of the external and internal reality of actual occasions. Such separations, and the doctrine of external relations in general, bifurcate nature into ontological publicity and privacy. The immanent understanding of extension is shown to be fundamental to Whitehead’s unification of nature.
Journal of the British Society of Phenomenology, 2021
This article examines Bergson's critique of intensive magnitude in Time and Free Will. I demonstr... more 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.
Philosophy Today , 2021
In What Is Philosophy? Deleuze and Guattari understand concepts in a very unconventional way. One... more 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.
Kant-Studien, 2019
Salomon Maïmon argues that the formal determination of experience
in Kant’s first Kritik insuffic... more 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.
Pli: Warwick Journal of Philosophy, 2018
In this paper I examine how the understanding of time as a form of implication is developed in th... more In this paper I examine how the understanding of time as a form of implication is developed in the philosophy of Bergson and Deleuze. This concept of time finds its origin in Bergson's notion of duration understood as a heterogeneous multiplicity in which the elements are qualitatively differentiated. It is further developed in Bergson's later theory of a continuum of durations and finds its final bergsonian form in his concept of the past being contracted in the present. As such, time is no longer understood in terms of succession, but in terms of coexistence of two ontologically distinguished levels of time. Deleuze takes it one step further and makes a distinction between the differentiation of the virtual past and the differenciation of actuality.
Books by Florian Vermeiren
Routledge, 2024
This book explores and compares the reflections on space and quantity found in the works of five ... more This book explores and compares the reflections on space and quantity found in the works of five philosophers: Spinoza, Leibniz, Bergson, Whitehead, and Deleuze. What unites these philosophers is a series of metaphysical concerns rooted in 17th-century rationalism and embraced in 20th-century philosophies of process and difference.
At the heart of these concerns is the need for a comprehensive metaphysical account of the diversity and individuality of things. This demand leads to a shared critique of Cartesian and Newtonian conceptions of space. The most problematic aspect of those notions of space is homogeneity. In essence, uniform space fails to explain the differences between locations, thus violating the principle of sufficient reason. Cartesian and Newtonian theories of space thus contradict the metaphysical requirement for explaining diversity and individuality. The traditional concept of quantity faces similar issues. Motivated by these problems, each of these philosophers develops alternative notions of space and quantity. By examining these alternatives, the book sheds new light on an unexplored aspect of rationalism and its aftermath in 20th-century Continental philosophy.
A Geometry of Sufficient Reason will appeal to scholars and graduate students working in Continental philosophy, history of philosophy, metaphysics, and the history and philosophy of science.
“Florian Vermeiren’s A Geometry of Sufficient Reason is impressive in both its scope and philosophical sensitivity. It’s a must-read for anyone interested in the history and philosophy of space and associated notions like quantity”. -- Professor Kristin Primus, Editor-in-Chief of Journal of Spinoza Studies, UC Berkeley, USA
Uploads
Papers by Florian Vermeiren
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.
Books by Florian Vermeiren
At the heart of these concerns is the need for a comprehensive metaphysical account of the diversity and individuality of things. This demand leads to a shared critique of Cartesian and Newtonian conceptions of space. The most problematic aspect of those notions of space is homogeneity. In essence, uniform space fails to explain the differences between locations, thus violating the principle of sufficient reason. Cartesian and Newtonian theories of space thus contradict the metaphysical requirement for explaining diversity and individuality. The traditional concept of quantity faces similar issues. Motivated by these problems, each of these philosophers develops alternative notions of space and quantity. By examining these alternatives, the book sheds new light on an unexplored aspect of rationalism and its aftermath in 20th-century Continental philosophy.
A Geometry of Sufficient Reason will appeal to scholars and graduate students working in Continental philosophy, history of philosophy, metaphysics, and the history and philosophy of science.
“Florian Vermeiren’s A Geometry of Sufficient Reason is impressive in both its scope and philosophical sensitivity. It’s a must-read for anyone interested in the history and philosophy of space and associated notions like quantity”. -- Professor Kristin Primus, Editor-in-Chief of Journal of Spinoza Studies, UC Berkeley, USA
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.
At the heart of these concerns is the need for a comprehensive metaphysical account of the diversity and individuality of things. This demand leads to a shared critique of Cartesian and Newtonian conceptions of space. The most problematic aspect of those notions of space is homogeneity. In essence, uniform space fails to explain the differences between locations, thus violating the principle of sufficient reason. Cartesian and Newtonian theories of space thus contradict the metaphysical requirement for explaining diversity and individuality. The traditional concept of quantity faces similar issues. Motivated by these problems, each of these philosophers develops alternative notions of space and quantity. By examining these alternatives, the book sheds new light on an unexplored aspect of rationalism and its aftermath in 20th-century Continental philosophy.
A Geometry of Sufficient Reason will appeal to scholars and graduate students working in Continental philosophy, history of philosophy, metaphysics, and the history and philosophy of science.
“Florian Vermeiren’s A Geometry of Sufficient Reason is impressive in both its scope and philosophical sensitivity. It’s a must-read for anyone interested in the history and philosophy of space and associated notions like quantity”. -- Professor Kristin Primus, Editor-in-Chief of Journal of Spinoza Studies, UC Berkeley, USA