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Modal World: Relation, Quantity and Space in the Metaphysics of Spinoza, Leibniz, Bergson, Whitehead and Deleuze

As Bergson says, space is a fundamental scheme that produces a certain kind of metaphysics and a certain manner of thought. The scheme of space as homogeneous multiplicity is the foundation for mechanistic and (simplistic) realistic conception of the world, which is criticized by all the philosophers mentioned in the title. Furthermore, it is also the fundamental scheme of a certain type of thought that Bergson names ‘intellectual’ and ‘analytic’. Contrary to how (early) Bergson rejects this scheme and attempts to purely ‘think in time’, I want to investigate how space, as the fundamental scheme of thought, can be conceived differently. In this different conception, space is constituted by internal instead of external relations and spatial quantity is intensive rather than extensive. Such an alternative conception of space results in a different metaphysics (a) and a different model of thought (b).

a.The scheme of space is constituted by three conceptual elements: relation, quantity and space itself. The model of space that is criticized by the philosophers mentioned above consists of a conception of relations as external, a conception of quantity as extensive and a conception of space as absolute and extensive. (i) The idea of external relations entails that terms and relations remain mutually independent of each other. This means that things can be detached from their relations without the things or the relations changing. This idea is very clear in the idea of place as something that does not defined what a thing is; in other words, the book remains the same when it is move from the table to the chair and the place on the chair and the table remain neutral to the what is placed there. (ii) Closely related to this idea is the notion of extensive quantity. This is the conception of quantity as a whole of homogeneous parts that remain external to each other. The latter entails that whole is divisible and the parts can be subtracted, added and displaced, without a change in the nature of the whole or the parts. In other words, parts can function as units of measurement. In this conception of quantity, parts have external relations to each other and the whole. (iii) Finally, such a model also entails a certain conception of space. First of all, space is understood as absolute, that is, it is not relative to the things that take up space. Spatial relations are thus external relations. Second, space is extensively quantitative and thereby homogeneous, metrical and divisible. These conceptions of relation, quantity and space result in the idea of the world as an absolute common and public space, in which things are extensive and have external relations. It is precisely this idea of an absolute actual and public world that is rejected in the philosophy of Spinoza, Leibniz, Bergson, Whitehead and Deleuze. Each of the three above mentioned elements is rethought in their philosophy: (i) Relations become internal, individual and individualizing. (ii) Quantity becomes intensive, heterogeneous and ordinal. (iii) And space as the set of individual(izing) relations becomes relative to what takes up space. Moreover, space becomes potential rather than actual, as it is actualized differently in each contraction/expression/prehension of space. This is what Whitehead calls ‘modal space’. It results in a conception of reality in which the notion of ‘the world’ disappears. The world is not public or actual anymore. There is only a potential for a world.

b. Bergson also shows how the mode of space is fundamental in intellectual thought that thinks through analysis. This is very clear in Descartes who took geometry as the model for ‘clear and distinguished’ thought. When this scheme of external relations, extensive quantity and absolute space is replaced with individual(izing) relations, intensive quantity and modal space, another ‘image of thought’ is made possible. When relations are internal, analysis is replaced with expression and synthesis. The idea of external relations can also be found in traditional propositional logic in which things are thought as detachable from their propositional relations. When relations become internal, the whole world becomes the undetachable predicate of each thing. Thinking a thing does thereby not involve grasping its substance-property-structure in a subject-predicate-logic. Neither does thinking entail the analysis of a thing as a set of properties. Instead, in this new metaphysics, thinking a thing entails expressing the world from its position. Concepts then become expressive. They do not refer to an object through their logical ‘extension’, but they express from their intensive content. Concepts thus get an intrinsic reality that cannot be reduced to the ‘extensive’ reference to external reality. Thought becomes autonomous and immanent to itself. Thought becomes a physics of thought. The value of thought does not lie in a relation to an external reality, but in thought itself. Thought has to be powerful and expressive.  Adequacy is not a matter of correlation or representation, but a matter of expression. This is why this mode of thought is thoroughly rationalistic: the foundations of though belong to thought itself. Freed from the model of homogeneous space and propositional essentialist logic, the rationalism of Spinoza and Leibniz becomes ‘delirious’, as Deleuze says. It thereby comes close to the ‘new rationalism’ of Bergson the ‘imaginative rationalism’ of Whitehead.

Date:15 Sep 2018 →  Today
Keywords:Deleuze, Spinoza, Leibniz, Bergson, Whitehead, Quantity, Space
Disciplines:Theory and methodology of philosophy, Philosophy, Metaphysics
Project type:PhD project