A Geometry of Sufficient Reason: Reconceiving Space With Spinoza, Leibniz, Bergson, Whitehead and Deleuze

Space is most commonly understood as a box in which things exist. The box itself is independent from and indifferent to the things that exist in it. Therefore, space itself is empty. However, understood as an empty box, space is homogeneous. In other words, if locations are indifferent to whoever occupies them, they must be without differences. Thus understood, there are no qualitative differences between different parts of space. However, given this uniformity, the location of things is without explanation. We cannot explain why something is here and not there when ‘here’ and ‘there’ are perfectly homogeneous. Location is thus ‘without sufficient reason’. This is one of the objections that Leibniz raises against Newton’s concept of space (which is very close to the idea of an empty box). Leibniz’s criticism is founded on the so-called ‘Principle of Sufficient Reason’. The latter states that nothing happens or nothing is the way it is without sufficient reason.

This rationalistic principle is also endorsed by Spinoza. But it can even be found in authors which are not generally associated with rationalism: Whitehead, Bergson and Deleuze. Although these are not rationalists in the traditional sense, they each develop a kind of renewed rationalism. The latter is not so much an epistemological theory but a metaphysical theory. The basis of rationalistic metaphysics is the idea of the complete determination of reality. This does not entail a rejection of freedom or creativity. Rationalistic metaphysics only rejects the traditional conception of creativity and freedom as indetermination. The idea of indetermination leaves things unexplained. Instead, these authors demand that metaphysics accounts for things like the creation of the new. More in general, the metaphysics of these authors is focused on conceptualizing the process of differentiation that leads to the diversity of reality. Leibniz’s objection to Newtonian space thus takes on a new meaning: The lack of sufficient reason in the traditional conception of space becomes a lack of difference. This criticism of traditional space also pertains to the traditional concept of quantity. Quantitative difference is most commonly understood as superficial difference that does not pertain to the nature of things: one liter of wine and two liters of wine are thus two quantities of the same thing. Traditionally conceived, quantitative difference is a difference distinguishing the identical. It is a hollowed-out form of difference that is, again, without sufficient reason.

My research examines how such metaphysical concerns lead to a reconception of space and quantity in the work of these five philosophers. I thus trace a hidden lineage in the history of philosophy. In this new conception, space and quantity are understood as individualized. They participate in the difference distinguishing individual things. The source of this diversity is found in relations. The structure of relations between things is understood as the principle of differentiation that produces the individuality and diversity of concrete reality. When both space and quantity are understood in terms of the relations that things have to each other, spatial difference and quantitative difference find their foundation and sufficient reason in the structure of reality.