Deleuze, Leibniz, and the Test of the Large and the Small

If philosophy is able to provide guidance on how to live that is superior to reliance on conventions, habits, or impulses, it is because the activity of philosophy embodies a distinctive and more reliable approach to practical reason. But this depends on whether philosophical representations of reality are accurate and comprehensive. There is reason to think that traditional philosophical accounts of how we represent reality are at best incomplete because they don’t explain how we deal with change, novelty, individuality, and the role of the unconscious. (See this post for a more detailed account of these issues.) Thus, I’m increasingly interested in the thought of Gilles Deleuze because he develops a metaphysics and epistemology designed to overcome these limitations. This post continues my series on how Deleuze addresses these issues.

When we last encountered Deleuze, he was arguing that Aristotelean-inspired classification schemes, in which differences create species within genera, leave out the accidental, contingent differences that create and define individuals. Furthermore, these classification schemes fail to create categories that help organize differences between genera. The result, Deleuze argues, is a metaphysics that cannot explain the being of individuals and that leaves us with a fragmented notion of being itself. Aristotle’s scheme, as Deleuze says, “fails the test of the large and the small.”

However, Deleuze is not the first thinker to express dissatisfaction with how differences are handled within the dominant philosophical traditions. The question naturally arises: Has a satisfactory alternative been developed within the history of philosophy? Deleuze’s answer is no, at least until he comes along, but it is important to see why he thinks the alternatives are unsatisfactory.

Gottfried Leibniz, the 17th Century German mathematician and philosopher, argued that an adequate, comprehensive concept of an entity must include the entire past, present, and future states of that entity. Leibniz agreed with Aristotle that the basic form of all entities is a substance characterized by properties—an apple is red, round, tastes sweet, etc. But Leibniz recognized that this picture of reality can’t account for relations. “Samantha is taller than Susan” entails that “Susan is shorter than Samantha.” There is an infinite number of these relations that must be incorporated into our concept of Samantha or Susan. Furthermore, since the two statements are logically equivalent, it isn’t clear which property attaches to which individual. Both statements are true of each individual. Moreover, causal interactions require relations between entities rather than a relationship between an entity and a property. How do we incorporate causal relations into the identity of an individual entity? Leibniz solves both problems by asserting that everything that happens to an entity as well as its’ relations to all other entities is part of the concept of that entity. Thus, each individual is essentially a window onto the world, an infinite list of properties and relations viewed from a perspective. (Leibniz calls this individual a monad.)

Deleuze finds this idea enormously attractive because it accounts for all those small differences that determine the individuality of an entity. For Aristotle, differences define species but individuals are left out of the picture. For Leibniz, infinitesimal differences define individuals thus correcting what Deleuze finds to be one of the primary limitations of Aristotelean-inspired classification schemes.

However, as it stands, Leibniz’s view leaves us with another problem. We now have an infinite heap of properties and relations that constitute an individual. What gives this heap it’s unity? These are not free-floating properties and relations but instead are properties and relations of an individual’s perspective on the world. Aristotle could answer this question through a series of negations—an individual is the product of a series of “this but not that” judgements that place it in the proper categories that constitute its essential nature. For instance, this object is living not inorganic, a plant, not an animal, fruit, not a vegetable, an apple, not an orange, etc. But this won’t work for Leibniz. Most of these infinitesimal differences between entities are not contradictory. That Samantha is taller than Susan is compatible with Samantha being shorter than Michelle. Thus, the identification of a property doesn’t neatly sort individuals into categories. Furthermore, only someone who can grasp an infinite list could know the principle that distinguishes one thing from another on Leibniz’s view.

Leibniz’s answer to what gives an individual unity is complex but at the end of the day the unity of the universe and of each individual in it is a product of God’s agency. The continuum of properties that makes up reality are unified, or as he says “in harmony,” because they are pre-selected by God as the best of all possible worlds.

Thus, although Leibniz successfully shows that small differences produce individuality, it’s not really difference that is doing the work of individuation—God orders the differences.

This raises a fundamental methodological consideration for Deleuze that will shape his entire philosophy. For Deleuze, we cannot explain empirical phenomena by invoking concepts that are beyond our experience the emergence of which remain unexplained. Whether its Kant’s transcendental ego, Hegel’s absolute spirit, or Leibniz’s infinite God of perfection, these cannot be the foundation of metaphysics unless we explain how they are generated in experience. Everything must be explained from within experience and thus Leibniz fails, according to this standard, since this infinite God is beyond our experience.

The other response to Aristotelean-inspired representations that Deleuze addresses is from Hegel, which I will cover in a subsequent post.

Previous posts in this series:

Published by Dwight Furrow

Wine, food, and travel writing, philosophy, aesthetics

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