Summary

The web content discusses Deleuze's philosophy of difference, particularly how it intersects with mathematical concepts, emphasizing the distinction between axiomatic and problematic mathematics as they relate to his ideas.

Abstract

The article delves into the interplay between Deleuze's philosophy and mathematical principles, focusing on the concept of difference as fundamental. It contrasts axiomatic mathematics, which is based on universally accepted principles and aligns with philosophies of identity, with problematic mathematics, exemplified by calculus, which deals with real-world motion and change. Deleuze sees calculus as a mathematical model that resonates with his philosophy of difference, as it addresses the infinitesimally small changes and pure becoming, rather than fixed identities. The text suggests that Deleuze's thought can be applied to practical philosophy and highlights the external relations and pure differences that calculus reveals, which are central to Deleuze's vision of becoming.

Opinions

The author believes that Deleuze's references to math and science further elucidate his philosophy of difference and its practical applications.
Deleuze is portrayed as viewing axiomatic mathematics as aligned with philosophies that prioritize identity, while problematic mathematics, particularly calculus, is seen as continuous with his own philosophy.
The article posits that calculus, with its focus on motion and change, is more in line with Deleuze's ideas than the static, identity-based nature of axiomatic mathematics.
The text suggests that Deleuze's philosophy can accommodate practical thought, indicating its relevance beyond theoretical discussions.
The author emphasizes the importance of external relations in Deleuze's work, as seen in the derivative's relation to the integral function in calculus, which underscores the concept of pure becoming.

Deleuze and Math 1

Perspectives on Deleuze: Math and Science

Deleuze made several references to math and science as a means of describing his philosophy of difference.

These references serve to illustrate further what is meant by a vision based on difference as primary, but also provide us with clues as to how Deleuze’s philosophy easily translates into one that can accommodate practical thought.

Philosophers have made connections with mathematics over the entire history of philosophy, but the references made tend to evolve with the mode of thought that predominated at any particular point in time.

Axiomatic Mathematics

Deleuze highlights two forms of mathematics that have been relevant to philosophy: axiomatic and problematic.

Axiomatic mathematics seeks out principles that are widely accepted because of their intrinsic merit, are a priori or inductively reasonable.

Axiomatic math is deterministic in the sense that the axiom solves via the application of rules and reason.

It is no wonder then that Plato would reference Euclidean geometry as continuous with his philosophy of the Forms, and that Descartes would reference the determinate relations of algebra and trigonometry as continuous with his rationalist philosophy.

We can see the axioms of both translate quite well into a vision of identity or extremes, eg.:

Hegel’s thesis-antithesis as the logical equivalent of = / does not =.

Axiomatic mathematics is language that requires no specific location in the real: it is an abstraction of logic and reason that stands on its own outside of the real world.

Axiomatic math by definition relates to identities, solves for identities.

Problematic Mathematics

On the other hand, in calculus, Deleuze finds a model that is continuous with his philosophy of difference.

Calculus is the mathematics of the real, created by Leibniz and Newton to quantitatively explain motion in the universe.

Calculus moves with the problem of motion, is designed as a mathematics of movement and change.

It is the not the extremes of identity or opposites that are primary here. Calculus solves for change that is infinitesimally small.

At the limit, change is no longer movement between positions, but a vanishing difference, pure movement, pure relations of change.

Calculus stays with the problem of difference, and behind it there is nothing.

The derivative explains the pure difference of the integral function. The second derivative explains the pure difference of the first derivative function, and so on.

The differential function is external to the points on the curve of its relative integral function. It is the external relations that remain of primary importance, not the terms themselves.

The derivative constitutes pure difference and at the limit, the terms themselves fall away.

All we are left with is pure change, pure becoming.

Relations of change are pure becoming.

I hope you enjoyed this article. Thanks for reading!

Tomas

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