0.2 The Proposed Path

"I would like this publication to mark an obvious fact: the nullity of the opposition between analytic thought and continental thought. And I would like this book to be read, appreciated, staked out, and contested as much by the inheritors of the formal and experimental sciences or of the law, as it is by [...] the wild militants of a de-alienated world, and by those who are deliciously isolated by amorous constructions. Finally, that they say to themselves, making the difficult effort to read me: that man, in a sense that he invents, is all of us at once."

- Alain Badiou, Introduction to Being and Event 

Alain Badiou's continuous output has been immense, and particularly so in the last 10-15 years as his popularity and the availability of his translated works have reached the Americas. Amidst the staggering body of his primary work and secondary publications (culled from interviews, lecture notes, and seminars) it can be difficult to know where to start reading Badiou or the most efficient path to take.

The general vector that I propose, based on what I consider the "foundational texts" of Badiou's system serving as the core of his philosophical project, is the following:

A few notes on this path, of which we will traverse just the works relevant to our task:

Badiou's work from the late 1980's to late 1990's circulates around his magnum opus Being and Event (1988), where Badiou proposes to return philosophy back to its roots in mathematics by reinterpreting the history and goals of philosophy by way of the modern mathematical foundations of set theory. In essence, Badiou is re-founding the very basic terms and tenants of philosophy based on his study of mathematics and its unique conceptual resources. In doing so, he is able to redefine classic notions such as "Truth" and the agent of truths (the "Subject"). Two significant publications that spin out of Being and Event are Manifesto for Philosophy (1989) and Number and Numbers (1990).

For scientists and the expected audience of this blog, I do not recommend reading through the Manifesto, as it is primarily focused with engaging with the history of philosophy in order to undo it and reformulate its foundations. Additionally (and as critics have pointed out) the English version has suffered from a poor translation that renders the book confusing and a tiresome read.

Number and Numbers, on the other hand, provides an excellent introduction to the history of mathematics and numbers. It covers the historical development of set theory, and introduces the core mathematical concepts needed for one to approach and appreciate the background of Being and Event. It also focuses on John Conway's theory of "surreal numbers", which holds a central place in Badiou's mathematical thinking, but which is barely referenced outside of this text. As such, we will spend some extended time on this concept and its grounding position in Badiou's system.

Badiou's work from the early 2000's to the present has circulated around his "sequel" to Being and Event: Logics of Worlds (2006), where Badiou attempts to describe how we actually experience the world and the advent of truths, by incorporating mathematical category theory (a rival foundation to set theory) into his system. In doing so, he is able to describe the local relativity of languages and knowledges, and the truths that erupt and cross over them. Accordingly, there is a Second Manifesto for Philosophy (2009) and a corresponding mathematical tract, Mathematics of the Transcendental (2014).

The Second Manifesto was published more for the general public and, especially if one has mastered the terms and concerns of Being and Event, is very readable. This Manifesto serves as a more direct critique of modern consumer society, Western militarism, "human rights", etc. utilizing Badiou's mathematico-philosophical resources up to this point. With praxis as his ever central mantra, Badiou is never hesitant to connect his "abstract" theories of revolution and change to the concrete world

Mathematics of the Transcendental is composed of Badiou's lecture and seminar notes outlining his study of category theory, modern logic, and the Heyting algebra-- all pulled together to compose his phenomenology in Logics of Worlds. We will spend some extended time on these concepts as a useful background for Logics of Worlds; particularly as secondary commentary on the critical possibilities opened up by Logics of Worlds and its use of category theory have been sparse and lacking.

In these posts I will primarily stick to Badiou's work on number theory and how it affects our understanding of science and revolutions within science. Therefore, I will not be covering the Manifestos in any detail. However, I will likely take a few detours into Badiou's shorter works and articles-- most significantly into his Ethics, which is most clearly grasped after one understands the concepts of Being and Event, and Briefings on Existence: A Short Treatise on Transitory Ontology, which acts as a transition/teaser text between Being and Event and Logics of Worlds.

As a nota bene, it can be fearsome approaching Badiou's texts, particularly if one is not used to this particular style of writing and engagement with "continental" philosophy. I maintain that-- versus writers such as Foucault, Derrida, or Lacan, whose labyrinthine and dizzying writing styles are part of the very point that they are respectively trying to make about the relation between language and reality-- Badiou's style is extremely precise once one begins to get the hang of his various neologisms and constructs. And especially so if one understands the mathematical concepts underlying them. After all, a truly revolutionary way of thinking about mathematics and reality beckons for a language and style adequate to the task.

So, how about we get started? As always, sound off in the comments!

- Dr. G

Next: Why mathematics?

0.1 Introduction

"The militant of truth is not only the political militant working for the emancipation of humanity in its entirety. He or she is also the artist-creator, the scientist who opens up a new theoretical field, or the lover whose world is enchanted."

- Alain Badiou, Being and Event xiii

Welcome!  

A blog on philosopher Alain Badiou’s work and its meaning for the sciences… This is a project that I’ve been meaning to start up for years now; certainly to educate the scientific public on Badiou’s revolutionary work on mathematics and philosophy, but also for my own sanity.

Badiou's work has been knocking around my head in one form or the other for at least the past 8 years, stemming from when I was originally assigned his Ethics as a reading assignment for a Continental Philosophy course in college. As an Engineering major (with a passing interest in Philosophy), Badiou's unabashed appeal to foundational mathematics in grounding his philosophy and ethics was a revelation to me, and set me on a whirlwind course towards understanding what philosophy can uncover using the resources of mathematics; resources that have long been forgotten even by contemporary scientists.

Much of what I will be placing here is compiled from various thoughts, notes, and unpublished essays that I have written for myself over the years in my attempt to understand the work of a true radical polymath and its implications for how we understand the very foundations of mathematics and science. The decision to present my thoughts on this "public" forum serves two distinct goals: 1) it allows others access to information that may be valuable or helpful to them in understanding the immensity, both in volume and breadth, of Badiou's work (as opposed to this information sitting in the limbo of my digital and physical notebooks), and 2) it gives me the motivation to stay engaged with these ideas and keeps me productive in this hobby of writing; particularly as I start my residency in emergency medicine.

As such, I don't promise to keep to a strict timetable of posting updates, given how gruelingly busy these next few years will be for me at the hospital, but I hope to keep hammering at this project as much as I can. 

The connection between philosophy and mathematics forms the very core of Badiou’s thinking, and tackling his work requires traversing both of these revered fields of thought. Without such engagement, the philosophers don't understand mathematics, the mathematicians and scientists don't understand philosophy, and Plato surely rolls in his grave.

I do believe that understanding the mathematics which informs Badiou's ontology greatly illuminates much of his philosophy; a philosophy that may otherwise appear obscure or opaque to those bereft of the mathematical knowledge underlying it. I hope that these posts will clarify the importance of mathematics and its history, and thereby help serve as an entry point for scientists into Badiou's philosophy. While Badiou's work covers and informs fields as afar as politics, art, theater, ethics, literature, and philosophy proper, my experience has been that very little attention has been placed on its consequences for understanding the physical sciences. As someone from a primarily science and engineering background myself, I will try and concentrate on concerns and examples relevant to Badiou's potential import for the sciences.

When speaking of "science" himself, Badiou almost exclusively refers to mathematics, and only by logical implication to the mathematicized science of physics. So while many of Badiou's meditations and examples come from mathematics and its history, I shall endeavor to elucidate the impact his thought has on physics and the other physical sciences. For example, one novel connection that I hope to unpack in the course of these dialogues is my conjecture that Badiou's work provides a mathematico-theoretical "motor" for Thomas Kuhn's classic theory of scientific revolutions; thereby providing the formal mechanism underlying what Kuhn was able to describe via experience and historical study. 

I do not intend for my review here to be exhaustive. Given the abundance of both primary and secondary literature on Badiou's work (amassed over at least the last 50 years), along with all of the primary mathematical literature, I can only hope to fill in the gap that I have recognized in assistance for those scientists interested in engaging with Badiou's work. As such, I recommend that any points leaving the reader confused or lost (or hopefully tickled curious!) be supplemented either by the primary documents or other resources. I will try and post helpful articles and videos as appropriate, but none of this is meant to substitute for the experience of reading Badiou's texts themselves. I only hope to aid the transition to reading his texts, and to add to-- and work through-- some of my own insights.

I will strive to present much of this in focused and manageable posts of information, especially given how deep one may sink into further researching any small aspect of Badiou's thought. So I hope not to make the length of this introductory piece a habit.

Feel free to sound off in the comments, and here’s to a fruitful journey!

- Dr. G

Next: The road to be traveled