"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."
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?
- 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?
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