Logics of Worlds is the sequel to Alain Badiou's masterpiece, Being and Event. Tackling the questions that had been left open by Being and Event, and answering many of his critics in the process, Badiou supplements his pioneering treatment of multiple being with a daring and complex theory of the worlds in which truths and subjects make their mark - what he calls a materialist dialectic. Drawing on his most ambitious philosophical predecessors - Leibniz, Kant, Hegel, Kierkegaard, Lacan, Deleuze – Badiou ends this important later work with an impassioned call to 'live for an Idea'.

A translation of one of the single most important works of recent French philosophy, Badiou's magnum opus, and a must-have for his growing following and anyone interested in contemporary Continental thought.

In Mathematics of the Transcendental, Alain Badiou painstakingly works through the pertinent aspects of category theory, demonstrating their internal logic and veracity, their derivation and distinction from set theory, and the 'thinking of being'. In doing so he sets out the basic onto-logical requirements of his greater and transcendental logics as articulated in his magnum opus, Logics of Worlds. Previously unpublished in either French or English, Mathematics of the Transcendental provides Badiou's readers with a much-needed complete elaboration of his understanding and use of category theory. The book is vital to understanding the mathematical and logical basis of his theory of appearing as elaborated in Logics of Worlds and other works and is essential reading for his many followers.

Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible world's model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been applied increasingly in domains such as program semantics, artificial intelligence, and more recently in the semantic web. Additionally, all these logics were also studied proof theoretically. The proof systems for modal logics come in various styles: Hilbert style, natural deduction, sequents, and resolution. However, it is fair to say that the most uniform and most successful such systems are tableaux systems. Given logic and a formula, they allow one to check whether there is a model in that logic. This basically amounts to trying to build a model for the formula by building a tree. This book follows a more general approach by trying to build a graph, the advantage being that a graph is closer to a Kripke model than a tree. It provides a step-by-step introduction to possible worlds semantics (and by that to modal and other nonclassical logics) via the tableaux method. It is accompanied by a piece of software called LoTREC (www.irit.fr/Lotrec). LoTREC allows to check whether a given formula is true at a given world of a given model and to check whether a given formula is satisfiable in a given logic. The latter can be done immediately if the tableau system for that logic has already been implemented in LoTREC. If this is not yet the case LoTREC offers the possibility to implement a tableau system in a relatively easy way via a simple, graph-based, interactive language.

The latter half of the 20 ...

Alain Badiou is one of the leading philosophers in the world today. His ground-breaking philosophy is based on a creative reading of set theory, offering a new understanding of what it means to be human by promoting an “intelligence of change”. Badiou’s philosophical system makes our capacity for revolution and novelty central to who we are, and develops an ethical position that aims to make us less anxious about this very capacity. This book presents a comprehensive and engaging account of Badiou’s philosophy, including an in-depth discussion of The Theory of the Subject, Being and Event and Logics of Worlds. In a clear and careful analysis, Ed Pluth considers exactly how Badiou’s theoretical “anti-humanism” is linked up to what is, for all intents and purposes, a practical humanism. Central to this is an account of Badiou’s theory of the subject, and his attempt to develop an “ethic of truths”. The role of set theory, Marxism, and Lacanian psychoanalysis in Badiou’s philosophy is also given close attention. This book will be of interest to students and scholars of philosophy, as well as to all those keen to develop a critical understanding of one of the most controversial and important thinkers of the twentieth century.

Alain Badiou is arguably the most original and influential philosopher working in France today. Working against the tide of postmodern orthodoxy, Badiou revitalizes philosophy's perennial attempt to provide a systematic theory of truth. Theoretical Writings presents, in Badiou's own words, 'the theoretical core of [his] Philosophy'. Beginning with the controversial assertion that ontology is mathematics, the chapters step the reader through his key concepts of being, subject and truth via startling re-readings of canonical figures including Spinoza, Kant and Hegel and engagements with poetry, psychoanalysis and radical politics. Theoretical Writings is an indispensable introduction to one of the great thinkers of our time.