We provide partial answers to the following problem: Is the class of Borel linear orders well-quasi-ordered under embeddability? We show that it is indeed the case for those Borel orders which are embeddable in R ω , with the lexicographic ordering. For Borel orders embeddable in R 2 , our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some $\mathbf{R}^n, n , and hyperprojective determinacy for the general case.

We prove two results about the embeddability relation between Borel linear orders: For $\eta$ a countable ordinal, let $2^\eta$ (resp. $2^{<\eta}$) be the set of sequences of zeros and ones of length $\eta$ (resp. $<\eta$), equipped with the lexicographic ordering. Given a Borel linear order $X$ and a countable ordinal $\xi$, we prove the following two facts. (a) Either $X$ can be embedded (in a $\triangle^1_1(X,\xi)$ way) in $2^{\omega\xi}$, or $2^{\omega\xi + 1}$ continuously embeds in $X$. (b) Either $X$ can (...) embedded (in a $\triangle^1_1(X,\xi)$ way) in $2^{\omega\xi}$, or $2^{\omega\xi}$ continuously embeds in $X$. These results extend previous work of Harrington, Shelah and Marker. (shrink)

We consider Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank. We relate the descriptive complexity of the equivalence relation to the nature of its complete invariants. A typical theorem is that E is potentially Π03 iff the invariants are countable sets of reals, it is potentially Π04 iff the invariants are countable sets of countable sets of reals, and so on. The proofs (...) use various techniques, including Vaught transforms, changing topologies, and the Scott analysis of countable models. (shrink)

The 2005 Avignon Theatre Festival sparked a vast controversy about the insistent presence of bodies (whether wounded, broken, or humiliated) on stage. Without subscribing to the reactionary critical response to the Festival, it is legitimate to return to the debate in order to question the ubiquity of the “victim body” in contemporary theatre. Such representations, far from being heterodox, are in fact part of the massive ideology of “the ethical”, as diagnosed by Alain Badiou. The oppressed body thus tends (...) to be assimilated to the body of the victim. The result is the obliteration of the resistance of subjects to their oppression, or of their active response to it, theatre being reduced to the maxims of a democratic materialism: “there are only bodies and languages”. (shrink)

Since the beginning of the War on Terror, Israel has become increasingly salient to imperial strategy and ever more aggressive in its policies toward the Palestinians. In this context, a key ideological weapon is the cynical accusation of "anti-Semitism." For historical reasons, this has been deployed most forcefully in France, and Alain Badiou and Eric Hazan caustically demolish the "anti-Semitism is everywhere" allegation, used to bludgeon opponents of the Israeli state and those who stand in solidarity with the banlieue (...) youth. Ivan Segre undertakes a meticulous deconstruction of a rampant "reactionary philo-Semitism" that identifies Jewish interests with the "democratic West.". (shrink)

Against the backdrop of an alarming rise in authoritarianism and the crisis of liberal democracy, few would consider extoling the virtues of politics today. Yet in this lively dialogue with journalist Aude Lancelin, leading French thinker Alain Badiou argues that it is precisely through politics that humanity can still achieve its most ambitious aims. As power becomes ever more concentrated in the hands of the state and global corporations, the role of the citizen is reduced to little more than (...) ritual. But Badiou emphasizes that politics is concerned not just with power and the state, but also with justice. So the central question of politics is “What is a just power?”, and the debate over politics is fundamentally about the norms to which power is subject and its relationship to a community – a community that is able to take control of its own destiny and provide its own direction, based on a shared standard of justice. This engaging dialogue, in which Badiou articulates his view of politics with exceptional clarity, will be of great value to anyone interested in radical politics today. (shrink)

Infinite Thought brings together a representative selection of the range of Alain Badiou's work, illustrating the power and diversity of his thought.

This volume, assembled with the collaboration of the author, presents for the first time in English a comprehensive outline of Badiou's ambitious system.

PT. 1. PHILOSOPHY AND CIRCUMSTANCES: Introduction -- Philosophy and the question of war today: 1. On September 11 2001: philosophy and the 'War against terrorism' -- 2. Fragments of a public journal on the American war against Iraq -- 3. On the war against Serbia: who strikes whom in the world today? -- The 'democratic' fetish and racism: 4. On parliamentary 'democracy': the French presidential elections of 2002 -- 5. The law on the Islamic headscarf -- 6. Daily humiliation -- (...) Openings/Affirmations: 7. The power of the open: A discourse on the necessity of fusing Germany and France -- 8. Third sketch of a manifesto of affirmationist art -- Notes to part one -- PT. 2. USES OF THE WORD 'JEW': Introduction -- 1. Israel: the country in the world where there are the fewest Jews? -- 2. The destruction of the European Jews and the question of evil (fragments from Ethics: an essay on the understanding of evil, translated by Peter Hallward) -- 3. A dialogue between a Jew from Darzia and an Arab from Epirus -- 4. Saint Paul and the Jews (excerpt from Saint Paul: the foundation of universalism, translated by Ray Brassier) -- 5. Against negationism -- 6. Local angel -- 7. Intervew at the Daily Haaretz -- 8. The master-signifier of the New Aryans (by Cécile Winter) -- 9. The word 'Jew' and the sycophant -- Notes to part two -- PT. 3. HISTORICITY OF POLITICS: LESSONS OF TWO REVOLUTIONS. 1. The Paris commune: a political declaration on politics -- 2. The cultural revolution: the last revolution? -- A brief chronology of the cultural revolution (translated by Bruno Bosteels) -- Notes to part three. (shrink)

Hegel once wrote that Truth could not be expressed within a single sentence. His statement could surely be taken as justification for the length of his ...

La philosophie est aujourd'hui possible, dans la plénitude de son ambition. La philosophie elle-même, telle que l'entendait Platon.Ce qui a entraîné son éclipse au XIXe siècle, c'est qu'elle s'est identifiée, « suturée », tour à tour à un seul des champs où se pose, par-delà le savoir, une vérité : le scientifique (positivisme), le politique (marxisme), puis, avec Nietzche et plus encore Heidegger, le poème.

A passionate critique of Enlightenment--both in its contemporary invocation and its historical and cultural use--and a call to arms to rethink human equality and liberty without the sacrifice of individual rights and ethnicities.

Louveau, A., S. Shelah and B. Velikovi, Borel partitions of infinite subtrees of a perfect tree, Annals of Pure and Applied Logic 63 271–281. We define a notion of type of a perfect tree and show that, for any given type τ, if the set of all subtrees of a given perfect tree T which have type τ is partitioned into two Borel classes then there is a perfect subtree S of T such that all subtrees of S of (...) type τ belong to the same class. This result simultaneously generalizes the partition theorems of Galvin-Prikry and Galvin-Blass. The key ingredient of the proof is the theorem of Halpern-Laüchli on partitions of products of perfect trees. (shrink)

Plato's _Republic_ is one of the best-known and most widely-discussed texts in the history of philosophy. But how might we get to the heart of this work today, 2,500 years after its original composition? Alain Badiou breathes life into Plato's landmark text and revives its universality. Rather than producing yet another critical commentary, he has instead worked closely on the original Greek and, through spectacular changes, adapted it to our times. In this innovative reimagining of Plato's work, Badiou has (...) removed all references specific to ancient Greek society--from lengthy exchanges about moral courage in archaic poetry to political considerations mainly of interest to the aristocratic elite--and has expanded the range of cultural references. Here, philosophy is firing on all cylinders: Socrates and his companions are joined by Beckett, Pessoa, Freud, and Hegel, among others. Together these thinkers demonstrate that true philosophy endures, ready to absorb new horizons without changing its essence. Moreover, Badiou--who is also a dramatist--has transformed the Socratic dialogue into a genuine oratorial contest. In his version of the _Republic_, the interlocutors do much more than simply agree with Socrates. They argue, stand up to him, put him on the spot, and show thought in motion. In this work of dramatic scholarship and philosophy, we encounter a modern version of Plato's text that is alive, stimulating, and directly relevant to our own world. (shrink)

Didacticism, romanticism, and classicism are the possible schemata for the knotting of art and philosophy, the third term in this knot being the education of subjects, youth in particular. What characterizes the century that has just come to a close is that, while it underwent the saturation of these three schemata, it failed to introduce a new one. Today, this predicament tends to produce a kind of unknotting of terms, a desperate dis-relation between art and philosophy, together with the pure (...) and simple collapse of what circulated between them: the theme of education. Whence the thesis of which this book is nothing but a series of variations: faced with such a situation of saturation and closure, we must attempt to propose a new schema, a fourth type of knot between philosophy and art. Among these “inaesthetic” variations, the reader will encounter a sustained debate with contemporary philosophical uses of the poem, bold articulations of the specificity and prospects of theater, cinema, and dance, along with subtle and provocative readings of Fernando Pessoa, Ste;phane Mallarme;, and Samuel Beckett. (shrink)

Uses the thoughts of such great minds as Kierkegaard, Plato, and Beckett to examine the concept of love and redefine it in the face of twenty-first century modernity.

Plato's _Republic_ is one of the best-known and most widely-discussed texts in the history of philosophy. But how might we get to the heart of this work today, 2,500 years after its original composition? Alain Badiou breathes life into Plato's landmark text and revives its universality. Rather than producing yet another critical commentary, he has instead worked closely on the original Greek and, through spectacular changes, adapted it to our times. In this innovative reimagining of Plato's work, Badiou has (...) removed all references specific to ancient Greek society--from lengthy exchanges about moral courage in archaic poetry to political considerations mainly of interest to the aristocratic elite--and has expanded the range of cultural references. Here, philosophy is firing on all cylinders: Socrates and his companions are joined by Beckett, Pessoa, Freud, and Hegel, among others. Together these thinkers demonstrate that true philosophy endures, ready to absorb new horizons without changing its essence. Moreover, Badiou--who is also a dramatist--has transformed the Socratic dialogue into a genuine oratorial contest. In his version of the _Republic_, the interlocutors do much more than simply agree with Socrates. They argue, stand up to him, put him on the spot, and show thought in motion. In this work of dramatic scholarship and philosophy, we encounter a modern version of Plato's text that is alive, stimulating, and directly relevant to our own world. (shrink)

The subtractive : preface by Francois Wahl -- Philosophy itself -- The (re)turn of philosophy itself -- Definition of philosophy -- What is a philosophical institution? -- Philosophy and poetry -- The philosophical recourse to the poem -- Mallarm's method : subtraction and isolation -- Rimbaud's method : interruption -- Philosophy and mathematics -- Conference on subtraction -- Truth : forcing and unnameable -- Philosophy and politics -- Philosophy and love -- What is love? -- Philosophy and psychoanalysis -- Subject (...) and infinite -- Antiphilosophy : Lacan and Plato -- Writing of the generic -- Writing of the generic : Samuel beckett. (shrink)

In this dialogue, Alain Badiou shares the clearest, most detailed account to date of his profound indebtedness to Lacanian psychoanalysis. He explains in depth the tools Lacan gave him to navigate the extremes of his other two philosophical "masters," Jean-Paul Sartre and Louis Althusser. Élisabeth Roudinesco supplements Badiou's experience with her own perspective on the troubled landscape of the French analytic world since Lacan's death--critiquing, for example, the link (or lack thereof) between politics and psychoanalysis in Lacan's work. Their (...) exchange reinvigorates how the the work of a pivotal twentieth-century thinker is perceived. (shrink)

La quatrième de couverture indique : Deleuze et Guattari étaient des lecteurs sans pareils. C'est la raison pour laquelle Alain Jugnon les lit dans ce livre ; plus précisément, il lit avec eux Artaud et Kafka, Lacan et Klossowski, Büchner et Nietzsche. N'ont-ils pas assez lu Lautréamont ; il les lit pour eux, comme eux l'auraient lu, l'ajoutant à leurs lectures, avec les outils qu'ils ont créés pour lire. Nul mieux qu'Alain Jugnon n'articule les lectures nécessaires à la (...) défaite de ce monde-ci et au surgissement d'un monde transformé : "Deleuze et Guattari ont commencé à dire dans leur livre premier, L'Anti-Oedipe : il n'y a plus de dialectique à penser ou bien d'histoires à raconter, mais il y aura des machines capitalistes et des machines désirantes, des guerres des sexes et des guerres des races, des combats de rue et des révolutions de palais, il y aura tout ça et plus encore, qui fera une bible humaine à revendre ou bien une philosophie populaire à inventer pour demain." (A.J.). (shrink)

Depuis le XIXe siècle et jusqu’à nos jours, l’expansion des activités physiques et sportives s’est accompagnée de différences et d’inégalités sociales. A fortiori parmi l’ensemble des femmes, rarement pensé comme étant un ensemble lui-même divisé et hiérarchisé. S’agissant de l’accès aux loisirs sportifs puis au sport, les rapports au temps et à toutes les formes de travail, les rapports au corps sont particulièrement différenciateurs pour elles. Jusqu’à la moitié du XXe siècle environ, le sport ne concerne, au regard des millions (...) de femmes paysannes, ouvrières et petites employées, qu’une minorité d’aristocrates, de mondaines puis de jeunes femmes cultivées. Nombre d’institutions (le mouvement olympique, le sport ouvrier, les fédérations existantes) s’opposeront au développement de ces activités pour celles qui demeurent avant tout des mères destinées au foyer. La massification du sport ces dernières décennies s’accompagne d’une persistance des inégalités parmi les femmes, y compris parmi les plus jeunes. (shrink)

Quali sono lo spazio e il tempo della filosofia nel sapere contemporaneo? È possibile tracciare dei confini e far emergere la figura di un sapere sullo sfondo di un'epoca e della sua forma di vita?

Overture -- Jacques Lacan -- Georges Canguilhem and Jean Cavaillès -- Jean-Paul Sartre -- Jean Hyppolite -- Louis Althusser -- Jean-François Lyotard -- Gilles Deleuze -- Michel Foucault -- Jacques Derrida -- Jean Borreil -- Philippe Lacoue-Labarthe -- Gilles Châtelet -- Françoise Proust -- A note on the texts.

English-speaking readers might be surprised to learn that Alain Badiou writes fiction and plays along with his philosophical works and that they are just as important to understanding his larger intellectual project. In _Ahmed the Philosopher_, Badiou's most entertaining and accessible play, translated into English here for the first time, readers are introduced to Badiou's philosophy through a theatrical tour de force that has met with much success in France. _Ahmed the Philosoph_er presents its comic hero, the "treacherous servant" (...) Ahmed, as a seductively trenchant philosopher even as it casts philosophy itself as a comic performance. The comedy unfolds as a series of lessons, with each "short play" or sketch illuminating a different Badiousian concept. Yet Ahmed does more than illustrate philosophical abstractions; he embodies and vivifies the theatrical and performative aspects of philosophy, mobilizing a comic energy that exposes the emptiness and pomp of the world. Through his example, the audience is moved to a living engagement with philosophy, discovering in it the power to break through the limits of everyday life. (shrink)

_The Incident at Antioch_ is a key play marking Alain Badiou's transition from classical Marxism to a "politics of subtraction" far removed from party and state. Written with striking eloquence and extraordinary poetic richness, and shifting from highly serious emotional and intellectual drama to surreal comic interlude, the work features statesmen, workers, and revolutionaries struggling to reconcile the nature and practice of politics. This bilingual edition presents _L'Incident d'Antioche_ in its original French and, on facing pages, an expertly executed (...) English translation. Badiou adds a special preface, and an introduction by the scholar Kenneth Reinhard connects the play to Paul Claudel's _The City_, Saint Paul and the early history of the Church, and the innovative mathematical thinking of Paul Cohen. The translation includes Susan Spitzer's extensive notes clarifying allusions and quotations and hinting at Badiou's intentions. An interview with Badiou encompasses the play's settings, themes, and events, as well as his ongoing literary and conceptual experimentation on stage and off. (shrink)

La culture moderne n'en a jamais fini de dissiper le mystère qu'elle constitue pour elle-même. Deux schémas principaux inspirent aujourd'hui cette autoréflexion de la modernité. Dans la mouvance de Heidegger, les Temps modernes assurent le règne sans partage du sujet au sein d'un univers réduit à être objet de maîtrise et de possession. Selon une inspiration tocquevillienne comme celle, en particulier, de Louis Dumont, c'est l'individualisme qui, rompant avec la domination traditionnelle du collectif, sert de fil conducteur omni-interprétatif. Ces lectures (...) ont pour point commun de rendre la modernité homogène, assimilée au 'tout-sujet' ou au 'tout-individu'. Et surtout, elles occultent la césure qui brise l'histoire du sujet moderne en infléchissant l'humanisme vers l'une de ses figures possible, problématique et évanouissante - l'individualisme. L'archéologie de cet énigmatique déplacement conduit Alain Renaut jusqu'à Leibniz. Là s'est décidée une profonde mutation - l'affirmation de l'individualité devient soudain compatible, au prix d'un dispositif intellectuel inédit, avec celle d'une rationalité du réel. Une culture de l'indépendance où chaque être, ne se souciant que d'accomplir sa nature, contribue à manifester l'ordre du monde, se greffe sur la valorisation de la raison. Ainsi débarrassée des fausses linéarités, la logique de la modernité apparaît sous un jour neuf - loin d'avoir sans cesse consolidé le pouvoir de la subjectivité, elle a été aussi le lieu de son éclipse... (shrink)