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)

Alain Badiou is arguably the most significant philosopher in Europe today. Badiou’s seminars, given annually on major conceptual and historical topics, constitute an enormously important part of his work. They served as laboratories for his thought and public illuminations of his complex ideas yet remain little known. This book, the transcript of Badiou’s year-long seminar on the psychoanalytic theory of Jacques Lacan, is the first volume of his seminars to be published in English, opening up a new and vital (...) aspect of his thinking. In a highly original and compelling account of Lacan’s theory and therapeutic practice, Badiou considers the challenge that Lacan poses to fundamental philosophical topics such as being, the subject, and truth. Badiou argues that Lacan is a singular figure of the “anti-philosopher,” a series of thinkers stretching back to Saint Paul and including Kierkegaard and Nietzsche, with Lacan as the last great anti-philosopher of modernity. The book offers a forceful reading of an enigmatic yet foundational thinker and sheds light on the crucial role that Lacan plays in Badiou’s own thought. This seminar, more accessible than some of Badiou’s more difficult works, will be profoundly valuable for the many readers across academic disciplines, art and literature, and political activism who find his thought essential. (shrink)

Published in 1973, "L'Etourdit" was one of the French philosopher Jacques Lacan's most important works. The book posed questions that traversed the entire body of Lacan's psychoanalytical explorations, including his famous idea that "there is no such thing as a sexual relationship," which seeks to undermine our certainties about intimacy and reality. In There's No Such Thing as a Sexual Relationship, Alain Badiou and Barbara Cassin take possession of Lacan's short text, thinking "with" Lacan about his propositions and what (...) kinds of questions they raise in relation to knowledge. Cassin considers the relationship of the real to language through a Sophist lens, while the Platonist Badiou unpacks philosophical claims about truth. Each of their contributions echoes back to one another, offering new ways of thinking about Lacan, his seminal ideas, and his role in advancing philosophical thought. (shrink)

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)

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.

Martin Heidegger was an ordinary Nazi and a loyal member of the provincial petty bourgeoisie. He was also a seminal thinker of the Continental tradition and one of the twentieth century's most important philosophers. How are we to make sense of this dual life? Should we factor Heidegger's domestic and political associations into our understanding of his thought, or should we treat his intellectual work independently of his abhorrent politics? How does any thinker reconcile the mundane with the ideal or (...) the pursuit of philosophical inquiry with the demands of civic engagement? In Heidegger, Alain Badiou and Barbara Cassin immerse themselves in the philosopher's correspondence with his wife Elfride to answer these questions as they relate to Heidegger and all thinkers vulnerable to the politics of their times. They focus on Heidegger's tormented relationship with his wife, with Hannah Arendt, and with numerous other women, bringing an unusual level of intimacy to his personal and intellectual worlds. (shrink)

L'oeuvre d'Alain Boureau, multiple et dense, se deploie sur les quarante dernieres annees en abordant de nombreux domaines de l'histoire du Moyen Age et du christianisme latin. Elle suit les peregrinations personnelles et professionnelles d'un chercheur a travers un monde peuple de silhouettes incertaines : figures de l'hagiographie, faux-semblants de l'Etat moderne, anges, demons, cadavres et somnambules, vagues individus scolastiques qui eux-memes parlent de creatures etranges. Autant de fantomes d'un passe persistant qu'il a suivis avec tenacite tout au long (...) de sa carriere, et qui nous embarquent a leur tour a travers l'histoire. Ce volume entend garder la trace vivante des deux journees qui furent organisees a Paris en mai 2015 autour de l'oeuvre d'Alain Boureau. Ce Liber amicorum d'un genre un peu particulier, production scolastique en quelque sorte, donne a voir les membres d'un studium, ce qu'etait le seminaire d'Alain Boureau : les amis, les collegues, les proches, celles et ceux qui l'ont accompagne au cours de ses annees passees a l'EHESS. Les textes rassembles rendent compte de trajectoires et de realisations, ils en montrent les apports scientifiques et les enjeux intellectuels. Ils racontent, aussi. Ainsi se manifeste la richesse d'une oeuvre singuliere, construite aux croisements de differentes pratiques des sciences sociales dans une demarche souvent collective, toujours originale et novatrice. (shrink)

Rethinking the terms we use to define a people.

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)

The sociology of knowledge is faced with a problem of historical temporality that it has carefully avoided up until now. The subject has been avoided or ignored because a discussion of it in depth would run the risk of questioning all modern scientific thought. The problem is that of the concept of absolute time as it is used in evolutionist theory. In this category of theory I include not only social evolutionism, abused for a long time and recently reanimated by (...) the “socio-biologists,” but also biological, paleontological, geological and other types of evolutionism, that is, those qualified as “scientific.”. (shrink)

A leading historian opens up a new terrain for understanding the past: the history of ignorance.

Quels enseignements tirer de la crise pandémique mondiale de 2020? La violence extrême du risque sanitaire nous a évidemment rappelé que nous étions mortels - quels que soient nos systèmes de santé. Mais au-delà, ce sont nos équilibres sociaux, éthiques, économiques ou politiques qui ont été remis en cause. Comment justifier éthiquement le tri des patients? Quelles décisions politiques prendre au moment où la protection de la santé est mise en rivalité avec la nécessité de soutenir une activité économique également (...) vitale? La mondialisation est-elle responsable de nos vulnérabilités? Autant de questions épineuses abordées dans cet essai, qui revendique la pertinence d'une approche philosophique de terrain, loin d'une réflexion abstraite sur la fragilité écologique ou d'une critique convenue de nos systèmes mondialisés. Si le risque incite au repli sur soi, l'enjeu est ici de comprendre que la résilience ne passera que par une plus grande solidarité internationale et une redéfinition de la souveraineté."--Page 4 of cover. (shrink)