There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski :891–939, 1951; 74:127–162, 1952). Another one The infinity project proceeding, Barcelona, 2012) comes from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as its main precursor. By a classical fact of general topology, the space of ultrafilters over a discrete space is (...) its largest compactification. The main result of Saveliev The infinity project proceeding, Barcelona, 2012), which confirms a canonicity of this extension, generalizes this fact to discrete spaces endowed with an arbitrary first-order structure. An analogous result for the former type of ultrafilter extensions was obtained in Saveliev. Results of such kind are referred to as extension theorems. After a brief introduction, we offer a uniform approach to both types of extensions based on the idea to extend the extension procedure itself. We propose a generalization of the standard concept of first-order interpretations in which functional and relational symbols are interpreted rather by ultrafilters over sets of functions and relations than by functions and relations themselves, and define ultrafilter models with an appropriate semantics for them. We provide two specific operations which turn ultrafilter models into ordinary models, establish necessary and sufficient conditions under which the latter are the two canonical ultrafilter extensions of some ordinary models, and obtain a topological characterization of ultrafilter models. We generalize a restricted version of the extension theorem to ultrafilter models. To formulate the full version, we propose a wider concept of ultrafilter models with their semantics based on limits of ultrafilters, and show that the former concept can be identified, in a certain way, with a particular case of the latter; moreover, the new concept absorbs the ordinary concept of models. We provide two more specific operations which turn ultrafilter models in the narrow sense into ones in the wide sense, and establish necessary and sufficient conditions under which ultrafilter models in the wide sense are the images of ones in the narrow sense under these operations, and also are two canonical ultrafilter extensions of some ordinary models. Finally, we establish three full versions of the extension theorem for ultrafilter models in the wide sense. The results of the first three sections of this paper were partially announced in Poliakov and Saveliev On two concepts of ultrafilter extensions of first-order models and their generalizations, Springer, Berlin, 2017). (shrink)

L'Auteur dégage et expose d'abord le modèle explicite proposé par Hobbes pour l'analyse des phénomènes sémioti- que, puis le contexte dans lequel ce modèle est élaboré, tout en montrant en quoi cette analyse peut encore intéresser les philosophes du langage contemporains. Il met ensuite en évi- dence les diverses perspectives empruntées par Hobbes dans son analyse, formule les principes sur lesquels elles reposent et décèle les problèmes de cohérence qui en résultent. Il propose enfin une interprétation qui permet de lever (...) certaines contradictions apparentes rencontrées dans l'analyse du mo- dèle proposé par Hobbes en réexaminant le contexte initial de cette analyse et les catégories ontologiques fondamentales qu'elle met en cause.The Author extricates and exposes at first the explicit model proposed by Hobbes to analyse semiotical phenomena, and the context in which this model is developped, showing by the way how this model, in many respects, might still be interesting for contemporary philosophers of language. Then, he reconstructs the approaches adopted by Hobbes, formulates the basic principles on which they rest, and identifies some problems of coherence resulting from the whole approach. He proposes, at last, an interpretation which enables us to solve some apparent contradictions met in the analysis of the model proposed by Hobbes by exploring anew the initial context of this model and the basic ontological categories which are implicated in Hobbes' semiotical analysis. (shrink)

Konstantin Leont'ev is one of those Russian thinkers about whom much has been said and written both in Russia and abroad. Interest in his works has increased steadily in the past five years: collections of his works are being published, special conferences are being held, and articles and monographs are being written. In the process it turns out that a thinker who died a hundred years ago is perceived in Russia as "our contemporary," as a clairvoyant and a prophet, but (...) also in large measure as a teacher to whom many are inclined to turn in their searches for intellectual world-view and ideological orientations. (shrink)

We are now, after some delay, beginning actively to discuss a theme—or is it still a problem?—that has become traditional for Western sociology and political science—namely, totalitarianism. If we start from the firmly established view that construes totalitarianism as a social structure in which the state devours and exercises maximum control over all spheres of the social life of individuals, i.e., a structure based on maximum coercion , we can, it would seem, simply make concrete extrapolations of the existing theoretical (...) model to the countries and regions we have chosen to study. But it seems to me that there are still a number of not fully worked out aspects in the methodology employed to study totalitarianism, and in applied studies this leads either to a pan-totalitarian view of history or to the localization of totalitarianism in a few countries . I think that this situation cannot be "harmonized" in the traditional manner by distinguishing between a "broad" and a "narrow" meaning of the term ‘totalitarianism.’ Hence, rather than trying to "not notice" the methodological problem, I propose dealing with it in all theoretical seriousness. (shrink)

La presente traducción fue realizada del original “Die Menschheit ist biblisch”, publicado en _Jüdisches Denken in Frankreich. Gespräche mit Pierre Vidal-Naquet, Jacques Derrida, Rita Thalmann, Emmanuel Lévinas, Léon Poliakov, Jean-François Lyotard, Luc Rosenzweig_ por Jüdischer Verlag. Frankfurt am Main en 1994, páginas 117-131. Agradezco a la profesora Elisabeth Weber, editora y traductora de la obra, por la autorización para publicar esta traducción. Asimismo agradezco a Sara Bertschik por sus agudos comentarios. Esta traducción fue realizada en el marco del proyecto (...) Fondecyt n. 1160479 ID 150811071. (shrink)

Ce texte a été présenté lors de la journée d'études « Diderot – théâtre & philosophie », organisée, à l'occasion du tricentenaire de sa naissance, le 28 mars 2013 au Lycée Claude Monet (Paris 13e), par Stéphane Poliakov. Avant de commencer à vous parler de Diderot, je voudrais vous dire quelques mots concernant la notion de rythme et expliquer, au moins en partie, le titre de mon intervention. Le mot rythme vient du grec rhuthmos. Or, avant que Platon ne (...) lui donne le sens de kineseos taxis, d'« ordre (...) - Philosophie – Nouvel article. (shrink)

Denjenigen, die mit der im Titel angesprochenen Thematik und Problematik auch nur halbwegs vertraut sind, fällt in der Regel sofort das Verdikt Fichtes über das Judentum aus dem Beitrag zur Berichtigung der Urtheile des Publicums über die französische Revolution von 1793 ein. Es gilt als eines der frühesten Dokumente eines Übergangs vom religiösen Antijudaismus zum politischen Antisemitismus avant la lettre. Nimmt man nun noch die Tatsache hinzu, daß derselbe Philosoph nach verbreitetem Verständnis mit seinen Reden an die deutsche Nation von (...) 1807/8 auch als einer der frühesten Begründer des Nationalismus in Deutschland gilt, so sehen viele Interpreten den weiteren Weg, der schließlich im chauvinistschen Rassenantisemitismus der NS-Zeit endete, geradezu zwanghaft vorgezeichnet. Ein Beispiel für viele andere, die man in der Einleitung meines Buches Fichtes Idee der Nation und das Judentum, das im Oktober 2000 bei Rodopi/amsterdam erschienen ist, zu Hauf finden kann, ist Léon Poliakov: Im 5. Band seiner großen Antisemitismusstudie versteigt er sich zu einer Aussage wie: Fichtes »nationalsozialistische Ausleger hatten es nicht nötig, diese Texte [= der Reden an die deutsche Nation] allzu sehr umzubilden, um den Nachweis erbringen zu können, daß er der erste Prophet der nationalsozialistischen Gottgläubigkeit und des ›arischen Glaubens‹, jenen Eckpfeilern der nebulösen Metaphysik Hitlers gewesen ist.« Nebenbei gesagt: Weder diese beiden Begriffe, noch was immer sie bezeichnen mögen, kommen auch nur entfernt bei Fichte vor, aber das hat weder Poliakov noch andere Fichte-Kritiker, die im Tenor ähnlich geurteilt haben, je gestört. (shrink)

Denjenigen, die mit der im Titel angesprochenen Thematik und Problematik auch nur halbwegs vertraut sind, fällt in der Regel sofort das Verdikt Fichtes über das Judentum aus dem Beitrag zur Berichtigung der Urtheile des Publicums über die französische Revolution von 1793 ein. Es gilt als eines der frühesten Dokumente eines Übergangs vom religiösen Antijudaismus zum politischen Antisemitismus avant la lettre. Nimmt man nun noch die Tatsache hinzu, daß derselbe Philosoph nach verbreitetem Verständnis mit seinen Reden an die deutsche Nation von (...) 1807/8 auch als einer der frühesten Begründer des Nationalismus in Deutschland gilt, so sehen viele Interpreten den weiteren Weg, der schließlich im chauvinistschen Rassenantisemitismus der NS-Zeit endete, geradezu zwanghaft vorgezeichnet. Ein Beispiel für viele andere, die man in der Einleitung meines Buches Fichtes Idee der Nation und das Judentum, das im Oktober 2000 bei Rodopi/amsterdam erschienen ist, zu Hauf finden kann, ist Léon Poliakov: Im 5. Band seiner großen Antisemitismusstudie versteigt er sich zu einer Aussage wie: Fichtes »nationalsozialistische Ausleger hatten es nicht nötig, diese Texte [= der Reden an die deutsche Nation] allzu sehr umzubilden, um den Nachweis erbringen zu können, daß er der erste Prophet der nationalsozialistischen Gottgläubigkeit und des ›arischen Glaubens‹, jenen Eckpfeilern der nebulösen Metaphysik Hitlers gewesen ist.« Nebenbei gesagt: Weder diese beiden Begriffe, noch was immer sie bezeichnen mögen, kommen auch nur entfernt bei Fichte vor, aber das hat weder Poliakov noch andere Fichte-Kritiker, die im Tenor ähnlich geurteilt haben, je gestört. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:An I for an I: Projection, Subjection, and Christian Antisemitism in The Service for RepresentingAdam1 Richard J. Prystowsky Irvine Valley College You know well enough how to look in a mirror: Now look at this hand for me, and tell If my heart is sick or healthy. The Servicefor Representing Adam Far from experience producing his idea of the Jew, it was the latter which explained his experience. If (...) the Jew did not exist, the anti-Semite would invent him. Jean-Paul Sartre, Anti-Semite and Jew These wretched Jews, my own kindred, /... have more to be unhappy about than other peoples. The Holy Resurrection No modern theorist has done more to help us understand the nature of inter- and intra-personal and communal violence than has René Girard. Perhaps his most important insight into the workings of such violence, an insight grounding his other provocative discoveries concerning human conflict, is that the antagonistic participants in acts ofinter- and intra-personal and communal violence are "doubles" of each other. By demonstrating that 1 In their hyphenated forms, the terms "anti-Semite," "anti-Semitism," and "anti-Semitic" have sometimes proved more problematic than helpful. In order to avoid "fosterfing] the false impression that there is a wider ethnic entity against which 'anti-Semitism' is leveled" (Telushkin 467), and in light of the importance of the concept of antisemitism to the history of Jewhating, throughout this essay I follow the lead of those scholars who do not hyphenate the words "antisemite," "antisemitism," or "antisemitic." For more information concerning this issue, see Telushkin. 140Richard J. Prystowsky people fight not because they are different, but because they are the same, Girard has shown us how "violence is a great leveler of men" and has helped us to understand the serious consequences that either follow or can follow from mimetic rivalry (Violence 79). For example, he has helped us see how the internal violence occurring in a community in which differentiation has broken down finds its outlet in scapegoating, that mechanism by means of which a community in conflict with itself attempts to save itselfby sacrificing an expendable, arbitrary victim (who lacks a champion but whose real guilt or innocence is irrelevant) onto whom the collective victimizers have projected their own guilt, their own mimetically-oriented self-hatred—their own "sins," we might say. Among other things, Girard's critique of the mimetic rivalry characteristic of what we might call "the conflicted communal Self" also sheds light on the nature of the violence and victimization that we find in the history of Christian persecution of Jews. Without referring to Girard's ideas, the eminent historian Léon Poliakov nevertheless captures a Girardian view of this tragic history when he writes that "to massacre first, and then, from fear of revenge, to accuse afterward; to attribute to the victims one's own aggressive intentions; to impute to them one's own cruelty: from country to country and from century to century, under various disguises, this is the device we find" (106-7). In the present essay, I will attempt to show that such vengeance-laden acts of Christian persecution of Jews, of the Jew-as-Other, derive from antisemitic Christians' mimetic rivalry with Jews—an "I" for an "I," as this essay's title would suggest—and that underlying this rivalry is the introjection ofreal or imagined Jewish self-hatred.2 1 hope to demonstrate that this projected intra-victimization is marked, in part, by Christians' mimetic appropriations of fantasized or real acts of Jewish self-incrimination, punishment, or more generalized suffering. Ultimately, I will try to provide support for the idea that, despite its obvious promise and appeal of love, peace, and brotherhood, Christianity cannot wrest itself entirely from its moorings in real or fantasized Jewish self-hatred, that is, in an appropriation of enacted or imagined Judaism against itself. If my contentions prove even partially legitimate, then an overwhelming question for good-faith Christians is whether or not the peculiar brand of antisemitism discussed above is endemic to Christianity and, if it is, whether 2Sander L. Oilman's Jewish Self-Hatredremains the preeminent work on the relationship between Jewish self-hatred and antisemitism. Among... (shrink)