The theories of apartness, equality, and n-stable equality are presented through contraction- and cut-free sequent calculi. By methods of proof analysis, a purely proof-theoretic characterization of the equality fragment of apartness is obtained.

The theories of apartness, equality, and n-stable equality are presented through contraction- and cut-free sequent calculi. By methods of proof analysis, a purely proof-theoretic characterization of the equality fragment of apartness is obtained.

Résumé Ce texte est une réponse de Toni Negri à trois objections proposées par Pierre Macherey à la notion de « multitude », telle que la développe le second livre de Hardt-Negri. L’auteur précise d’abord que l’importance mise sur les nouveautés du travail immatériel ne nie nullement l’inertie, voire l’exacerbation, des rapports d’exploitation, soulignés à juste titre par la pensée critique. Il invite ensuite à considérer la communication, non comme un principe de circulation vide, mais comme un terrain, (...) effectif et efficace, de constitution matérialiste de la singularité productive. Enfin, il reconnaît que la transformation de la multitude de chair en corps n’a aucune solution magique à proposer aux dilemmes politiques, mais a bien plutôt le statut d’une question ouverte. Avec pour premier élément de réponse un principe directeur : la multitude n’a pas pour ambition de prendre le pouvoir, mais de gérer le commun. (shrink)

Résumé Aujourd’hui, la démocratie ne se trouve plus seulement devant (et contre) la rente absolue, terrienne (foncière et immobilière) : elle doit surtout affronter la rente financière, le capital que l’argent mobilise de manière globale comme instrument fondamental de la governance des multitudes. La financiarisation est la forme actuelle du commandement capitaliste. Bien évidemment, celle-ci est encore liée à la rente, et elle en répète l’intentionnalité violente — tout comme elle reprend les ambiguïtés et les contradictions de n’importe quelle figure (...) de l’exploitation capitaliste. Il serait donc stupide de penser que le capital financier ne représente pas en lui-même un moment antagoniste — car il comprend toujours en son sein cet élément nécessaire qu’est la force de travail, et qui est à la fois un producteur de capital et une menace pour celui-ci. (shrink)

With Empire, Michael Hardt and Antonio Negri reinvigorated debates in political theory and radical philosophy about the cultivation of revolutionary subjectivity. Their theorization of Empire and multitude has also significantly affected the tenor of critical approaches to educational theory during the past two decades. In this article, we discuss Hardt and Negri’s contribution to what we call the biopolitical turn in educational theory, emphasizing the influence of autonomist Marxism on their work. Even more specifically, we discuss the impact (...) of the autonomist tradition on their formulation of the nature of the relationship between the multitude and Empire: that the multitude is the generative force of the social world, whereas Empire is merely an apparatus of capture. This autonomist approach reveals a set of questions regarding subjectivity, materialism, and social ontology, which we argue are ripe for engagement by educational theorists, and indicate the enduring relevance of Empire as a valuable text for educational theorists interested in matters of biopolitical production, collective opposition, and revolutionary subjectivity. (shrink)

This article examines the productive capacity of emotion through the concept of emotional fundamentalism. Emotional fundamentalism combines several key concepts—fundamentalism, affective labor, biopolitics, and capitalism’s contradictions—developed by Michael Hardt and Antonio Negri in Empire, Multitude, and Commonwealth to describe the intensified attention to the body in education. I investigate the implications of the increased organizational and corporate interest in emotion using an ongoing socio-emotional learning study and the introduction of artificial intelligence aggression detectors in schools. Doing so demonstrates the (...) tendency of Empire to manage emotions in order to ensure viable production by educating the body as data and human capital. However, though Empire depends on emotions as a resource, these same emotions display a creative unruliness that exposes potential avenues to reproduce the common and enact multitude. (shrink)

This article focuses upon monstrously generous teaching styles, enacted in neocolonial educational contexts, where the interactions between students and teachers are sometimes tense and mistrustful. The tensions between students and teachers are explained by discussing the ways in which schools—in the theoretical perspective of Roberto Esposito—operate to immunize the society against youth deemed improper. Utilizing the theories of Antonio Negri, James Baldwin, and W.E.B. Du Bois, the characterization of students as monstrous is discussed and an inversion is suggested, whereby (...) students deemed to be monstrous are considered the source of reinvigorating visions of society. The pedagogical approaches of teachers who seek to welcome and nurture monstrous students are described, relying upon the accounts of great teachers offered by educators and sociologists. In practice, monstrously generous teachers make supererogatory gestures in their interactions with students, as a way of signaling to heavily-armored youth that they are willing to enter reciprocal relationships with them. Once youth drop their armor and begin to share their perspectives, monstrously generous teachers develop multiple means of helping youth develop their worldviews, without surveillance or censor. (shrink)

El artículo se propone abordar el concepto de multitud tal y como ha sido elaborado por el filósofo italiano Antonio Negri, incluyendo los trabajos escritos con Michael Hardt. El texto reconstruye la oposición del concepto de multitud al de pueblo, central en el pensamiento y en las instituciones políticas modernas; y la diferencia entre el concepto de multitud y el de clase obrera moderna, del que va más allá. Finalmente se hará hincapié en el pasaje del ser al hacer (...) multitud. (shrink)

_Factory of Strategy_ is the last of Antonio Negri's major political works to be translated into English. Rigorous and accessible, it is both a systematic inquiry into the development of Lenin's thought and an encapsulation of a critical shift in Negri's theoretical trajectory. Lenin is the only prominent politician of the modern era to seriously question the "withering away" and "extinction" of the state, and like Marx, he recognized the link between capitalism and modern sovereignty and the need (...) to destroy capitalism and reconfigure the state. Negri refrains from portraying Lenin as a ferocious dictator enforcing the proletariat's reappropriation of wealth, nor does he depict him as a mere military tool of a vanguard opposed to the Ancien Régime. Negri instead champions Leninism's ability to adapt to different working-class configurations in Russia, China, Latin America, and elsewhere. He argues that Lenin developed a new political figuration in and beyond modernity and an effective organization capable of absorbing different historical conditions. He ultimately urges readers to recognize the universal application of Leninism today and its potential to institutionally--not anarchically--dismantle centralized power. (shrink)

Large portions of mathematics such as algebra and geometry can be formalized using first-order axiomatizations. In many cases it is even possible to use a very well-behaved class of first-order axioms, namely, what are called coherent or geometric implications. Such class of axioms can be translated to inference rules that can be added to a sequent calculus while preserving its structural properties. In this work, this fundamental result is extended to their infinitary generalizations as extensions of sequent calculi for both (...) classical and intuitionistic infinitary logic. As an application, a simple proof of the infinitary Barr’s theorem without the axioms of choice is shown. (shrink)

Antonio Negri, one of the world's leading scholars on Baruch Spinoza (1632-1677) and his contemporary legacy, offers a straightforward explanation of the philosopher's elaborate arguments and a persuasive case for his ongoing relevance. Responding to a resurgent interest in Spinoza's thought and its potential application to contemporary global issues, Negri demonstrates the thinker's special value to politics, philosophy, and related disciplines. Negri's work is both a return to and an advancement of his initial affirmation of Spinozian thought (...) in _The Savage Anomaly_. He further defends his understanding of the philosopher as a proto-postmodernist, or a thinker who is just now, with the advent of the postmodern, becoming contemporary. Negri also connects Spinoza's theories to recent trends in political philosophy, particularly the reengagement with Carl Schmitt's "political theology," and the history of philosophy, including the argument that Spinoza belongs to a "radical enlightenment." By positioning Spinoza as a contemporary revolutionary intellectual, Negri addresses and effectively defeats twentieth-century critiques of the thinker waged by Jacques Derrida, Alain Badiou, and Giorgio Agamben. (shrink)

In Subversive Spinoza , Antonio Negri spells out the philosophical credo that inspired his radical renewal of Marxism and his compelling analysis of the modern state and the global economy by means of an inspiring reading of the challenging metaphysics of the seventeenth-century Dutch-Jewish philosopher Spinoza. For Negri, Spinoza's philosophy has never been more relevant than it is today to debates over individuality and community, democracy and resistance, modernity and postmodernity.

Philosophe et penseur du politique, intellectuel marxiste et militant communiste, enseignant, directeur de collection... : à travers le rayonnement de son oeuvre et de sa personne, Louis Althusser a renouvelé la théorie politique et la philosophie de l'histoire, de Machiavel à Marx. Parmi ses contemporains, Michel Foucault exhorte : " Ouvrez les livres d'Althusser! ", Jacques Derrida évoque " la force rayonnante et provocante de sa pensée ", Gilles Deleuze salue l'" Althusser's Band ", et pour Roland Barthes, " le (...) seul modèle acceptable de la science est celui mis au jour par les études d'Althusser sur Marx ". Aliocha Wald Lasowski converse avec vingt écrivains et philosophes qui ont lu, rencontré, parfois travaillé avec Althusser, quand ils n'ont pas fait partie de ses proches. Où l'on mesure à quel point la pensée d'Althusser demeure d'une actualité brûlante. (shrink)

By providing an interdisciplinary reading of advance directives regulation in international, European and domestic law, this book offers new insights into the most controversial legal issues surrounding the debate over dignity and autonomy ...

Das Buch bietet die erste kritische Edition der Artikel XXV-XXVII der Summa (Quaestiones ordinariae) des Heinrich von Gent. Dabei leistet es einen Beitrag zur Geschichte der Formen und Pfade der Ideenvermittlung im Mittelalter und zur mittelalterlichen Buchkultur. Die Kollationierung der Handschriften der Artikel XXV-XXVII und die Untersuchung ihrer materiellen Überlieferung haben der Editorin erlaubt, den Prozess der Ausarbeitung, Publikation und Verbreitung einer Portion von Heinrichs Summa über einen längeren Zeitraum in großer Detailgenauigkeit zu rekonstruieren. Die hier edierten Artikel enthalten ein (...) Kernstück von Heinrichs theologischem und metaphysischem System. In der Behandlung von Einheit, Natur und Leben Gottes entfalten sie eine rationale Darstellung des ersten Prinzips. (shrink)

Discusses how cultural and economic changes around the world have caused a shift in the concepts that shape modern politics and defined the new global order.

Comprende tres obras, distintas en su estructura, pero coincidentes en el significado que atribuyen al Derecho y a sus relaciones con el poder.

Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...) explanation of the rules. (shrink)

Negri, a leading Marxist philosopher, has inspired anti-empire movements around the world through his writings and personal example. This work, which began as a conversation between Negri and literary critic Casarino, is the most complete review of the philosopher's work.

That every first-order theory has a coherent conservative extension is regarded by some as obvious, even trivial, and by others as not at all obvious, but instead remarkable and valuable; the result is in any case neither sufficiently well-known nor easily found in the literature. Various approaches to the result are presented and discussed in detail, including one inspired by a problem in the proof theory of intermediate logics that led us to the proof of the present paper. It can (...) be seen as a modification of Skolem’s argument from 1920 for his “Normal Form” theorem. “Geometric” being the infinitary version of “coherent”, it is further shown that every infinitary first-order theory, suitably restricted, has a geometric conservative extension, hence the title. The results are applied to simplify methods used in reasoning in and about modal and intermediate logics. We include also a new algorithm to generate special coherent implications from an axiom, designed to preserve the structure of formulae with relatively little use of normal forms. (shrink)

Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic (...) to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated. (shrink)

Various sources in the literature claim that the deduction theorem does not hold for normal modal or epistemic logic, whereas others present versions of the deduction theorem for several normal modal systems. It is shown here that the apparent problem arises from an objectionable notion of derivability from assumptions in an axiomatic system. When a traditional Hilbert-type system of axiomatic logic is generalized into a system for derivations from assumptions, the necessitation rule has to be modified in a way that (...) restricts its use to cases in which the premiss does not depend on assumptions. This restriction is entirely analogous to the restriction of the rule of universal generalization of first-order logic. A necessitation rule with this restriction permits a proof of the deduction theorem in its usual formulation. Other suggestions presented in the literature to deal with the problem are reviewed, and the present solution is argued to be preferable to the other alternatives. A contraction-and cut-free sequent calculus equivalent to the Hubert system for basic modal logic shows the standard failure argument untenable by proving the underivability of DA from A. (shrink)

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...) following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (shrink)

In this article, we begin from the assertion that global war does not affirm itself as an imperial ordering power without `opacifying' every regulative idea of peace, which is thereby reduced to the status of a deceptive illusion. `Postmodern' peace, which is absolutely contemporaneous with war, is deduced from war in the guise of the `post-democratic' institution of a permanent state of exception, of a continuation of war by other means, and of a reduction of sovereignty to the imbalance of (...) terror, in accordance with the principle of distinction that opposes friend and enemy. Once war, peace and barbarism interact with no rule other than the common sense of the unworldly squalor, only Combat against War can destroy the sensorial evidence of a false social peace and open on to the construction of a World that is once again possible for the singularities that we are in common. Whence derives the character of social threat that marks out contemporary art when it focuses on the mediatic world-image by putting to work a new transversalist aesthetic paradigm, exposing itself to the tearing asunder of the sensible in the over-exposition of peace to war. This could be art's new address, tracing its difference in a creative machination of affects that can no longer find support in any remembrance of the being of peace. (shrink)

A constructivisation of the cut-elimination proof for sequent calculi for classical, intuitionistic and minimal infinitary logics with geometric rules—given in earlier work by the second author—is presented. This is achieved through a procedure where the non-constructive transfinite induction on the commutative sum of ordinals is replaced by two instances of Brouwer’s Bar Induction. The proof of admissibility of the structural rules is made ordinal-free by introducing a new well-founded relation based on a notion of embeddability of derivations. Additionally, conservativity for (...) classical over intuitionistic/minimal logic for the seven (finitary) Glivenko sequent classes is here shown to hold also for the corresponding infinitary classes. (shrink)