Résumé À partir d’expériences concrètes, les auteurs montrent les dimensions politiques des démarches micro-urbaines et d’une reconstruction de l’espace de proximité à partir des marges, des bords et des interstices de la ville capitaliste. Ces interventions permettent la constitution d’une subjectivité collective et synaptique capable d’appropriations territoriales poreuses et de transformations politiques à partir du quotidien. Une démocratisation continue de l’espace de proximité par « agencement jardinier », un agir interstitiel et biopolitique « en bas de chez soi ».

This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim (...) is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians. (shrink)

Constituent power : the concept of a crisis -- Virtue and fortune : the machiavellian paradigm -- The Atlantic model and the theory of counterpower -- Political emancipation in the American constitution -- The revolution and the constitution of labor -- Communist desire and the dialectic restored -- The constitution of strength.

A general method for generating contraction- and cut-free sequent calculi for a large family of normal modal logics is presented. The method covers all modal logics characterized by Kripke frames determined by universal or geometric properties and it can be extended to treat also Gödel-Löb provability logic. The calculi provide direct decision methods through terminating proof search. Syntactic proofs of modal undefinability results are obtained in the form of conservativity theorems.

A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. A comparison to natural deduction is given through translation of derivations between the two systems. It is proved that if a cut formula is never principal in a derivation leading to the right premiss of cut, it is a subformula of the conclusion. Therefore (...) it is sufficient to eliminate those cuts that correspond to detour and permutation conversions in natural deduction. (shrink)

A philosopher and political thinker describes a new political grammar free of modernist assumptions. In 2004 and 2005, Antonio Negri held ten workshops at the Collège International de Philosophie in Paris to formulate a new political grammar of the postmodern. Biopolitics, biopowers, control, the multitude, people, war, borders, dependency and interdependency, state, nation, the common, difference, resistance, subjective rights, revolution, freedom, democracy: these are just a few of the themes Negri addressed in these experimental laboratories. Postmodernity, Negri (...) suggests, can be described as a “porcelain factory”: a delicate and fragile construction that could be destroyed through one clumsy act. Looking across twentieth century history, Negri warns that our inability to anticipate future developments has already placed coming generations in serious jeopardy. Describing the years 1917-1968 as the “short century,” Negri suggests that by the end of it, all of the familiar markers of modernity had lost their relevance. Confronted with an intolerable reality, indignation and the revolutionary will to transform the world have both taken new forms and must be understood anew, free of modernist assumptions. In the impassioned debates recounted in this book, Antonio Negri attempts to describe the formation of an alternative political horizon and looks for a way to define the practices and modes of expression that democracy could take.Antonio Negri is a philosopher and essay writer. A political and social activist in the 1960s and 1970s in Italy, he taught political sciences for many years and has written numerous books on political philosophy including Marx beyond Marx, The Savage Anomaly, Insurgencies ; and in collaboration with Michael Hardt, Empire and Multitude. (shrink)

This the first of a new three-part series in which Antonio Negri, a leading political thinker of our time, explores key ideas that have animated radical thought and examines some of the social and economic forces that are shaping our world today. In this first volume Negri shows how the thinking of Marx and Foucault were brought together to create an original theoretical synthesis - particularly in the context of Italy from May ’68 onwards. At around that time, (...) the structures of industry and production began to change radically, with the emergence of new producer-subjects and new fields of capitalist value creation. New concepts and theories were developed by Foucault, Deleuze and Guattari and others to help make sense of these and related developments - concepts such as biopower and biopolitics, subjectivation and subsumption, public and common, power and potentiality. These concepts and theories are examined by Negri within the broader context of the development of European philosophical discourse in the twentieth century. Marx and Foucault provides a unique account of the development of radical thought in the late 20th and early 21st centuries and will be a key text for anyone interested in radical politics today. (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)

A way is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also the rules of weakening and contraction can be eliminated. Applications include a system of predicate logic (...) with equality in which also cuts on the equality axioms are eliminated. (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.

A way is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also the rules of weakening and contraction can be eliminated. Applications include a system of predicate logic (...) with equality in which also cuts on the equality axioms are eliminated. (shrink)

The main result of this paper is a normalizing system of natural deduction for the full language of intuitionistic linear logic. No explicit weakening or contraction rules for -formulas are needed. By the systematic use of general elimination rules a correspondence between normal derivations and cut-free derivations in sequent calculus is obtained. Normalization and the subformula property for normal derivations follow through translation to sequent calculus and cut-elimination.

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)

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.

A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined.

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)

Nine letters on art, written to friends from exile in France in the 1980s. Starting from earlier materialist approaches to art, Negri relates artistic production to the structures of social production characteristic of each historical era. This enables him to define the nature of both material and artistic production in the era of post-modernity and post-Fordism - the era Negri characterizes as that of immaterial labour. Negri then seeks to define artistic beauty in this new era, and (...) this he does in terms of concepts that have become fundamental to his thinking - singularity, multitude, abstraction, collective work, event, the biopolitical, the common. Art is living labour, and therefore invention of singularity, of singular figures and objects. But this expressive act only achieves beauty when the signs and language through which it expresses itself turn themselves into community, when they are contained within a common project. The beautiful is not the act of imagining, but an imagination that has become action. Art, in this sense, is multitude. (shrink)

Dos ideas fundamentales están la base de Imperio, el libro que he escrito a cuatro manos con Michael Hardt, entre la guerra del Golfo y la de Kosovo. La primera es que no existe un mercado global (en la forma en que se habla desde la caída del Muro de Berlín, es decir, no solamente como paradigma macro-económico sino como categoría política) sin forma de estructura jurídica, y que el orden jurídico no puede existir sin un-poder que garantice su eficacia. (...) La segunda es que el orden jurídico de.. (shrink)

A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. A comparison to natural deduction is given through translation of derivations between the two systems. It is proved that if a cut formula is never principal in a derivation leading to the right premiss of cut, it is a subformula of the conclusion. Therefore (...) it is sufficient to eliminate those cuts that correspond to detour and permutation conversions in natural deduction. (shrink)

Geometric theories are presented as contraction- and cut-free systems of sequent calculi with mathematical rules following a prescribed rule-scheme that extends the scheme given in Negri and von Plato. Examples include cut-free calculi for Robinson arithmetic and real closed fields. As an immediate consequence of cut elimination, it is shown that if a geometric implication is classically derivable from a geometric theory then it is intuitionistically derivable.

In a recent paper, Negri and Pavlović (Studia Logica 1–35, 2020) have formulated a decidable sequent calculus for the logic of agency, specifically for a deliberative see-to-it-that modality, or dstit. In that paper the adequacy of the system is demonstrated by showing the derivability of the axiomatization of dstit from Belnap et al. (Facing the future: agents and choices in our indeterminist world. Oxford University Press, Oxford, 2001). And while the influence of the latter book on the study of (...) logics of agency cannot be overstated, we note that this is not the only axiomatization of that modality available. In fact, an earlier (and arguably purer) one was offered in Xu (J Philosophical Logic 27(5):505–552, 1998). In this article we fill this lacuna by proving that this alternative axiomatization is likewise readily derivable in the system of Negri and Pavlović (Studia Logica 1–35, 2020). (shrink)

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)

Antonio Negri wrote the two essays that comprise Time for Revolution while serving a prison sentence for alleged involvement with radical left-wing groups. Although the essays were written two decades apart, their concerns are the same: is there a place for resistance in a society utterly subsumed by capitalism? In the wake of the global crisis of capitalism heralded by the 2008 crash, the question has never been more relevant and Negri remains an insightful and passionate guide to (...) any attempt to answer it. (shrink)

We introduce the concept of partial event as a pair of disjoint sets, respectively the favorable and the unfavorable cases. Partial events can be seen as a De Morgan algebra with a single fixed point for the complement. We introduce the concept of a measure of partial probability, based on a set of axioms resembling Kolmogoroff’s. Finally we define a concept of conditional probability for partial events and apply this concept to the analysis of the two-slit experiment in quantum mechanics.

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)

Humility was perceived in the Christian Middle Ages as a fundamental moral and intellectual quality, opening the way for access to the divine. How this access occurred, and for what kind of people, was dependent on different theological and philosophical presuppositions. The role of humility was thus moulded according to different anthropological and noetical models. By the end of the 13th century, the «question de l’humilité», as Alain de Libera posed it, had also become a locus for confrontation and definition (...) between different intellectual identities. This study focuses on the role that the secular master Henry of Ghent assigned to humility for approaching and transmitting divine truth, both from the perspective of the single individual and of the Christian community. Some topical categories describing essential features of humility – low/high, the ladder, interior/exterior, empty/full – aid in the analysis of some passages from the works of this theologian. (shrink)

This article investigates three major contexts in which Henry of Ghent’s Summa quaestionum ordinariarum was received from the thirteenth to the fifteenth century. The study takes into account the material features of a group of relevant manuscripts of the Summa: Paris, where the Summa was copied and annotated by Godfrey of Fontaines and his socii; the Dominican convent in Bologna at the beginning of the fourteenth century, to which Aimericus de Placentia gave a copy of the Summa corrected against the (...) very manuscript of Godfrey of Fontaines; the Roman Papal Court, where the Summa attracted the special attention of the humanist Pope Nicholas V, who employed the manuscript from the Bolognese convent for producing new copies of the work. In this study, I endeavour to present a late-medieval history of the Summa as a book, and to contribute to the debate about the mutual relationships among some of the most important witnesses of the text. I pay particular attention to the marginal annotations in t... (shrink)

The paradox marking Spinoza’s reappearance in modernity is well known. If Mendelssohn wished to “give him new credence by bringing him closer to the philosophical orthodoxy of Leibniz and Wolff,” and Jacobi, “by presenting him as a heterodox figure in the literal sense of the term, wanted to do away with him definitively for modern Christianity”—well, “both failed in their goal, and it was the heterodox Spinoza who was rehabilitated.” The Mendelssohn-Jacobi debate can be grafted onto the crisis of a (...) specific philosophical model. It generates a figure of Spinoza capable of assuaging the exacerbated spiritual tension of that epoch, and of constituting the systematic preamble of the relation between power and substance—between subject and nature. Spinoza, the damned Spinoza, had a resurgence in modernity as a Romantic philosopher. Lessing won out by recognizing in Spinoza an idea of nature which was capable of balancing the relation between feeling and intellect, freedom and necessity, and history and reason. Herder and Goethe, against the subjective and revolutionary impatience of the Sturm und Drang, based themselves on this powerful image of synthesis and recomposed objectivity: Spinoza is not only the figure of Romanticism; he constitutes its grounding and its fulfillment. The omnipotence of nature was no longer to break off into the tragedy of feeling, but it was to triumph over it, by opposing it to a kingdom of completed forms. Spinoza’s first reception within Romanticism was thus an aesthetic reception, a perception of motion and perfection, of dynamism and forms. And it remained such, even when the general frame and the particular components of Romanticism were subjected to the labor of philosophical critique. Fichte, the real philosophical hero of Romanticism, considered both Spinoza’s and Kant’s systems to be “perfectly coherent,” in the incessant ontological movement of the I. For the Schelling of the 1790s, the assertion of a radical opposition between 1 critical philosophy and dogmatic philosophy—that is, between a philosophy of the absolute I founding itself on the critical philosophy and a dogmatic philosophy of the absolute object and Spinozism—was quickly resolved into an analysis of action which dialectically took on the weight of the objective. Far from becoming antinomial, the absolute position of the I composes itself into a necessary process which, above tragedy, exalts the “spiritual automatism” of the relation between subject and substance. The aesthetic dimension of this synthesis consists in ceaselessly and tirelessly bringing back power and substance, the productive element and the form of production, to perfection. Romanticism, according to Hegel, is characterized by a capacity to overcome the pure objectivity of the ideal and the natural as a true idea of beauty and truth, initially to destroy the union of the idea and its reality, and to locate the latter in the difference, so as then to bring to manifestation the inner world of absolute subjectivity and reconstruct its objectivity where the overcoming of sensibility is appeased in the absolute character of the result. The filiation of this process is still Lessingian, but the new dialectic expresses and articulates its motivations, while insisting on the propaedeutic of the beautiful along the path leading to the absolute. Spinoza, a certain Spinoza, becomes the central figure in this process. (shrink)

It is in Sein und Zeit that Heidegger decrees the end of the Geisteswissenschaften and their tradition, when, as he is commenting on the Briefwechsel [exchange of letters] between Dilthey and Yorck von Wartenburg, he pays homage to the latter for “his full understanding of the fundamental character of history as virtuality [...] [which he] owes to his knowledge of the character of being of human Dasein itself.” Consequently, Heidegger continues, “the interest of understanding historicality” is confronted with the task (...) of an elaboration of the “generic difference between the ontic and the historical.” But he must part ways with Yorck when the latter, after having clearly established that difference, moves from virtuality to mysticism. If, on the other hand, once separated from the ontic, “the question of historicality shows itself to be an ontological question which inquires into the constitution of being of historical being”, it is once again towards Dilthey that one must turn, in spite of his confused vitalism. Heidegger effects two operations at once. On the one hand, he expels the Geisteswissenschaften from the position they occupied at the heart of metaphysics, as the inheritors of the Enlightenment and the outcome of Hegelianism. On the other hand, he brings to fulfillment the critical labor which had precisely shown its value in Dilthey’s historicism —acritical labor which develops the search for the meaning of historicity and allows one to move from the theory of objectivity to that of expression, from the acknowledgment of historiography in the context of the critique of cognition to its definition at the heart of the transcendental schematism. Historicity is then posited as an ontological dimension and leaves only its ontic residue for historiography. (shrink)

Writings by Negri on the brief thaw in the cold winter of neoliberalism, Thatcherism, Reaganomics, and counterrevolution. Automation and information technology have transformed the organization of labor to such an extent that the processes of exploitation have moved beyond the labor class and now work upon society as a whole. If this displacement has destroyed the political primacy of the labor class, it has not, however, eliminated exploitation; rather, it has broadened it, implanting it within the given conditions of (...) the most diverse spheres of society. —from The Winter Is Over In late 1995, in opposition to the conservative agenda of Jacques Chirac and his prime minister Alain Juppé and their proposed widespread welfare cuts, French students rose up against their government; public sector workers, together with all the major trade unions, went on strike. When railway workers and Paris Metro personnel joined in the protests, France's public transportation system came to a halt. These extensive social upheavals, the likes of which had not been seen in France since 1968, found widespread public support and fuelled the creation of many political organizations. Chirac backed down from restructuring the public retirement system. Antonio Negri's The Winter is Over comes out of the glimmer of optimism created by the events of 1995, when the long, cold season of neoliberalism, Thatcherism, Reaganomics, reaction, and counterrevolution appeared to have run its course. Published in Italian in 1996, The Winter is Over brings together a series of articles, speeches, and other documents written by Negri between 1989 and 1995 at the threshold of this thaw. It offers a revealing and wide-reaching account of those years of change and brink-of-change, focusing on such topics as the networks of social production, the decline of “limp thought,” the end of applied socialism, the Gulf War, and, finally, Italy's transition to its so-called “Second Republic,” as seen by an exile. (shrink)

L'articolo analizza i vari volumi di A.Negri dedicati al pensiero di Nietzsche.

The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.

_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)