We define a generic notion of cut that applies to many first-order theories. We prove a generic cut elimination theorem showing that the cut elimination property holds for all theories having a so-called pre-model. As a corollary, we retrieve cut elimination for several axiomatic theories, including Church's simple type theory.

The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed [lgr]-calculus, i.e. to solve the equation a = b where a and b are simply typed [lgr]-terms and b is ground. The decidability of this problem is still open. We prove the decidability of the particular case in which the variables occuring in the problem are at most third order.

Nominal terms extend first-order terms with binding. They lack some properties of first- and higher-order terms: Terms must be reasoned about in a context of ‘freshness assumptions’; it is not always possible to ‘choose a fresh variable symbol’ for a nominal term; it is not always possible to ‘α-convert a bound variable symbol’ or to ‘quotient by α-equivalence’; the notion of unifier is not based just on substitution.Permissive nominal terms closely resemble nominal terms but they recover these properties, and in (...) particular the ‘always fresh’ and ‘always rename’ properties. In the permissive world, freshness contexts are elided, equality is fixed, and the notion of unifier is based on substitution alone rather than on nominal terms’ notion of unification based on substitution plus extra freshness conditions.We prove that expressivity is not lost moving to the permissive case and provide an injection of nominal terms unification problems and their solutions into permissive nominal terms problems and their solutions.We investigate the relation between permissive nominal unification and higher-order pattern unification. We show how to translate permissive nominal unification problems and solutions in a sound, complete, and optimal manner, in suitable senses which we make formal. (shrink)

We give a simple and direct proof that super-consistency implies the cut-elimination property in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes ideas from the semantic proofs of cut elimination that proceed by proving the completeness of the cut-free calculus. As an application, we compare our work with the cut-elimination theorems in higher-order logic that involve V-complexes.

Comprendre les origines de l’informatique demande de s’intéresser à quatre concepts fondamentaux : ceux d’algorithme, de machine, d’information et de langage. De leur combinaison naît cette science nouvelle qu’est l’informatique.

Nominal terms extend first-order terms with binding. They lack some properties of first- and higher-order terms: Terms must be reasoned about in a context of ‘freshness assumptions’; it is not always possible to ‘choose a fresh variable symbol’ for a nominal term; it is not always possible to ‘α-convert a bound variable symbol’ or to ‘quotient by α-equivalence’; the notion of unifier is not based just on substitution. Permissive nominal terms closely resemble nominal terms but they recover these properties, and (...) in particular the ‘always fresh’ and ‘always rename’ properties. In the permissive world, freshness contexts are elided, equality is fixed, and the notion of unifier is based on substitution alone rather than on nominal terms’ notion of unification based on substitution plus extra freshness conditions. We prove that expressivity is not lost moving to the permissive case and provide an injection of nominal terms unification problems and their solutions into permissive nominal terms problems and their solutions. We investigate the relation between permissive nominal unification and higher-order pattern unification. We show how to translate permissive nominal unification problems and solutions in a sound, complete, and optimal manner, in suitable senses which we make formal. (shrink)

Review of Dowek, Gilles, Computation, Proof, Machine, Cambridge University Press, Cambridge, 2015. Translation of Les Métamorphoses du calcul, Le Pommier, Paris, 2007. Translation from the French by Pierre Guillot and Marion Roman.

"Gill's and Ryan's Parmenides is, simply, superb: the Introduction, more than a hundred pages long, is transparently clear, takes the reader meticulously through the arguments, avoids perverseness, and still manages to make sense of the dialogue as a whole; there is a fine selective bibliography; and those parts of the translation I have looked at in detail suggest that it too is very good indeed." --Christopher Rowe, _Phronesis_.

Suggests an open system of psychological exploration to cut through accepted norms of morality, language, and politics.

"Le projet le plus général de Nietzsche consiste en ceci : introduire en philosophie les concepts de sens et de valeur. Nietzsche n'a jamais caché que la philosophie du sens et des valeurs dut être une critique. Que Kant n'ait pas mené la vraie critique, parce qu'il n'a pas su en poser le problème en termes de valeurs, tel est même un des mobiles principaux de l'oeuvre de Nietzsche". Cette analyse rigoureuse et critique de la philosophie de Nietzsche est une (...) lumineuse introduction à l'oeuvre d'un philosophe trop souvent réduit au nihilisme, à la volonté de puissance et l'image du surhomme. Gilles Deleuze remarque que "la philosophie moderne présente des amalgames, qui témoignent de sa vigueur et de sa vivacité, mais qui comportent aussi des dangers pour l'esprit" et que la force du projet philosophique de Nietzsche dans le "dépassement" de la métaphysique est "de dénoncer toutes les mystifications qui trouvent dans la dialectique un dernier refuge. La philosophie de Nietzsche a une grande portée polémique". (shrink)

Machine generated contents note: -- Preface to the English edition \ Translators' Introduction \Preface to the French Edition \ 1. Theses on Movement: First Commentary onBergson \ 2. Frame and Short, Framing and Cutting \ 3. Montage \ 4. TheMovement-Image and its Three Varieties: Second Commentary on Bergson \ 5. ThePerception-Image \ 6. The Affection-Image Face and Close-Up \ 7. TheAffection-Image: Qualities, Powers, Any-Space-Whatevers \ 8. From Affect toAction: The Impulse Image \ 9. The Action-Image: The Large Form \ 10. (...) The Action-Image:The Small Form \ 11. Figures, or the Transformation of Forms \ 12. The Crisisof the Action-Image \ Glossary \ Notes \ Index. (shrink)

Praised for its rare combination of scholarly rigor and imaginative interpretation, _Nietzsche and Philosophy_ has long been recognized as one of the most important analyses of Nietzsche. It is also one of the best introductions to Deleuze's thought, establishing many of his central philosophical positions. In _Nietzsche and Philosophy_, Deleuze identifies and explores three crucial concepts in Nietzschean thought-multiplicity, becoming, and affirmation-and clarifies Nietzsche's views regarding the will to power, eternal return, nihilism, and difference. For Deleuze, Nietzsche challenged conventional philosophical (...) ideas and provided a means of escape from Hegel's dialectical thinking, which had come to dominate French philosophy. He also offered a path toward a politics of difference. In this new edition, Michael Hardt's foreword examines the profound influence of Deleuze's provocative interpretations on the study of Nietzsche, which opened a whole new avenue in postwar thought. (shrink)

‘A rare and remarkable book.’ Times Literary SupplementGilles Deleuze (1925-1995) was Professor of Philosophy at the University of Paris VIII. He is a key figure in poststructuralism, and one of the most influential philosophers of the twentieth century.F\’elix Guattari (1930-1992) was a psychoanalyst at the la Borde Clinic, as well as being a major social theorist and radical activist. A Thousand Plateaus is part of Deleuze and Guattari’s landmark philosophical project, Capitalism and Schizophrenia - a project that still sets the (...) terms of contemporary philosophical debate. A Thousand Plateaus provides a compelling analysis of social phenomena and offers fresh alternatives for thinking about philosophy and culture. Its radical perspective provides a toolbox for ‘nomadic thought’ and has had a galvanizing influence on today’s anti-capitalist movement.Translated by Brian Massumi>. (shrink)

La philosophie théorique de Spinoza est une des tentatives les plus radicales pour constituer une ontologie pure : une seule substance absolument infinie, avec tous les attributs, les êtres n'étant que des manières d'être de cette substance. Mais pourquoi une telle ontologie s'appelle-t-elle Ethique? Quel rapport y a-t-il entre la grande proposition spéculative et les propositions pratiques qui ont fait le scandale du spinozisme? L'éthique est la science pratique des manières d'être. C'est une éthologie, non pas une morale. L'opposition de (...) l'éthique avec la morale, le lien des propositions éthiques avec la proposition ontologique, sont l'objet de ce livre qui présente, de ce point de vue, un dictionnaire des principales notions de Spinoza. D'où vient la place très particulière de Spinoza, la façon dont il concerne immédiatement le non-philosophe autant que le philosophe? (shrink)

Until recently, cognitive science focused on such mental functions as problem solving, grammar, and pattern-the functions in which the human mind most closely resembles a computer. But humans are more than computers: we invent new meanings, imagine wildly, and even have ideas that have never existed before. Today the cutting edge of cognitive science addresses precisely these mysterious, creative aspects of the mind.The Way We Think is a landmark analysis of the imaginative nature of the mind. Conceptual blending is already (...) widely known in research laboratories throughout the world; this book, written to be accessible to both lay readers and interested scientists, is its definitive statement. Gilles Fauconnier and Mark Turner show that conceptual blending is the root of the cognitively modern human mind, and that conceptual blends themselves are continually combined and reblended to create the rich mental fabric in which we live.The Way We Think shows how this blending operates; how it is affected by (and gives rise to) language, identity, culture, and invention; and how we imagine what could be and what might have been. The result is a bold and exciting new view of how the mind works. (shrink)

Many terminally ill patients perceive themselves to be a burden to loved ones who care for them. The self-perception of being a burden can play a significant role in terminal patients’ decisions to take courses of action, such as ceasing life-sustaining treatment or requesting physician-assisted suicide, that hasten death. I will use the term ‘burden-based decision’ as a shorthand for cases in which a terminal patient’s perception that she is a burden to her loved ones influences her decision to hasten (...) death. When should we view a terminal patient’s inclination to make a burden-based decision to be an ethical problem or a failure of treatment? And when should we view it to be an acceptable response rather than a problem or failure? I argue here that such decisions are acceptable more often than many who write on this topic imply. (shrink)

Avec Hume, l'empirisme ne se définit plus essentiellement par l'origine sensible des idées. Il développe trois problèmes, les relations, les cas, les illusions. D'une part, les relations sont toujours extérieures à leurs termes, et dépendent de principes d'association qui en déterminent l'établissement et l'exercice (croyance). D'autre part, ces principes d'association n'agissent qu'en fonction des passions, pour indiquer des "cas" dans un monde de la culture ou du droit : c'est tout l'associationnisme qui est au service d'une pratique du droit, de (...) la politique et de l'économie (suffit-il, pour devenir propriétaire d'une cité abandonnée, de lancer un javelot sur la porte, ou faut-il toucher la porte du doigt?). Enfin, de telles règles de légitimité des relations peuvent-elles être séparées des fictions, des croyances illégitimes qui les accompagnent ou les doublent? Si bien que la philosophie est moins critique des erreurs que dénonciation des illusions inévitables. Dans tous ces domaines, l'empirisme opère la substitution de la croyance pratique au savoir, dans une entreprise athée qui consiste à naturaliser la croyance. (shrink)

This chapter contains section titled: Functives and Concepts.

A posthumous collection of writings by Deleuze, including letters, youthful essays, and an interview, many previously unpublished. Letters and Other Texts is the third and final volume of the posthumous texts of Gilles Deleuze, collected for publication in French on the twentieth anniversary of his death. It contains several letters addressed to his contemporaries (Michel Foucault, Pierre Klossowski, François Châtelet, and Clément Rosset, among others). Of particular importance are the letters addressed to Félix Guattari, which offer an irreplaceable account (...) of their work as a duo from Anti-Oedipus to What is Philosophy? Later letters provide a new perspective on Deleuze's work as he responds to students' questions. his volume also offers a set of unpublished or hard-to-find texts, including some essays from Deleuze's youth, a few unusual drawings, and a long interview from 1973 on Anti-Oedipus with Guattari. (shrink)

The flames of Alexandria continue to rage. After twenty centuries, they still dazzle us, as though the Mouseion were the only massacred library. One would believe that Julius Caesar, Theophilus of Antioch and Omar (the three pyromaniacs, the pagan, the Christian and the Moslem) had had no predecessors or imitators. But the race of incendiaries is as numerous as the waves of the sea. It is monotonous, it is indestructible, it is equal to that of the ants. It was born (...) at the same time as the first Babylonian tablets. In 1988, it continues its work. All over the world and in all times, the incendiaries were there with their torches. They burned parchments, wood or clay tablets, leather manuscripts, papyrus or folios. The same warriors who profaned temples set fire to incunabula. The same ones who slaughtered the Aztecs threw their firebrands into the collection of codices. What is it, this unleashed fury of prince and priest, judge and soldier against these small monuments of clay or paper, against these sepulchres in which the dead say that they have lived and loved, suffered and hoped? (shrink)

Introduction. Exister, c'est être seul -- 1. Conformisme et aristocratisme -- 2. Penser et lire -- 3. Communauté et économie -- 4. De la politique à l'enseignement -- 5. Des degrés de communauté -- 6. L'épreuve du collectif -- 7. Du "je" au "nous" -- 8. Une communauté à deux? -- 9. Le collectif en conflit -- 10. Ennemis et adversaires -- Conclusion. Quelques-uns.

Examines the philosophy of Henri Bergson, explains his concepts of duration, memory, and elan vital, and discusses the influence of science on Bergson.

Dans cet essai, Gilles Deleuze entreprend une analyse de la méthode philosophique employée par Kant dans ses trois grands livres, Critique de la raison pure, Critique de la raison pratique, Critique du jugement. " Il nous suffit de retenir le principe d'une thèse essentielle de la Critique en général : il y a des intérêts de la raison qui diffèrent en nature. Ces intérêts forment un système organique et hiérarchisé qui est celui des fins de l'être raisonnable. " Mais, (...) précise Gilles Deleuze, " une faculté législatrice ne supprime pas tout emploi des autres facultés... Suivant chaque Critique, l'entendement, la raison, l'imagination entreront clans des rapports divers sous la présidence d'une de ces facultés. ". (shrink)

Of fundamental importance to literary critics and philosophers, Difference and Repetition develops two central concepts -- pure difference and complex ...

A critical examination of the figure of Oedipus in psychoanalysis and Western culture as it relates to the history of society and capitalism.

Pour un artiste ou un chercheur, s'emparer du problème de l'extériorité revient à se confronter à une relation aporétique au monde, aux choses, aux êtres et à son oeuvre. Poser la question de l'extériorité est irréductible à toute tentative de définition et contradictoire avec le désir d'en délimiter les contours, car ces tentatives dévitaliseraient l'idée même d'extériorité. Entrer dans le sillage de l'extériorité ou se lancer sur sa piste c'est alors accepter l'épreuve de l'autre. Cette expérience réintroduit à l'égard du (...) monde et des hommes une possibilité d'ouverture à l'imprévisible, à l'innommable et à l'inconnaissable. Elle expose la temporalité à l'accueil de l'inattendu et de la surprise. Cette épreuve de l'autre ne réduit pas l'autre moi-même à l'anonymat, elle lie le chercheur, l'artiste et tout homme à un autre dont il est impossible d'être quitte. (shrink)

Les textes de Benny Lévy restent méconnus, car l'image que l'on a de lui fait obstacle à leur lecture. Ecartant cette image, nous nous en tiendrons à sa manière si singulière de lire les textes, quels qu'ils fussent, de leur donner vie. Qu'un texte puisse, grâce à la voix qui le porte et le déplie, grâce au travail, acharné et patient, de la lecture qui en explore les articulations les plus manifestes mais aussi les plus secrètes, parler à chacun en (...) propre, l'atteindre en son point sensible : telle est la vie dont nous parlons, plus forte que la mort qui menace tous les textes. Car la voix risque de disparaître dans l'épaisseur même des lettres ; les textes réifiés de perdre leur pouvoir de dire. Re-susciter la voix au coeur de la lettre, faire retentir son grain, son souffle, son amplitude et ses nuances : telle doit être l'ambition d'une véritable lecture. Pour Benny Lévy, la pensée fut indissociable d'un tel travail de lecture, l'amenant à reprendre à neuf les textes, à en renouveler la compréhension. Cette puissance de lecture produisit dans son geste de pensée cinq exigences qui guideront notre réflexion : réformer la pensée, sortir du politique, penser l'universel autrement, faire retour au Nom, produire, enfin, des événements de lecture. (shrink)

Deleuze and Guattari differentiate between philosophy, science, and the arts - seeing each as a means of confronting chaos - and challenge the common view that philosophy is an extension of logic. The authors also discuss the similarities and distinctions between creative and philosophical writing. Fresh anecdotes from the history of philosophy illuminate this book, along with engaging discussions of composers, painters, writers, and architects.

Creative encounters, appreciating difference: an introduction -- Appreciating difference : encountering, moving, naming -- Moving beyond place -- Territory -- I don't want to be a mystic! : on self-moving and religious experience -- Not by any name -- Creations of encounter -- Mother earth and numbakulla -- Storytracking the arrernte through the academic bush -- Mother earth : an American myth -- Aesthetic of impossibles -- Myth and an aesthetic of impossibles -- Tomorrow's eve and the next gen study (...) of religion -- Gesture -- Gesture posture prosthesis -- They jump up of themselves -- As prayer goes so goes religion -- Play -- No place to stand : Jonathan Z. Smith as homo ludens, the academic study of religion sub specie ludi -- To risk meaning nothing : Charles Sanders Peirce & the logic of discovery -- Creative encounters -- Creative encounters. (shrink)