Cet article étudie le rapport entre pouvoir spirituel et pouvoir temporel dans la pensée de l’augustinien Jacques de Viterbe († 1307/8), à la lumière de l’édition de deux sermones de mortuis inédits, écrits et prononcés entre 1303 et 1305, lorsqu’il était archevêque de Naples. Cette étude vise donc à offrir une interprétation de la pensée politique de Jacques, à travers la lecture diachronique de ses œuvres, à partir de la Disputatio prima de quolibet jusqu’à ses derniers écrits, afin de suivre (...) l’évolution de sa théorie politique, de son ouverture progressive à la perspective de Thomas d’Aquin et de la réception du principe aristotélicien de la naturalitas de la société humaine. (shrink)

On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a “state-event-probability” (SEVP) structure, using a quite standard “fuzzification” procedure, a set of unsharp events (or “effects”) is constructed and the corresponding “state-effect-probability” (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an (...) orthomodular complete lattice. As customary, by these orthocomplementations the two modal-like necessity and possibility operators are introduced, and it is shown that Ludwig's and Jauch-Piron's approaches to quantum physics are “interpreted” in complete SEFP. As a marginal result, a standard procedure to construct a lot of unsharp realizations starting from any sharp realization of a fixed observable is given, and the relationship among sharp and corresponding unsharp realizations is studied. (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)

The history of Fuzziness in Italy is varied and scattered among a num- ber of research groups. As a matter of fact, “fuzziness” spread in Italy through a sort of spontaneous diffusion, and, also subsequently, no one felt the need to cre- ate some “national” common structure like an Association or similar things. Since a cohesive retelling would be next to impossible, a few members of the Italian fuzzy community have been asked to recount their experience and express their hopes (...) for the future. (shrink)

The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (indiscernibility) relation R U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric.We generalize the notion of approximation space as a pair consisting of a universe U and a discernibility or preclusivity (irreflexive and symmetric) relation, not necessarily induced from an equivalence relation. In this case the "elementary" (...) sets are not mutually disjoint, but all the theory of generalized rough sets can be developed in analogy with the standard Pawlak approach. On the power set of the universe, the algebraic structure of the quasi fuzzy-intuitionistic "classical" (BZ) lattice is introduced and the sets of all "closed" and of all "open" definable sets with the associated complete (in general nondistributive) ortholattice structures are singled out. (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.

Fuzzy intuitionistic quantum logics (called also Brouwer-Zadeh logics) represent to non standard version of quantum logic where the connective not is split into two different negation: a fuzzy-like negation that gives rise to a paraconsistent behavior and an intuitionistic-like negation. A completeness theorem for a particular form of Brouwer-Zadeh logic (BZL 3) is proved. A phisical interpretation of these logics can be constructed in the framework of the unsharp approach to quantum theory.

Some algebraic structures determined by the class σ(þ) of all effects of a Hilbert space þ and by some subclasses of σ(þ) are investigated, in particular de Morgan-Brouwer-Zadeh posets [it is proved that σ(þ n )(n<∞) has such a structure], Brouwer-Zadeh * posets (a quite trivial example consisting of suitable effects is given), and Brouwer-Zadeh 3 posets which are both de Morgan and *.It is shown that a nontrivial class of effects of a Hilbert space exists which is a BZ (...) 3 poset. An ɛ-preclusivity relation on the set of all vectors of þ is introduced, and it is shown that it satisfies the regularity condition also for ε∃ [1/2, 1]. (shrink)

We discuss the problem of how a (commutative) generalized observable in a finite-dimensional Hilbert space (communtative effect-valued resolution of the identity) can be considered as an unsharp realization of some standard observable (projection-valued resolution of the identity). In particular, we give a concrete procedure for constructing such a standard observable. Some results about the “uniqueness” of the resulting observable are also examined.

The theoretical scheme proposed by Aerts for describing two separated entities as a whole within a question-state structure is considered. The quoted author claims that two relevant axioms characterizing quantum physics cannot hold for a quantum, nonclassical entity consisting of two quantum separate entities. We suggest that Aerts' theory is not adequate, from the empirical point of view, to describe this situation.

This article presents and compares various algebraic structures that arise in axiomatic unsharp quantum physics. We begin by stating some basic principles that such an algebraic structure should encompass. Following G. Mackey and G. Ludwig, we first consider a minimal state-effect-probability (minimal SEFP) structure. In order to include partial operations of sum and difference, an additional axiom is postulated and a SEFP structure is obtained. It is then shown that a SEFP structure is equivalent to an effect algebra with an (...) order determining set of states. We also consider σ-SEFP structures and show that these structures distinguish Hilbert space from incomplete inner product spaces. Various types of sharpness are discussed and under what conditions a Brouwer complementation can be defined to obtain a BZ-poset is investigated. In this case it is shown that every effect has a best lower and upper sharp approximation and that the set of all Brouwer sharp effects form an orthoalgebra. (shrink)

The notion of coexistence between questions is introduced in the framework of Piron's approach to quantum physics, using Aerts' notion of performable-together questions. Relationships between coexistence of questions and Piron's compatibility of propositions are investigated. In particular, properties generated by coexistent and primitive questions are compatible.

The mathematical description of the three distinct fundamental notions of “individual sample” of “preparing procedure,” and of “Piron's state” of a physical entity are precisely introduced in the framework of the Piron's “preparation-question structure” (without specific axioms C, P, A) based on Ludwig's “selection structure.” We compare our realization of the above notions with a similar use of the standard terminology of the “Geneva School” adopted by Pykacz and Santos in a recent paper.

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

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Of all the works attributed to Ovid but of disputed authenticity, the epistle of Sappho to Phaon is notoriously the one which has most perplexed scholars. Most philologists at the end of the 19th century asserted the Ovidian paternity of the epistle; but in recent years the discussion has flared up once again, especially following an important contribution, tending in the opposite direction, by R. J. Tarrant, and today, above all in Anglo-American studies, the pendulum seems to be swinging more (...) in the direction of inauthenticity, according to the movement typical in debates of this kind. The present article obviously does not intend to discuss the whole question once again nor to reaffirm tout court the attribution to Ovid, but brings to the attention of scholars certain arguments which should not be neglected in the discussion . I do not mean to underestimate the linguistic, stylistic, and metrical anomalies which scholars up to Tarrant and beyond have imputed to the epistula Sapphus, but rather to indicate some characteristics, above all of compositional technique, which have not been considered but which I think have a not insignificant weight in the debate on authenticity. (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.

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)

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)

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)

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)