The problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo-Fraenkel which is already complete with respect to the ∀*∀ class of sentences. NP-hardness and NP-completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.

As is well-known, the Bernays-Schönfinkel-Ramsey class of all prenex ∃*∀* -sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are ∈ and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability problem for (...) the BSR class is proved by following a purely semantic approach, the remaining part of the decidability result being postponed to a forthcoming paper. (shrink)

Being able to state the principles which lie deepest in the foundations of mathematics by sentences in three variables is crucially important for a satisfactory equational rendering of set theories along the lines proposed by Alfred Tarski and Steven Givant in their monograph of 1987. The main achievement of this paper is the proof that the 'kernel' set theory whose postulates are extensionality. (E), and single-element adjunction and removal. (W) and (L), cannot be axiomatized by means of three-variable sentences. This (...) highlights a sharp edge to be crossed in order to attain an 'algebraization' of Set Theory. Indeed, one easily shows that the theory which results from the said kernel by addition of the null set axiom, (N), is in its entirety expressible in three variables. (shrink)

This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth problem. (...) The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic. (shrink)

As proved recently, the satisfaction problem for all prenex formulae in the set-theoretic Bernays-Shönfinkel-Ramsey class is semi-decidable over von Neumann's cumulative hierarchy. Here that semi-decidability result is strengthened into a decidability result for the same collection of formulae.

Hasta el final de su vida, y durante más de diez años, Publio Virgilio Marón (70-19 a.C.) estuvo dedicado a la composición de la Eneida, unánimemente reconocida como el más perfecto exponente del clasicismo romano. Virgilio pretendió con ella ofrecer al público romano la gran epopeya de sus orígenes, que sirviera al tiempo como justificación y exaltación del nuevo régimen impuesto por el emperador Augusto. El resultado sería esta magistral combinación entre el pasado legendario de Roma y su historia reciente. (...) Más allá de las evidentes funciones políticas y sus distintos niveles temáticos, la Eneida nos ofrece la gesta de un héroe exiliado de su patria. Tras la quema de Troya a manos de los griegos, Eneas parte hacia una tierra extraña, en la que había de encontrar su nuevo hogar. En su viaje por mar, el hijo de Venus arrostrará numerosas dificultades hasta llegar a su destino en la costa italiana, e incluso allí se verá obligado a entablar una guerra contra los pueblos itálicos, para conseguir al fin fundar una ciudad llamada a convertirse en cabeza del mundo. (shrink)

How has the concept of democracy been understood, manifested, reimagined and represented through the ages? In a work that spans 2,500 years these fundamental questions are addressed by 66 experts, each contributing their overview of a theme applied to a period in history. With the help of a broad range of case material they illustrate the physical, social and cultural contexts of democracy in Western culture from antiquity to the present. Individual volume editors ensure the cohesion of the whole, and (...) to make it as easy as possible to use, chapter themes are identical across each of the volumes. Superbly illustrated, the full six-volume set combines to present the most comprehensive and authoritative survey available on democracy throughout history. The six volumes cover: 1 - Antiquity (500 BCE-565 CE); 2 - Medieval Age (565-1450); 3 - Renaissance (1450-1650); 4 - Age of Enlightenment (1650-1800); 5 - Age of Empire (1800-1920); 6 Modern Age (1920-present) The ten themes are: Sovereignty; Liberty and the Rule of Law; The 'Common Good'; Economic and Social Democracy; Religion and the Principles of Political Obligation; Citizenship and Gender; Ethnicity, Race and Nationalism; Democratic Crises, Revolutions and Civil Resistance; International Relations; Beyond the Polis. The page extent for the pack is approximately 2016pp. Each volume opens with Notes on Contributors and an Introduction and concludes with Notes, Bibliography, and an Index. The Cultural Histories Series A Cultural History of Democracy is part of The Cultural Histories Series. Titles are available both as printed hardcover sets for libraries needing just one subject or preferring a one-off purchase and tangible reference for their shelves, or as part of a fully-searchable digital library available to institutions by annual subscription or on perpetual access (see www.bloomsburyculturalhistory.com). (shrink)

Dai saggi raccolti in questo volume da Garin emergono le linee di una storia della civiltà del Rinascimento italiano. Lo studio dello stretto intreccio tra vita intellettuale e vita politica, soprattutto nella Firenze fra Tre e Quattrocento, costituisce il punto di partenza per una nuova interpretazione di questo periodo. Le origini dell'Umanesimo vanno cercate nel rapporto fra la tradizione di libertà e democrazia della repubblica fiorentina e l'immagine ideale della repubblica come erede di Roma.

Sulla dignità umana -- Bioetica senza fondamento? -- Una sovranità limitata per la ricerca scientifica: ossimoro o truismo -- Ius quia iussum e ius quia iustum (considerazioni su alcuni passi del libro della genesi) -- La pace come problema -- A proposito di religioni, identità nazionali e diritto -- Su costituzioni e costituzionalismo -- A proposito del trattato politico di Spinoza -- A proposito dei lineamenti fondamentali di filosofia del diritto di Hegel -- A proposito degli elementi di scienza politica (...) di Mosca -- Su Michels -- Su luigi einaudi 'italiano del tutto particolare' -- Guerra e pace secondo cotta -- Una postilla non scientifica (ovvero: un dittico contro Schmitt). (shrink)

1. Le fe por la palabra -- 2. Topía y Utopía -- 3. Luz en la caverna.

v. 1. Proceedings, Rome, 2001-2004 -- v. 2. Giornate di studi, 2005-2008.

This volume illustrates to the public, and legal experts, the basic principles of the field of neuroscience, that commonly goes under the name of Neurolaw. First, it illustrates the relationship between neuroscience, natural sciences and social sciences. Furthermore, it highlights numerous problems concerning the fundamental philosophical concepts used by Neurolaw and evaluates the validity of the method and the limits of a neuroscientific approach to the problems of law and justice. The volume explores the possibility of application of these concepts (...) on the fundamentals of the general theory of law and legal dogmatics. It also examines the main problems of Neurolaw in relation to public, private, criminal and procedural law. In conclusion, the book follows a systematic method that makes it an thorough manual for the introduction to Neurolaw. (shrink)

Partial proceedings of the 17th World Congress, International Association for Philosophy of Law and Social Philosophy, Bologna, 1995.