Volume II of Classical Recursion Theory describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, ranging from small (...) time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It also deals with primitive recursive functions and larger classes, which are of interest to the proof theorist. The second half of the book starts with the classical theory of recursively enumerable sets and degrees, which constitutes the core of Recursion or Computability Theory. Unlike other texts, usually confined to the Turing degrees, the book covers a variety of other strong reducibilities, studying both their individual structures and their mutual relationships. The last chapters extend the theory to limit sets and arithmetical sets. The volume ends with the first textbook treatment of the enumeration degrees, which admit a number of applications from algebra to the Lambda Calculus. The book is a valuable source of information for anyone interested in Complexity and Computability Theory. The student will appreciate the detailed but informal account of a wide variety of basic topics, while the specialist will find a wealth of material sketched in exercises and asides. A massive bibliography of more than a thousand titles completes the treatment on the historical side. (shrink)

This multifaceted collection of essays, reminiscences, and professional papers combine to create an exceptional tribute to the unusual, enigmatic, and ultimately fascinating personality of Georg Kreisel. An eminently influential logician and mathematical philosopher, Kreisel is revealed as much more in this entertaining juxtaposition of viewpoints from famous contributors like Verena Huber-Dyson, Sol Feferman, and Francis Crick. Mathematics fans and armchair philosophers will delight in this look at Kreisel as he conveys his unique personal and intellectual influence.

Reviewed Works:Andrea Sorbi, Complexity, Logic, and Recursion Theory.Klaus Ambos-Spies, Elvira Mayordomo, Resource-Bounded Measure and Randomness.Marat Arslanov, Degree Structures in Local Degree Theory.Jose L. Balcazar, Ricard Gavalda, Montserrat Hermo, Compressibility of Infinite Binary Sequences.S. Barry Cooper, Beyond Godel's Theorem: The Failure to Capture Information Content.Robert A. Di Paola, Franco Montagna, Progressions of Theories of Bounded Arithmetic.Rodney G. Downey, On Presentations of Algebraic Structures.Sophie Fischer, Lane Hemaspaandra, Leen Torenvliet, Witness-Isomorphic Reductions and Local Search.William Gasarch, Carl H. Smith, A Survey of Inductive Inference (...) with an Emphasis on Queries.Andre Nies, A Uniformity of Degree Structures.Piergiorgio Odifreddi, Short Course on Logic, Algebra, and Topology.Andrea Sorbi, The Enumeration Degrees of the $\sigma^0_2$ Sets.Peter van Emde Boas, The Convenience of Tilings. (shrink)

The notion of forms of life points to a crucial aspect of Wittgenstein’s philosophical approach that challenges an influential line in the philosophical tradition. He portrays intellectual activities in terms of a cohesion of things held together in linguistic scenes rooted in the lives of people and the facts of the world. The original inspiration with which Wittgenstein worked on this approach is still relevant today in the recent technological turn associated with AI. He attacked a conception that treated human (...) activities as material to be examined by external models of rationality. Along with other modernists such as Musil, he saw the danger of losing faith in human intellectual and moral capacities. In contrast, Wittgenstein elucidates and substantively defends an idea of forms of life in which the great normative enterprises, from science to the works of the imagination, are based on our individual capacity to take the next step from a normative authority that rests entirely with us, as agents who can claim it in the name of others, in the name of arithmetic, in the name of our native language, in the name of justice, and so on. Forms of life are the place to look to claim this authority over the mistrust we feel compelled to cultivate in our human endeavors. (shrink)

Scanning the corpus and repertoire of anthropological science, insofar as we wish and are able to, we note that ethnological observations and studies on theatre are not lacking, but that they seem to have been isolated opportunities for investigation that have never grown into a research tradition.

Il campo di esperienza che Galvano della Volpe ha aperto nella filosofia italiana del Novecento non si chiude con la fine di una stagione culturale.

A lesion to the brain is not necessary for a successful neural transplantation. Embryonic Purkinje cells placed on the surface of an uninjured adult cerebellum can develop and migrate into the host molecular layer. Both the Purkinje cells that migrated into the host cerebellum and those that remained in the graft were innervated by collateral sprouting of adult intact climbing fibers.

Actin is a key protein in numerous cellular functions. One recent study has identified a large set of genes, associated with the actin cytoskeleton, which could be grouped into a wide spectrum of cytoplasmic and nuclear functions, such as protein biosynthesis and gene transcription.1 Deletions of many of the identified genes affected cellular actin organization,1 suggesting a functional link between different actin fractions probably regulated through changes in actin dynamics. The data are very exciting; speculations on the crosstalk between cytoplasmic (...) and nuclear actin fractions in different cellular contexts may help placing the results in perspective to further understand how actin‐mediated signalling affects cellular functions, such as gene expression. BioEssays 29:407–411, 2007. © 2007 Wiley Periodicals, Inc. (shrink)

Gianni Vattimo, a leading philosopher of the continental school, has always resisted autobiography. But in this intimate memoir, the voice of Vattimo as thinker, political activist, and human being finds its expression on the page. With Piergiorgio Paterlini, a noted Italian writer and journalist, Vattimo reflects on a lifetime of politics, sexual radicalism, and philosophical exuberance in postwar Italy. Turin, the city where he was born and one of the intellectual capitals of Europe (also the city in which Nietzsche (...) went mad), forms the core of his reminiscences, enhanced by fascinating vignettes of studying under Hans Georg Gadamer, teaching in the United States, serving as a public intellectual and interlocutor of Habermas and Derrida, and working within the European Parliament to unite Europe. Vattimo's status as a left-wing faculty president paradoxically made him a target of the Red Brigades in the 1970s, causing him to flee Turin for his life. Left-wing terrorism did not deter the philosopher from his quest for social progress, however, and in the 1980s, he introduced a daring formulation called "weak thought," which stripped metaphysics, science, religion, and all other absolute systems of their authority. Vattimo then became notorious both for his renewed commitment to the core values of Christianity (he was trained as a Catholic intellectual) and for the Vatican's denunciation of his views. Paterlini weaves his interviews with Vattimo into an utterly candid first-person portrait, creating a riveting text that is destined to become one of the most compelling accounts of homosexuality, history, politics, and philosophical invention in the twentieth century. (shrink)

Je pose une question concernant la place du Tractatus de Wittgenstein dans la tradition éthique. Le Tractatus et la tradition éthique Les remarques que je ferai sont à considérer dans le contexte d'une interprétation du Tractatus qui a été qualifiée de lecture résolue de cette œuvre, ainsi que de la philosophie de Wittgenstein en général Comme l'a écrit Cora Diamond, le Tractatus travaille sur la libération des besoins et des désirs philosophiques, une libération de la philosophie effectuée avec des outils (...) philosophiques : la situation du Tractatus est similaire à celle évoquée dans les Recherches et dans l'œuvre ultérieure, qui se consacre également au projet de se libérer de la philosophie pour le bien de la philosophie. (shrink)