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)

While we are sympathetic to Balcetis’s approach, we feel that using motivational direction as the sole organizing structure for influences of affect on perception may be unnecessarily limiting. Three reasons for this concern are discussed.

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)

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.

La reconstruction est encore incomplète et lacunaire, mais l’on devine déjà l’allure complète du projet. Le trait les plus importants en sont les suivants. -/- i) Le premier niveau empirique correspond à ce que Piaget a appelé les tableaux perceptifs, et à leurs copies dans la mémoire, mais sans ordre temporel, sans structure spatiale et ne contenant pas encore des objets. ii) La première construction théorique permet d’obtenir le temps. iii) A partir de l’ordre temporel, une première structure spatiale (bidimensionnelle) (...) est possible, sans introduction de nouveaux niveaux théoriques. Ces niveaux théoriques semblent en revanche être nécessaires pour la construction d’une structure spatiale tri- dimensionnelle. Ce pas n’a pas encore été franchi. Il sera cer- tainement relié à la construction de la notion d’objet. iv) Ici la construction présente un premier grand vide. Un saut est effectué jusqu’à une théorie générale de la substance, appelée système physique. Il s’agit en réalité d’une théorie de la mesure, c’est-à-dire du procédé qui permet à la fois de connaître les propriétés des systèmes physiques, propriétés qui exigent un niveau théorique propre, et de définir un premier critère d’acceptation de l’identification des substances. Il s’agit d’une théorie holiste relative à l’introduction de termes théoriques. v) Cette description générale permet les premiers pas vers une théorie de la mécanique quantique. vi) Il est aussi possible dans le même cadre de recomprendre les notions élémentaires de la mécanique classique, sans présupposer les notions de masse et de force. vii) Dans d’autres travaux, qui ont servi de préparation à celui-ci, les notions de sujet, d’intersubjectivité et de conscience ont également été approchées d’une façon constructiviste. L’esquisse de la construction a même été prolongée jusqu’au domaine de la morale. Ces dernières notions ne font pas l’objet de cette recherche. -/- Ces éléments ont été évoqués ici pour donner une vision d’ensemble du projet, qui peut être visualisé dans le schéma suivant. (shrink)

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.

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)

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.

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.

J. S. Mill lays great emphasis on the importance of the notion of the individual as a progressive being. The idea that we need to conceive the self as an object of cultivation and perfection runs through Mill’s writings on various topics, and has played a certain role in recent interpretations. In this paper I propose a specific interpretation of Mill’s understanding of the self, along the lines of what Stanley Cavell identifies as a “perfectionist” concern for the self. Various (...) texts by Mill, ranging from the Logic to On Liberty, show an understanding of the self in which both the theoretical and the practical domain are presented as being internally connected to the transformation of the self. Mill elaborates a criticism of a notion of truth articulated by doctrines having a life independent of the self, as well as a notion of choice which is not the expression of one’s inner self. This internal relation of truth and choice to the self generates a special dialectic within the self, which Mill explores in On Liberty’s second and third chapters by means of several contrasts, such as passive vs. active knowledge, living vs. dead beliefs, or being oneself vs. liking and choosing in crowds. (shrink)

The article explores aspects of the notion of forms of life in the Wittgensteinian tradition especially following Iris Murdoch’s lead. On the one hand, the notion signals the hardness and inexhaustible character of reality, as the background needed in order to make sense of our lives in various ways. On the other, the hardness of reality is the object of a moral work of apprehension and deepening to the point at which its distinctive character dissolves into the family of connections (...) we have gained for ourselves. The two movements of thought are connected and necessary. (shrink)