In "The View from Above," Jeanne Haffner traces the evolution of the science of social space from the interwar period to the 1970s, illuminating in particular the role of aerial photography in this new way of conceptualizing socio-spatial ...

Dans cet article, je considère la pratique et la conception de la ri­gueur chez Richard Dedekind qui se dégagent de l’étude d’une sélection de ses travaux les plus importants. Une analyse des mentions multiples de réquisits de rigueur dans les textes de Dedekind amène à constater qu’il lie très étroi­tement la rigueur à la généralité. La première partie de l’article donne à voir les liens serrés tissés par Dedekind entre généralité et rigueur, dans sa théorie des fonctions algébriques co-écrite avec (...) H. Weber, ainsi que dans ses travaux fondationnels et dans ses travaux de théorie des nombres. Dans la seconde partie, j’examine les critères de rigueur qui apparaissent dans la pratique ma­thématique de Dedekind. Je discute l’idéal logique de rigueur dans l’essai de Dedekind sur les entiers naturels, étudié par M. Detlefsen sous l’appellation « Dedekind’s principle » ; puis je m’intéresse à la stratégie de Dedekind pour arithmétiser les mathématiques afin de mettre en évidence qu’il ne s’agit pas d’une approche guidée par un principe purement logique. Ainsi, l’idéal logique de rigueur apparaît comme intimement lié à la pratique d’une autre norme épistémique : la généralité, en lien avec la quête, par Dedekind, de définitions et preuves générales. Dans la dernière partie, j’analyse la demande de généra­lité et la pluralité de conceptions de la généralité que recouvre cette demande, et termine en mettant en avant la relation des définitions aux preuves et de quelle manière une définition générale se pose en condition de rigueur dans les mathématiques dedekindiennes. (shrink)

The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems. The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, (...) and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory. It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions. (shrink)

There is sufficient evidence from more recent experiments in psychology that equal retinal stimulus-elements do not lead to equal experiences and reactions except under certain rather specific conditions. An unsophisticated observer will find himself surprised to be able to cover with his own finger a person entering the door of his living room. When the finger is moved to the right or left, thus doing away with the precise retinal coincidence with the person, the observer will soon become unable to (...) recognize intuitively the actual retinal stimulus equality of the two distant things. This usually holds even for the case when he is making every inner effort towards an antagonistic, analytic perceptual attitude of the type which is used by painters or draughtsmen in order to represent the environmental situation in a similar way as it would project itself on a photographic plate or on a retina. (shrink)

This article raises the question of whether standard economics with the general equilibrium model at its core applies situational analysis in a Popperian sense. Contrary to Popper's own view, the authors come to the conclusion that this is not the case. Standard economics fails to represent elements essential to any social situation in an adequate manner. It comprises uncertainty, time and space, social interaction, unintended effects, as well as culture and institutions. The authors suggest, therefore, the socioeconomic context as an (...) alternative approach to analyzing social situations. It consists of four basic elements: (1) dominant worldviews, (2) institutions and technologies, (3) relative prices, and (4) political instruments. The alternative approach was applied with some success to analyzing inter alia problems of unemployment as well as of transformation. (shrink)

ABSTRACTPeople's relationship between positive and negative affect varies on a continuum from relatively independent to bipolar opposites, with stronger bipolar opposition being termed affective bipolarity. Experiencing more depressive symptoms is associated with increased bipolarity, but the processes underlying this relation are not yet understood. Here, we sought to replicate this link, and to examine the role of two potential mediating mechanisms: emotion regulation ability, and trait brooding. Drawing from the Dynamic Model of Affect, we hypothesised that a poor ability to (...) regulate negative emotion, and the tendency to brood over one's depressed feelings would predict stronger affective bipolarity, and mediate the relationship between depressive symptoms and affective bipolarity. To measure affective bipolarity, we calculated within-person affect correlations using two weeks of experience sampling data from a community sample. Mediation analyses indicated that baseline assessments o... (shrink)

In the Consolation of Ontology, Czech poet-philosopher Egon Bondy examines the substantial model of reality — the notion that there is some sort of substance, some "thing", idea, being, or principle that creates, underlies, transcends, or gives meaning to the universe in which we live. He shows how the substantial model, in both its theistic and mechanical materialist versions, is logically untenable and dangerous in its consequences. From there, Bondy shows how the nonsubstantial alternative — prefigured in the thinking (...) of cultures that developed independently of Greece — is simpler and more logically consistent. More importantly, it is free from the negative consequences of the substantial model and instead opens the way toward genuine human freedom, creativity, and responsibility, toward a corresponding and supportive form of social organization, and toward an unclouded understanding of ontological reality. Previously untranslated, the book asks that we leave behind comfortable assumptions and understand how the struggles for a genuinely human future and for ontological clarity presuppose each other and are mutually interdependent. (shrink)

Our century thinks scientifically. Nothing would be more plausible than that it has the same relation to the world as does Sein und Zeit. This, however, is not the case. For Heidegger, Science and Technology are essential characteristics of our time. Both are rooted in man insofar as he is a "Will to Will." Scientific man is man as subject. As such he does not wish to see the world the way it appears by itself but rather as a field (...) that may be tilled by him and is preordained for him and his activity. The world as the object of action does not merely come to man as a legacy; instead he violently grasps it and makes it his hunting ground. "Man becomes that Seiende, on which is based all Seiende in the manner of its Being and its Truth". Man of the machine-age does not allow for a world "where Being is as Being." The Subject "sets" its world and therefore has a Welt-bild and Welt-anschauungen, all of these being bifurcations indicating the separation of subject and world. A uniform world is replaced by Ego over against World. In this kind of "world" man makes God in his own image by setting the "world" as the stage for his Welt-anschauung, one which aims at utility and plasticity. Man is the director staging the world of his idea. As the objects which are handled have properties which reflect back on the producer, the directing is all the more dangerous. He who in everything that he thinks and does is staging himself might become the victim of his own production; the world of the calculating man has the character of its producer. "The calculating mind, adapting itself, invents 'values'. Value is the transformation of the Essence of Essence into the quantitative and the gigantic." In Holzwege Heidegger shows that the gigantic is a consequence of the way the subject places himself in the world. The world does not appear as what it is, but as what man makes of it. The world of the machine-age is a world-less world and the "world" as it is described in Sein und Zeit and more so in the essay "Vom Wesen des Grundes" does not appear in it. (shrink)

This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.

In this chapter, we will provide an overview of Richard Dedekind's work on continuity, both foundational and mathematical. His seminal contribution to the foundations of analysis is the well-known 1872 booklet Stetigkeit und irrationale Zahlen (Continuity and irrational numbers), which is based on Dedekind's insight into the essence of continuity that he arrived at in the fall of 1858. After analysing the intuitive understanding of the continuity of the geometric line, Dedekind characterized the property of continuity for the real numbers (...) in terms of what are nowadays called 'Dedekind cuts' on the rational numbers. This treatment, which can be characterized as being 'arithmetical' as well as 'axiomatic', will be presented in detail. To better position Dedekind's contributions in their historical context, we will also consider some of his more mathematical treatments of continuity in addition to his foundational work. Of particular interest is the definition of the Riemann surface in his joint work with Heinrich Weber (1882). Moreover, Dedekind's reflections on space and continuity in his unpublished papers 'Allgemeine Sätze über Räume' (General theorems about spaces; before 1870) and 'Beweis und Anwendungen eines allgemeinen Satzes über mehrfach ausgedehnte stetige Gebiete' (Proof and applications of a general theorem about multiply extended continuous domains; 1892) illustrate the wide range and general coherency of his thoughts. By discussing Dedekind's works in which the notion of continuity plays a central role, we will show how Dedekind's approaches became increasingly abstract, while at the same time retaining a common methodology. (shrink)

We capture the principal models of computation and specification in the literature by a uniform set of transparent mathematical descriptions which—starting from scratch—provide the conceptual basis for a comparative study.1.

Von den Spiralen.--Von den drei Sphären.--Von der Gefahr.--Von der Mitte.--Von den Gründen.--Von der Beliebtheit.--Vom Mythos der Sprache.--Von den Namen.--Von den Farben.--Vom Dichten, Denken, und Deuten.

This book, which brings together historians, philosophers and mathematicians, is a tribute to the works of Hourya Benis-Sinaceur, internationally recognized specialist of history and philosophy of mathematics.

Cet article étudie l’édition des œuvres de mathématiciens au xixe siècle Je me concentre sur une étude de cas : l’édition des œuvres du mathématicien allemand B. Riemann, par R. Dedekind et H. Weber, publiées pour la première fois en 1876, puis republiées en 1892 et en 1902, par Teubner, et partiellement traduites en français en 1898 chez Gauthier-Villars. Pour l’édition des textes de mathématiciens au xixe siècle, les éditeurs ne sont plus historiens ou philologues, mais eux-mêmes des mathématiciens de (...) premier plan. Le mathématicien éditeur devient celui qui à la fois lit et fabrique le texte à publier. Le cas des œuvres de Riemann est particulièrement intéressant, car une large majorité du travail éditorial s’est effectué par lettres. Ces lettres, ainsi que les Nachlässe de Riemann et Dedekind fournissent une documentation exceptionnellement riche. Il est possible d’obtenir une vision détaillée du processus d’édition. Après avoir replacé l’édition des œuvres de Riemann et ses rééditions dans leur contexte, j’étudierai certains choix faits par les éditeurs dans la sélection des textes à publier. Enfin, je considérerai la question des modifications et adaptations des textes de Riemann par les éditeurs. (shrink)