Hans Hahn

Lucky Gödel who, after his pièce célèbre on incompleteness of 1931, faced with enthusiasm the nascent science of mathematical logic. That very same year, he was invited to write a summary of the state of research in logic and foundations, under the title Mathematische Grundlagenforschung. His mathematics professor Hans Hahn made him also responsible for a Seminar on Mathematical Logic in Vienna in 1931/32, to which he contributed profusely through his results on completeness and incompleteness, and by many further results about the nature of intuitionistic logic.

Brouwer has, as is well known, put up the claim that the law of excluded middle is no reliable means of proof in mathematics. His justification is that for many a mathematical proposition, it is today completely out of the question to decide whether it is true or false – and such a decision is perhaps impossible in general. The claim that each proposition should be either true or false, completely disregarding whether one can determine the one or the other, that Brouwer holds to be senseless. Brouwer has later drawn various conclusions from his claim, in a more or less systematic way. It is only with his student Heyting that this question has been engaged with axiomatically. Namely, he has put up an axiom system for logic, more precisely the narrowest part of logic, the propositional calculus, from which the law of excluded middle cannot be derived.

This book is a record of a seminar on mathematical logic Kurt Gödel and Hans Hahn held in Vienna in 1931-32. The seminar proceedings, given in English translation, are a unique witness of the state of research in logic and foundations of mathematics right after Gödel had published his celebrated incompleteness theorems. The seminars explain Gödel's results in logic in detail, in contrast to his publications of the time that often were quite laconic and extremely short. This book also contains Gödel's trial lecture on intuitionistic logic held in Vienna in 1933. The manuscript, recently found among the Gödel papers kept in Princeton, is preserved in Gödel's forgotten German shorthand and published here in an English translation. The book also adds an important aspect to the intellectual history of Vienna, as both Gödel and Hahn were members of the Vienna Circle group of philosophers and scientists.

Material culture, strictly speaking, is substance culture. Nevertheless, studies on material culture are almost exclusively concerned with things. The specificities in the perception of substances and the related everyday practices are rarely taken into consideration. Although this can be explained by the history of anthropology, the bias towards associating material culture with “formed matter” is a foundational shortcoming. In consequence, particular perspectives on the material remain understudied, and the cultural relevance of substances as such is rarely taken into consideration. Taking a perspective grounded in anthropology and phenomenology, this article intends to provide new approaches to substances that elucidate the particular modes of their perception, reveal their characteristics and reflect on particular notions implicit to substances. The final section of this contribution discusses two exemplary studies on substances and proposes transformation and incorporation as new fields of research that would contribute to a more explicit engagement with substances in material culture studies

Autour du Manifeste de Vienne se trouvent reunis des textes fondateurs ecrits autour de 1929. Leurs auteurs: Carnap, Hahn, Neurath, Schlick l'ame du Cercle de Vienne, et Waismann plus proche de Wittgenstein, temoignent d'un courant philosophique constituant aujourd'hui la tradition analytique de source continentale a la fois empiriste et logique. Forme de maniere informelle a Vienne, au coeur de l'Europe, le Cercle reunissait des savants de differentes branches qui voulaient se donner une philosophie susceptible d' unifier leurs vues. Echo aux reves d'unite de la science, cette philosophie en exprime aussi le renversement complet. Veritable Discours de la methode, mais d'esprit anti-cartesien, elle entend reconstruire la science de maniere a evincer la speculation metaphysique, le but etant qu'aucun enonce ne soit laisse a l'exterieur de cette grande architecture de symboles s'il etait pourvu de sens. La declaration de guerre contre la metaphysique est un geste de militance a une epoque riche en differents manifestes. Incomprehensible en dehors du contexte socio-politique viennois de ces annees, elle porte aussi un programme de reconstruction rationnelle qui, au dela du langage de la science, devait toucher tous les secteurs de la vie. Plus complexe qu'il n'y parait, ce programme contient, en reference a Wittgenstein, son prestigieux representant a cote d'Einstein et Russell, une mise en garde contre differentes formes d'irrationalismes, qui est d'actualite.

Am Wiener Kreis scheiden sich die Geister, trat er doch mit dem dezidierten Anspruch auf, mit den Mitteln der modernen Logik den metaphysischen Schutt von Jahrtausenden aus dem Weg zu räumen. Statt einer homogenen Bewegung, die sich empiristischen Dogmen verschrieb, erscheint der Wiener Kreis in der philosophischen Forschung jedoch heute als eine heterogene Gruppe von eigenständigen Denkern, die gemeinsam die Grundlagen der modernen Wissenschaftstheorie legten. In jeweils spezifischer Weise setzten sie sich von der philosophischen Tradition ab oder versuchten, einzelne Teile davon in die wissenschaftliche Weltauffassung zu integrieren. Der Band enthält eine repräsentative Auswahl von Aufsätzen der Mitglieder des Wiener Kreises. Sie beschränkt sich mit Ausnahme dreier Frühschriften der Gründer bewußt auf die Jahre des historischen Kreises vom Beginn der Treffen 1924 bis zur Ermordung Schlicks 1936, obwohl einige der Hauptideen erst in den USA ihre volle Wirkung entfalteten und von dort Ende der sechziger Jahre wieder in die deutschsprachige Philosophie zurückwirkten. In ihrer Einleitung skizzieren die Herausgeber die historische Entwicklung des Kreises und erläutern die zentralen thematischen Fragestellungen. Die Anmerkungen identifizieren die internen wie externen Opponenten und erklären den Kontext der zeitgenössischen Wissenschaft.