On June 4, 1925, Hilbert delivered an address to the Westphalian Mathematical Society in Miinster; that was, as a quick calculation will convince you, almost exactly sixty years ago. The address was published in 1926 under the title Über dasUnendlicheand is perhaps Hilbert's most comprehensive presentation of his ideas concerning the finitist justification of classical mathematics and the role his proof theory was to play in it. But what has become of the ambitious program for securing all of mathematics, once (...) and for all? What of proof theory, the very subject Hilbert invented to carry out his program? The Hilbertian ambition reached out too far: in its original form, the program was refuted by Gödel's Incompleteness Theorems. And even allowing more than finitist means in metamathematics, the Hilbertian expectations for proof theory have not been realized: a constructive consistency proof for second-order arithmetic is still out of reach. Nevertheless, remarkable progress has been made. Two separate, but complementary directions of research have led to surprising insights: classical analysis can be formally developed in conservative extensions of elementary number theory; relative consistency proofs can be given by constructive means for impredicative parts of second order arithmetic. The mathematical and metamathematical developments have been accompanied by sustained philosophical reflections on the foundations of mathematics. This indicates briefly the main themes of the contributions to the symposium; in my introductory remarks I want to give a very schematic perspective, that is partly historical and partly systematic. (shrink)

Wilfred Sieg. Relative Consistency and Accesible Domains.

Wilfried Sieg and John Byrnes. AnModel for Parallel Computation: Gandy's Thesis.

Wilfred Sieg. Mechanical Procedures and Mathematical Experience.

David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations.

René Girard's stance towards the Western philosophical tradition was somewhat ambivalent. On the one hand, he acknowledged that major philosophers had influenced him and had contributed valuable insights on questions of desire, religion, violence, and the sacred. On the other hand, he felt that Western philosophy often, if not always, neglected the founding violence that lies at the origin of culture. The relevance of this contention is the pivotal question of the two volumes of René Girard and the Western Philosophical (...) Tradition. The chapters in these books engage the French anthropologist in a dialogue with key figures in the history of Western philosophy. Volume 1 features chapters on Plato, Augustine of Hippo, Niccolò Machiavelli, Thomas Hobbes, Blaise Pascal, Baruch Spinoza, Jean-Jacques Rousseau, Adam Smith, Immanuel Kant, Georg Wilhelm Friedrich Hegel, Friedrich Wilhelm Joseph Schelling, Alexis de Tocqueville, Søren Kierkegaard, as well as René Girard. Volume 2 features chapters on the pre-Socratics, Aristotle, René Descartes, Friedrich Nietzsche, Carl Schmitt, Martin Heidegger, Jean-Paul Sartre, Emmanuel Levinas, Simone Weil, Michel Foucault, Jacques Derrida, and Giorgio Agamben. (shrink)

Zuerst im 2CV, dann im umgebauten VW-Bus: Das Zürcher Fotografenpaar Margrit und Ernst Baumann, 1929 bzw. 1928 geboren, begann in den 1950er-Jahren rund um den Erdball zu reisen. Ihre Fotografien publizierten sie in Zeitschriften und Zeitungen wie Stern, Neue Zürcher Zeitung oder Das gelbe Heft und brachten so die Welt in die Wohnzimmer. Kosmopolitan und neugierig kamen sie zu Motiven mit Seltenheitswert: Farbporträts von Che Guevara gehören ebenso dazu wie Reportagen über die letzten Kopfjäger im ecuadorianischen Urwald. Ein Schwerpunkt dieser (...) reich bebilderten Doppelmonografie ist ihre Reise entlang der “Panamericana” 1957-1959, die Süd- und Nordamerika verbindet. Sie fotografierten Reportagen, Porträts und Landschaftsbilder und drehten den wohl ersten Farbfilm über den legendären Verkehrsweg. Dieser Film und ein Filporträt über die beiden Fotografen sind dem Buch auf DVD beigefügt. Das Buch präsentiert Funde aus ihrem Fotoarchiv - viele Bilder erstmals im Originalausschnitt - sowie Publikationen in Zeitschriften. Der Historiker und Schriftsteller Wilfried Meichtry erzählt vom ereignisreichen Leben des Paars, das sich zeitlebens als journalistische Handwerker verstanden hat. Der Fotohistoriker Markus Schürpf ordnet ihr Werk in die Foto- und Pressegeschichte ein, Nadine Olonetzky verfasst Begleittexte zu den Bildern. Eine Entdeckung in der Schweizer Fotogeschichte. (shrink)

Hilbert's finitist program was not created at the beginning of the twenties solely to counteract Brouwer's intuitionism, but rather emerged out of broad philosophical reflections on the foundations of mathematics and out of detailed logical work; that is evident from notes of lecture courses that were given by Hilbert and prepared in collaboration with Bernays during the period from 1917 to 1922. These notes reveal a dialectic progression from a critical logicism through a radical constructivism toward finitism; the progression has (...) to be seen against the background of the stunning presentation of mathematical logic in the lectures given during the winter term 1917/18. In this paper, I sketch the connection of Hilbert's considerations to issues in the foundations of mathematics during the second half of the 19th century, describe the work that laid the basis of modern mathematical logic, and analyze the first steps in the new subject of proof theory. A revision of the standard view of Hilbert's and Bernays's contributions to the foundational discussion in our century has long been overdue. It is almost scandalous that their carefully worked out notes have not been used yet to understand more accurately the evolution of modern logic in general and of Hilbert's Program in particular. One conclusion will be obvious: the dogmatic formalist Hilbert is a figment of historical (de)construction! Indeed, the study and analysis of these lectures reveal a depth of mathematical-logical achievement and of philosophical reflection that is remarkable. In the course of my presentation many questions are raised and many more can be explored; thus, I hope this paper will stimulate interest for new historical and systematic work. (shrink)

Wilfred Sieg and Dirk Schlimm. Dedekind's Analysis of Number: Systems and Axioms.

We establish by elementary proof-theoretic means the conservativeness of two subsystems of analysis over primitive recursive arithmetic. The one subsystem was introduced by Friedman [6], the other is a strengthened version of a theory of Minc [14]; each has been shown to be of considerable interest for both mathematical practice and metamathematical investigations. The foundational significance of such conservation results is clear: they provide a direct finitist justification of the part of mathematical practice formalizable in these subsystems. The results are (...) generalized to relate a hierarchy of subsystems, all contained in the theory of arithmetic properties, to a corresponding hierarchy of fragments of arithmetic. The proof theoretic tools employed there are used to re-establish in a uniform, elementary way relationships between various fragments of arithmetic due to Parsons, Paris and Kirby, and Friedman. (shrink)

This chapter contains section titled: Human Rights in Rawls's The Law of Peoples Human Rights as Universal Claim Rights Human Rights Minimalism and the Problem of Justification Acknowledgments Notes.

Wilfried Sieg. Calculations by Man and Machine: Mathematical Presentation.

Natural Formalization proposes a concrete way of expanding proof theory from the meta-mathematical investigation of formal theories to an examination of “the concept of the specifically mathematical proof.” Formal proofs play a role for this examination in as much as they reflect the essential structure and systematic construction of mathematical proofs. We emphasize three crucial features of our formal inference mechanism: (1) the underlying logical calculus is built for reasoning with gaps and for providing strategic directions, (2) the mathematical frame (...) is a definitional extension of Zermelo–Fraenkel set theory and has a hierarchically organized structure of concepts and operations, and (3) the construction of formal proofs is deeply connected to the frame through rules for definitions and lemmas. To bring these general ideas to life, we examine, as a case study, proofs of the Cantor–Bernstein Theorem that do not appeal to the principle of choice. A thorough analysis of the multitude of “different” informal proofs seems to reduce them to exactly one. The natural formalization confirms that there is one proof, but that it comes in two variants due to Dedekind and Zermelo, respectively. In this way it enhances the conceptual understanding of the represented informal proofs. The formal, computational work is carried out with the proof search system AProS that serves as a proof assistant and implements the above inference mechanism; it can be fully inspected at (see link below). (shrink)

Dedekind’s structuralism is a crucial source for the structuralism of mathematical practice—with its focus on abstract concepts like groups and fields. It plays an equally central role for the structuralism of philosophical analysis—with its focus on particular mathematical objects like natural and real numbers. Tensions between these structuralisms are palpable in Dedekind’s work, but are resolved in his essay Was sind und was sollen die Zahlen? In a radical shift, Dedekind extends his mathematical approach to “the” natural numbers. He creates (...) the abstract concept of a simply infinite system, proves the existence of a “model”, insists on the stepwise derivation of theorems, and defines structure-preserving mappings between different systems that fall under the abstract concept. Crucial parts of these considerations were added, however, only to the penultimate manuscript, for example, the very concept of a simply infinite system. The methodological consequences of this radical shift are elucidated by an analysis of Dedekind’s metamathematics. Our analysis provides a deeper understanding of the essay and, in addition, illuminates its impact on the evolution of the axiomatic method and of “semantics” before Tarski. This understanding allows us to make connections to contemporary issues in the philosophy of mathematics and science. (shrink)

English summary: Does pastoral care require ethical competence in order to fulfil its task properly? And, conversely, to what extent does ethical reflection require feedback from pastoral experience in order to remain true to life and of practical relevance? Wilfried Sturm examines the way hospital pastors deal with ethical challenges and conflict situations in neonatal clinics and enquires into the insights that can be gained from them for the relationship of pastoral care and ethics. German description: Braucht Seelsorge ethische (...) Kompetenz, um ihrem Auftrag gerecht zu werden? Inwiefern bedarf umgekehrt die ethische Reflexion der Ruckkopplung an seelsorgerliche Erfahrung, um lebensnah und praxisrelevant zu bleiben? Wilfried Sturm untersucht den Umgang von Klinikseelsorgerinnen und -seelsorgern mit ethischen Herausforderungen und Konfliktsituationen in der Fruh- und Neugeborenenmedizin und fragt, welche Einsichten sich daraus fur das Verhaltnis von Seelsorge und Ethik gewinnen lassen. (shrink)

The paper discusses the problem of global distributive justice. It proposes to distinguish between principles for the domestic and for the global or intersocietal distribution of wealth. It is argued that there may be a plurality of partly diverging domestic conceptions of distributive justice, not all of which need to be liberal egalitarian conceptions. It is maintained, however, that principles regulating the intersocietal distribution of wealth have to be egalitarian principles. This claim is defended against Rawls's argument in The Law (...) of Peoples that egalitarian principles of distributive justice should not be applied globally. Moreover, it is explained in detail, why Rawls's “duty of assistance to burdened societies” cannot be an appropriate substitute for a global principle of distributive justice. (shrink)

This paper will address René Girard’s critique of the “humanization of nothingness” in modern Western philosophy. I will first explain how the “desire for death” is related to a phenomenon that Girard refers to as “obstacle addiction.” Second, I will point out how mankind’s desire for death and illusory will to self-divinization gradually tend to converge within the history of modern Western humanism. In particular, I will show how this convergence between self-destruction and self-divinization gradually takes shape through the evolution (...) of the concept of “the negative” from Hegel to Kojève, Sartre and Camus. Finally, we shall come to see that in Girard’s view “the negative” has tended to become an ever-preoccupying and unacknowledged symptom of mankind’s addiction to “model/obstacles” of desire. (shrink)

The main contention of this article is that, since the 20th century, violence has gradually turned into a purely technological concept. This great change amounts to a paradigm shift which can be traced back to Johan Galtung’s seminal article “Violence, Peace, and Peace Research” (1969). First, I show why the traditional view of violence revolving around the notions of force, intent and harm has been thrown into crisis by the technological evolution of the Western world. Second, I indicate how Galtung’s (...) thorough redefinition of violence as “the cause of the difference between the potential and the actual” proves more compatible to technological societies. Finally, I suggest that this new definition of violence has become ever more appealing today in the age of artificial intelligence. (shrink)

The Belgian polyarchy has developed into a «particracy» in which the political parties have a preponderant impact on the political decisionmaking.As in every polyarchy, the political parties fulfill a set of vital functions in the Belgian system. But that does not explain its «particratie» particularity. The particracy arises as a consequence of four factors. The parties are fixed by the «zuilen» into an «internal-imperialistic» role. The power of the parties increased considerably, an increase of which the politization of the instruments (...) for, and the agencies of, policy is one of the most important, together with the capability of making and unmaking issues. The impact and power of the opponents of the parties in the decision-making process have been diminished to a considerable extent. This weakening involves the king, the parliament, theadministration, the electorate, and, ultimately, the cabinet because of the growing impact of the parties on policy design and policy output as well as on the appointment of ministers. Finally, the choice of the consociational pattern of politics of accomodation by the elite indicates the instrumental function of particracy in Belgian politics. (shrink)

This commentary focuses on Hommel et al.'s inferences on action planning. It discusses the relevance of anticipated extrinsic movement effects for action control, the problems of a feature-based representation of actions, and the necessity of the acquisition of conditional movement-effect associations.

We still lack an operational theory for a complete analysis of early socialization processes. Bourdieu has stressed their bodily dimension but has done so at the expense of more symbolic aspects. This theoretical option corresponds to a very general goal of the Bourdieusian theory of practice: analysing sociality without suffering an intellectualist bias. However, symbolic activity and socializing language in particular can be approached as a practical phenomenon (i.e. habitual, informal, unconscious, etc.). From this viewpoint, the sociology of embodiment may (...) have much to learn from cultural psychology, which has focused on early language as it is naturally performed – when people speak to children, and when children speak. The work of cultural psychologists on the role of everyday words and narratives in the making of the self can be extended through a sociological ethnography of language. The features and interests of such an ethnography are discussed in the final section of the article, on the basis of fieldwork conducted in a nursery. This final development illustrates and analyses the concrete appropriation of caregiver injunctions by 2- to 3-year-old children. (shrink)

Thema der vorliegenden Arbeit ist der dialektische Gehalt der wichtigsten bildungstheoretischen Abhandlungen des padagogischen Theoretikers Josef Derbolav. Ergebnis der zum grossten Teil immanent durchgefuhrten Analyse ist der Aufweis, dass Derbolav die dialektische Fassung didaktischer, anthropologischer und handlungstheoretischer Prinzipien aufgrund metaphysischer Denkstrukturen nicht oder nur teilweise gelingt. Inwieweit einige dieser Prinzipien dialektisches Potential enthalten konnten, zeigt der Verfasser anhand der Entwicklung eines eigenen, an der hermeneutischen Philosophie orientierten dialektischen Standpunktes.".

Les vœux du nouvel an à la nation constituent un genre d’allocutions présidentielles traditionnellement rattachées aux grands discours du Président de la République. Le temps du bilan de l’année écoulée, de même que l’annonce de l’agenda politique pour l’année qui suit, sont autant de sujets dans la communication politique de l’Élysée pour s’adresser aux citoyens et leur parler d’eux-mêmes, du pays, du récit national en cours et à écrire. Le cas échéant, les vœux aux Français constituent une opportunité dans le (...) calendrier pour actualiser la vision ou le projet politique que porte le Président, renouveler aussi l’image de celui-ci dans le regard du citoyen. Cependant, la scène englobante d’énonciation infléchit ce genre discursif vers un certain lyrisme : la solennité du 31 décembre appelle en effet un temps de pause pour porter un regard réflexif sur l’expérience citoyenne empirique, en particulier sur le « faire commun » en tant que membre de la communauté nationale. Dans ce contexte d’énonciation, le discours du chef de l’État met donc en jeu et actualise l’imaginaire social collectif autour du sentiment d’appartenance à un destin national évocateur. Or, si le pathos est bien inscrit dans l’écriture des vœux du nouvel an à la nation, son emploi surprend l’auditeur ou le lecteur attentif car il déjoue l’empathie du Président envers le citoyen et réoriente l’usage de ces discours. La rhétorique du pathos dans les vœux a tendance au contraire à inverser le rapport d’identification et d’adhésion du citoyen à un projet pour la nation dicté par le chef de l’État. Et cette intention politique sous-jacente se joue notamment dans les ressorts stylistiques de la littérarité et dans le travail sur le verbe présidentiel prétendument lyrique et porteur d’une proposition de récit actualisé et souhaité au nom de et pour la nation française. (shrink)

L'ambition de cet ouvrage est d'illustrer à la fois comment la philosophie conceptualise le conflit et comment elle s'efforce d'en résoudre les dangers inhérents. Plutôt que de proposer un aperçu purement abstrait de la notion de « conflit », l'ensemble des travaux se focalise sur la confrontation des philosophes à des problèmes historiques tels que la guerre, la dissension sociale, la tyrannie, ou encore le sport. -/- .