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

Wilfred Sieg. Relative Consistency and Accesible Domains.

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.

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)

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)

There is a tension between the idea of popular sovereignty and our understanding that basic constitutional rights and liberties have a normative authority which is independent from the results of democratic decision‐making procedures. On the one hand there is the claim that the content of political justice, at least as far as the basic liberties are concerned, is to be fixed solely by substantive moral and political argument, while on the other there is the claim that it is the people (...) who determine the specific scheme of basic liberties that they live under. The apparent tension between the two claims can be resolved by introducing, firstly, a distinction between the concept of justice and the concept of legitimacy and, secondly, between proto‐rights and constitutional rights. Unlike constitutional rights, proto‐rights are moral, not legal, rights, and they are less specific than constitutional rights: one set of proto‐rights allows for various schemes of legal constitutional rights. Proto‐rights are part of the principles of justice and can be established only by substantive argument while constitutional rights have to be established by the procedures of democratic legitimization, and, therefore, they are a result of the exercise of popular sovereignty. The correlated distinctions between justice and legitimacy, and between proto‐rights and constitutional rights, allow us to specify the scope of the two claims and, hence, to affirm both simultaneously. The philosophical and legal relevance of the distinctions made is elucidated by a brief discussion of the constitutional rights of freedom of speech in the US and Germany. (shrink)

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California in 1988. (...) Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought. (shrink)

The highly ordered neuronal projections from the retina to the tectum mesencephali (optic tectum) in several vertebrate groups have been intensively studied. Several hypotheses so far have been proposed, suggesting mechanisms to explain the topographical and biochemical specificity of the retinotectal projections during ontogeny. In the present paper we compare the main hypotheses of retinotectal development with respect to the nature of specificity envisaged, the activity-dependence versus inheritance criterium and the strategy of argument, in casu the descriptive versus interferential type (...) of argument. Matching of the current developmental hypotheses and mechanisms for elimination or persistance of contralateral, respectively ipsilateral connections, is attempted with respect to the known neuroanatomical connectivity data in the amphibian optic tectum and with respect to the symmetry relations between ipsilateral and contralateral connection patterns described in amphibians and other vertebrate groups. Local mechanisms influencing the survival potential of synaptic contacts between retinal afferents and tectal neurons are probably essential for generating global symmetry patterns. Finally, a global topological approach is discussed with respect to its applicability in the amphibian retinotectal projection system. Basic assumptions of topological modeling appear to rely on anatomical and functional properties of the visual system like left-right symmetry, dichotomy, (absence of) convergence and segregation of fibers and neurons into columnar information units. It is concluded however, that more neuroanatomical, physiological and ultrastructural data are needed to establish a formalized operation model of the amphibian retinotectal system. (shrink)

In this article we prove that a certain intuitionistic version of the well-known fixed point theory \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\widehat{\rm ID}_1$\end{document} is conservative over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mbox{\sf HA}$\end{document} for almost negative formulas.

Wilfred Sieg. Mechanical Procedures and Mathematical Experience.

In this article we give a unifying approach to the theory of fundamental sequences and their related Hardy hierarchies of number-theoretic functions and we show the equivalence of the new approach with the classical one.

The Federation of Belgian companies is a confederation which groups 36 branch associations covering 30. 000 individual firms. About 85 % are small and medium-sizedfirms occupying less than 50 employees. The VBO/FEB is the most important exponent of the high degree of affiliation on the employers' side. The process of decision making reflects the structure of the federation. The mandate is defined in the board of the VBO/FEB, composed by a representative ofeach branch association. This representative holds his mandate on (...) the basis of the deliberations held in the elected board of his association. The guiding principle is consensus, which is not synonymous of unanimity. When a consistent and representative majority emerges from the debate, the members holding another opinion join that majority in a spirit ofemployers' solidarity. The decision making process aims in this way to combine efficiency and democracy. This is particularly important for the VBO/FEB, as that organisation not only acts as a lobby but also as a social partner able to conclude agreements. In the Belgian system, social partners are consulted by the authorities, because of their representativeness. It must however be clear that they may not interfere with the political decisions which in our democratic system rest with government and parliament. (shrink)

It is a remarkable fact that Hilbert's programmatic papers from the 1920s still shape, almost exclusively, the standard contemporary perspective of his views concerning (the foundations of) mathematics; even his own, quite different work on the foundations of geometry and arithmetic from the late 1890s is often understood from that vantage point. My essay pursues one main goal, namely, to contrast Hilbert's formal axiomatic method from the early 1920s with his existential axiomatic approach from the 1890s. Such a contrast illuminates (...) the circuitous beginnings of the finitist consistency program and connects the complex emergence of existential axiomatics with transformations in mathematics and philosophy during the 19th century; the sheer complexity and methodological difficulties of the latter development are partially reflected in the well known, but not well understood correspondence between Frege and Hilbert. Taking seriously the goal of formalizing mathematics in an effective logical framework leads also to contemporary tasks, not just historical and systematic insights; those are briefly described as “one direction” for fascinating work. (shrink)

The covariant and relativistic generalization of the Helmholtz integral vorticity theorems and Thomson's circulation theorem are derived.

While the Historische Kulturwissenschaft is introduced as a new way of writing history the question has to be answered what Kultur means or how it should be interpreted. The paper deals primarily with the special German notion of ‘Kultur’. The distinction between ‘intension’ and ‘extension’ is made and contrasted with both the narrow and the wide concept of ‘Kultur’. Writing history as new cultural history is shaped at least by five aspects: space, perspective, language, acting and time which are discussed (...) in this thesis. The intension of ‘Kultur’ in Historische Kulturwissenschaft leads to popularisation. The sense of the popular approach to history emphasizes modality in the conception and writing of history. (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)

We introduce a system of simply typed lambda terms and show that a rather comprehensive class of recursion equations on streams or non-wellfounded trees can be solved in our system. Moreover certain conditions are presented which guarantee that the defined functionals are primitive recursive. As a major example we give a co-recursive treatment of Mints’ continuous cut-elimination operator.

Etwa seit Beginn der 90er Jahre des letzten Jahrhunderts hat die innerdeutsche wie die internationale Wahrheitsdebatte einen ausserordentlichen und so nicht vorhersehbaren Aufschwung genommen. Dies lasst sich parallel auf philosophischem wie auf theologischem Gebiet beobachten - ein geistesgeschichtlich durchaus bemerkenswerter, vielleicht einzigartiger Umstand. Differenzierte Reflexe dieser erneuten Aufmerksamkeit fur Eigenart und Bedeutung des Wahrheitsproblems bieten auch die vier Beitrage des vorliegenden Bandes. Aus religionsgeschichtlicher, exegetischer und fundamentaltheologischer Perspektive nahern sie sich je auf ihre Weise einer Antwort auf diejenigen Fragen, die (...) in diesem Zusammenhang den Kern des Problems ausmachen: Was ist Wahrheit, christlich verstanden? Was ist Christentum in Wahrheit? Ist das Christentum wahr? (shrink)

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.".

The relativistic formulation of Hide's “magnetic analogue” of Ertel's potential vorticity theorem is Dirac's “new classical theory of electrons”.

[1] Textteil : Grundlagen, Prozeduren, Evaluation -- [2] Anhang : Interviewleitfaden, Tonbandtranskript und Auswertungsbeispiele.