In this paper we introduce a Gentzen calculus for (a functionally complete variant of) Belnap's logic in which establishing the provability of a sequent in general requires \emph{two} proof trees, one establishing that whenever all premises are true some conclusion is true and one that guarantees the falsity of at least one premise if all conclusions are false. The calculus can also be put to use in proving that one statement \emph{necessarily approximates} another, where necessary approximation is a natural dual (...) of entailment. The calculus, and its tableau variant, not only capture the classical connectives, but also the `information' connectives of four-valued Belnap logics. This answers a question by Avron. (shrink)

Non-therapeutic circumcision violates boys’ right to bodily integrity as well as to self-determination. There is neither any verifiable medical advantage connected with the intervention nor is it painless nor without significant risks. Possible negative consequences for the psychosexual development of circumcised boys (due to substantial loss of highly erogenous tissue) have not yet been sufficiently explored, but appear to ensue in a significant number of cases. According to standard legal criteria, these considerations would normally entail that the operation be deemed (...) an ‘impermissible risk’—neither justifiable on grounds of parental rights nor of religious liberty: as with any other freedom right, these end where another person's body begins. Nevertheless, after a resounding decision by a Cologne district court that non-therapeutic circumcision constitutes bodily assault, the German legislature responded by enacting a new statute expressly designed to permit male circumcision even outside of medical settings. We first criticise the normative foundations upon which such a legal concession seems to rest, and then analyse two major flaws in the new German law which we consider emblematic of the difficulty that any legal attempt to protect medically irrelevant genital cutting is bound to face. (shrink)

The semantic valuations of classical logic, strong Kleene logic, the logic of paradox and the logic of first-degree entailment, all respect the Dunn conditions: we call them Dunn logics. In this paper, we study the interpolation properties of the Dunn logics and extensions of these logics to more expressive languages. We do so by relying on the \ calculus, a signed tableau calculus whose rules mirror the Dunn conditions syntactically and which characterizes the Dunn logics in a uniform way. In (...) terms of the \ calculus, we first introduce two different interpolation methods, each of which uniformly shows that the Dunn logics have the interpolation property. One of the methods is closely related to Maehara’s method but the other method, which we call the pruned tableau method, is novel to this paper. We provide various reasons to prefer the pruned tableau method to the Maehara-style method. We then turn our attention to extensions of Dunn logics with so-called appropriate implication connectives. Although these logics have been considered at various places in the literature, a study of the interpolation properties of these logics is lacking. We use the pruned tableau method to uniformly show that these extended Dunn logics have the interpolation property and explain that the same result cannot be obtained via the Maehara-style method. Finally, we show how the pruned tableau method constructs interpolants for functionally complete extensions of the Dunn logics. (shrink)

This book is a protest against some geopolitical agendas that are pushing the world toward a major global war and possibly toward a nuclear apocalypse. As an antidote, Fred Dallmayr issues a call to people everywhere to oppose this rush to destruction and to restore the "wholeness of humanity" through the quest for just peace.

In this paper we summarize some results about sets in Frege structures. The resulting set theory is discussed with respect to its historical and philosophical significance. This includes the treatment of diagonalization in the presence of a universal set.

In this paper I want to deal with game theory, experience and rationality, and I will try to put these into historical perspective.

In dem Aufsatz werden zwei wichtige Paradigmen für "kontinuierliche" empirische Reihen behandelt: erstens Reihen, deren Glieder stufenlos ineinander übergehende, wahrnehmbare Qualitäten sind, und zweitens Reihen von aufeinanderfolgenden Zeitpunkten. Dabei geht es vor allem um die Frage, welche logischen Voraussetzungen erforderlich sind, um derartige Reihen formal zu explizieren.Im ersten Teil wird Körners Auffassung untersucht, wonach die klassische, zweiwertige Logik keine adäquate Explikationsbasis für Qualitätsreihen darstellt. Körner bezieht sich dabei besonders auf den Begriff der empirischen Vagheit und den der empirischen Kontinuität. Es (...) wird gezeigt, daß Körners Position infolge zahlreicher logischer Schwierigkeiten zur Lösung der vorliegenden Probleme nicht ausreicht.Im zweiten Teil geht es hauptsächlich um Russells Zeittheorie. Insbesondere wird das Problem der Reduzierbarkeit von Zeitpunkten auf Zeitspannen und das Problem der Existenz von Zeitpunkten behandelt. Weiterhin werden einige Voraussetzungen angegeben, mit deren Hilfe die Dichte der Zeitreihe beweisbar is. (shrink)

A true systematic philosophy can only be, to quote Descartes, a "sagesse humaine". However,this is not a system that opens up to itself beyond what is systematic, being thus likewise capable of explaining in itself the most extreme problems of existence.

This paper is divided into a surveying and argumentative part and a slightly longer documentary part, which is meant to verify or at least make more plausible claims made in the first part. The first part deals in broad outline with the relationship of Frank and von Mises to the Vienna Circle of Logical Empiricism on the one hand and to the physicists and mathematicians in the German-speaking world on the other. The varying special positions, partly the non-conformity of the (...) two Austrian scientists are emphasized, in particular, their adherence to Ernst Mach’s epistemology and their shared interest in probability theory and applied mathematics. The impact of emigration and the after-effects in the U.S. are discussed. This leads to new insights into the fine structure of the Vienna Circle and the latter’s relationship to German academia within ‘Weimar Culture’. P. Forman’s interpretation (1971) of von Mises’ position is critically discussed. The second, documentary part, uses recently discovered correspondence between Frank and von Mises, and, to a lesser extent, von Mises’ personal diary. It aims at further substantiating some of the introductory theses and will at the same time provide material for a thorough biographical appreciation of the two scholars and friends. (shrink)

Diese Studie beschäftigt sich mit dem Status von empirischen Naturgesetzen in Immanuel Kants kritischer Philosophie. Insbesondere geht es um die Beantwortung der Frage, welche argumentativen Ressourcen Kant im Rahmen seines Ansatzes bereitstellt, um empirischen Naturgesetzen den Status der Notwendigkeit zuzusprechen. Außerdem wird geklärt, welche Art Notwendigkeit dabei erfüllt wird.

It is known that C. G. J. Jacobi wrote his first two letters to E. E. Kummer in the year 1834. Thanks to a find in the archive of the Mittag-Leffler Institute there is now the missing link , Kummer’s reply letter to Jacobi’s first letter. This letter seems to be the earliest one from Kummer still in existence (at least to a mathematician). Kummer tells in his letter about his situation as a teacher in Liegnitz, gives further a version (...) of his later paper on the summation of slowly convergent series and discusses Euler’s summation formula in connection with the practice of its use in numerical calculations. The article contains the complete texts of the three letters (up to those parts in Kummer’s letter identically contained in his published article) together with a commentary on their contents. (shrink)

SummaryIn Ethiopia, despite some recent improvements, the health and nutritional status of children is very poor. A better understanding of the main socioeconomic determinants of child health and nutrition is essential to address the problem and make appropriate interventions. In the present study, an attempt is made to explore the effect of maternal characteristics on the health and nutritional status of under-five children using the 2005 Ethiopian Demographic and Health Survey. The health and nutritional status of children are measured using (...) the two widely used anthropometric indicators height-for-age and weight-for-height. In the ordinary least squares estimation, it is observed that maternal characteristics have a significant impact on child health and nutritional status. The magnitudes of the coefficients, however, are found to slightly increase when maternal education is instrumented in the 2SLS estimation. Moreover, in the quantile regression estimation, the impacts of maternal characteristics are observed to vary between long-term and current child health and nutritional status. (shrink)