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)

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)

In 2000, Rüdiger Thiele [1] found in a notebook of David Hilbert, kept in Hilbert's Nachlass at the University of Göttingen, a small note concerning a 24th problem. As Hilbert wrote, he had considered including this problem in his famous problem list for the International Congress of Mathematicians in Paris in 1900.

Are human rights universal, and, if so, in what sense? Starting with the opposition between "foundational" universalism (as articulated in modern natural law and rationalist liberalism) and "antifoundational" skepsis or relativism (from Jeremy Bentham to Richard Rorty) and steering a path beyond this dichotomy, an inquiry is made into the "rightness" of rights-claims, a question that calls for situated, prudential judgment. With specific reference to "Asian values," Henry Rosemont's emphasis is followed on the need to differentiate between "concept clusters" and (...) reflecting different modes of human flourishing--clusters that are neither radically incommensurable nor blandly uniform and exchangeable. What this emphasis suggests is that the globalism or universalism of human rights is not a pre-given premise but rather a challenge and practical task--requiring intensive inter-human and cross-cultural learning and (what Tu Wei-ming calls) the ongoing "humanization" of humankind. (shrink)

Bd. 1. 1791-1794.--Bd. 2. 1793-1795.--Bd. 3.--1794-1796.--Bd. 4. 1797-1798.--Bd. 5. 1798-1799.--Bd. 6. 1799-1800.--Bd. 7. 1800-1801.--Bd. 8. 1801-1806.--Bd. 9. 1806-1807.--Bd. 10. 1808-1812.

Globalization is often seen as a process of universal standardization under the auspices of market economics, technology, and hegemonic power. Resisting this process without endorsing parochial self-enclosure, Fred Dallmayr explores alternative visions that are rooted in distinct vernacular traditions and facilitate cross-cultural learning in an open-ended global arena.

Bd. 1. 1791-1794.--Bd. 2. 1793-1795.--Bd. 3.--1794-1796.--Bd. 4. 1797-1798.--Bd. 5. 1798-1799.--Bd. 6. 1799-1800.--Bd. 7. 1800-1801.--Bd. 8. 1801-1806.--Bd. 9. 1806-1807.--Bd. 10. 1808-1812.

In 2000, Rüdiger Thiele [1] found in a notebook of David Hilbert, kept in Hilbert's Nachlass at the University of Göttingen, a small note concerning a 24th problem. As Hilbert wrote, he had considered including this problem in his famous problem list for the International Congress of Mathematicians in Paris in 1900.

The market seems to have substituted politics as a coordination model in modern societies. While philosophy's complementarity to politics is well-acknowledged, its importance for economic markets can be questioned. Economics deals with optimization, but as markets are constituted by real persons with individual beliefs and normative values the economic tool box is not sufficient to describe market behavior. This is especially true whenever technologicalinnovations challenge established market rules. Philosophy supplies analytical instruments for a better, more complete description of markets including (...) theirnormative aspects. For this complementary function philosophy should be placed at the core of any theory of markets. (shrink)

"Each nation can do well, as in the life of individuals, only if things go equally well in all of her neighboring nations; the life of sciences is similar to that of states whose interest demands that everything be in order within individual states as properly as their relations be in good order among themselves. Understanding this correctly, the most important carriers of mathematical thoughts have always shown great interest in the law and order in neighboring sciences and, above all (...) for the benefit of mathematics, have cultivated the relations to the neighboring sciences, in particular to physics and epistemology. The essence of these relations and the ground of their fertility will be made most distinct, I believe, if I sketch to you that general method of inquiry which appears to grow more and more significant in modern mathematics; the axiomatic method, I mean." (David Hilbert, 1917). (shrink)

The article examines how the rules on formation of contract and on mistake, contained in the various transnational model rules that have been published over the past two decades, have taken shape. The approach adopted here is based on an analysis of the ‘textual stratification’ of European private law. The relevant instruments (Convention on Contracts for the International Sale of Goods, Principles of European Contract Law, UNIDROIT Principles of International Commercial Contracts, Draft Common Frame of Reference, Principes contractuels communs) are (...) analysed and compared in their historical sequence. To what extent and why have the texts been transformed in the process? The article demonstrates that there is a very considerable common ground reflecting the state of the art of comparative research in these fields over the past hundred years. It also highlights issues on which consensus must still be reached and it suggests patterns towards reaching such consensus. It is argued that the Principles of European Contract Law, rather than the Draft Common Frame of Reference, should provide the point of departure for future discussions. The scene for the article is set by a critical examination of the concepts of contract and legal act, as used in the Draft Common Frame of Reference. (shrink)

ExcerptIf recent discussions of Schmitt in these pages have made a broad case for the centrality of culture for his thinking, the current issue both specifies and generalizes this approach. The specificity derives from our focus on one key text by Schmitt that is often passed over but is in fact crucial for understanding his work. The generality is a result of the breathtaking sweep of issues that this text opens up for the contributors to this issue: the relation of (...) sovereignty to popular will, the ontological status of modernity, the role of myth in society, the representational structure of…. (shrink)

The present volume is devoted to the theme of Divine Father in Second Temple Jewish and early Christian tradition and in its ancient pagan contexts. It brings together proceedings of a conference under the same title, held in Gottingen in September 2011. Selected articles by well-known scholars focus on religious and philosophical concepts of divine parenthood in antiquity, from the Hebrew Bible and Second Temple Judaism (the Dead Sea Scrolls, Targums, Philo and Josephus) to the field of the New Testament. (...) In addition, the volume deals with the designation of deity as father or mother from the broad spectrum of ancient Egypt and classical antiquity (Homer, Hesiod, Plato, and its reception) to late antiquity (Plotinus and Porphyry).". (shrink)

Hermeneutik gilt heutzutage meistens als Bestandteil der Philosophie. Das ist aber eine verkürzte Sicht ihrer Gegenwart und erst recht ihrer Geschichte. Denn von Haus aus bezeichnet Hermeneutik alle Verfahren zur Auslegung von Texten. Sie begann in der Antike mit der Neu-Interpretation klassischer Dichter. Anschließend lernten die Christen die jüdische Bibel im Sinne ihres Evangeliums auszulegen. Sodann brauchte auch schriftliches Recht Interpretation, ebenso die philologisch-historische Quellenkritik der Geschichtswissenschaft. Jetzt erst führte die Philosophie die verschiedenen Varianten zu einer allgemeinen Hermeneutik zusammen. Daneben (...) hatten aber vier andere Wissenschaften eigene Auslegungstheorien und Methodenlehren entwickelt. Diese fünf Entwicklungspfade des gesamten Feldes werden hier zum ersten Mal von den Anfängen bis zur Gegenwart im Überblick dargestellt. (shrink)

"Fichte-Kolloquium zum 80. Geburtstag von Reinhard Lauth, Universiteat Genua, 19.-20. November 1999"--T.p. verso.

What follows shall provide an introduction to a predominantly philosophical and polemical, but historically revealing, paper on the foundations of the theory of probability. The leading Russian probabilist Aleksandr Yakovlevich Khinchin wrote the paper in the late 1930s, commenting on a slightly older, but still competing approach to probability theory by Richard von Mises. Together with the even more influential Andrey Nikolayevich Kolmogorov, who was nine years his junior, Khinchin had revolutionized probability theory around 1930 by introducing the modern measure-theoretic (...) approach, which is still standard today and which allowed for a sufficiently general treatment of important new notions such as “stochastic processes.” This development had its first culmination in Kolmogorov's booklet, Grundbegriffe der Wahrscheinlichkeitsrechnung, written in German in 1933, which has exerted an enormous influence world wide. (shrink)

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)

ArgumentIn the decade between 1983 and 1993, Herbert Mehrtens in West Berlin and I in East Berlin communicated closely about our parallel work on mathematics under the National Socialist (NS) regime. For a short period (1988–89), we worked on a joint book on this topic. We agreed that the book should be based primarily on empirical historical material, using a theoretical approach largely guided by Mehrtens’ work on social systems in mathematics (Mehrtens1981, 1987a). However, parallel work for his habilitation thesis (...) on modernity in mathematics increasingly captivated Mehrtens’ interests. This, together with ongoing resistance among older mathematicians and the insecurities of our individual careers during times of considerable political change, particularly in East Germany, led to the failure of our joint project.This paper aims at reconstructing—mostly by drawing on correspondence—parts of the dialogue between Mehrtens and me at the time. Our dialogue was influenced by our different upbringing and socialization in the two parts of Germany, and by different, though complementary, views about the combination of empirical and theoretical approaches to the historiography of mathematics.In the epilogue, I describe how my later work in the decades from the 1990s on the history of mathematics profited much from Mehrtens’ early theoretical and empirical work but was less influenced by his book on modernity. That later work of mine was, however, mostly done at a time when Mehrtens had largely left the field and considered himself increasingly as a “cultural scientist” (Kulturwissenschaftler). (shrink)

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)

This paper develops a semantics for a fragment of English that is based on the idea of `impossible possible worlds'. This idea has earlier been formulated by authors such as Montague, Cresswell, Hintikka, and Rantala, but the present set-up shows how it can be formalized in a completely unproblematic logic---the ordinary classical theory of types. The theory is put to use in an account of propositional attitudes that is `hyperfine-grained', i.e. that does not suffer from the well-known problems involved with (...) replacing expressions by logical equivalents. (shrink)

Force, Fate, and Freedom serves as an introduction to historical sociology, as well as a critical analysis of the belief in economic and political progress through social knowledge. Reinhard Bendix offers a development of the historicist approach to social change first championed by Max Weber, and presents an overview of the foundations of political authority in Japan, Russia, Germany, France, and England.