サイエンス・ウォーズそのものを扱った長編論文。サイエンス・ウォーズという現象が起きた理由を理論的に跡づけるために、その学問的背景に関する分析の試み。そして、ケーススタディという構成。.

Ce texte propose un essai d’interprétation des contes de Kenji Miyazawa à la lumière de la théorie de l’imagination matérielle de Gaston Bachelard. Il s’agit d’une mise à l’épreuve de ce cadre conceptuel dans un contexte culturel totalement différent. Ces contes de fées japonais sont relus en fonction de leurs évocations des quatre éléments d’Empédocle. Ces quatre éléments révèlent une source d’inspiration inconsciente des expressions et des intrigues de cet auteur japonais. Dans son cas, je montrerai que la terre est (...) l’élément dominant. (shrink)

We propose an idea called ``ontology reuse'' to develop ontology (or taxonomy) for information search more easily by its development cost reduction. For its feasibility demonstration, we developed a prototype system that converts taxonomy information of web contents to RDF format, collects it into a server and visualizes taxonomy infomation as a 2D map for editing itself and searching information. And our goal is to realize ``ontology circulation'', which means that ontology information flows freely and easily over the Internet and (...) an intranet. (shrink)

This paper axiomatizes a recursive utility model that captures both intertemporal utility smoothing defined across time and ambiguity aversion defined over states. The resulting representation adapts Wakai model of intertemporal utility smoothing as an aggregator function, where the utility of the certainty equivalent of future uncertainty is computed by Gilboa and Schmeidler multiple-priors utility. The model also permits the separation of intertemporal utility smoothing from ambiguity aversion.

Die Arbeit verbindet in subtiler Weise begriffsgeschichtliche, quellengeschichtliche, kontextanalytische und kompositionsanalytische Fragestellungen, um die schwierigen Probleme, die die Freiheitsantinomie der Kritik der reinen Vernunft aufwirft, einer Losung naherzubringen. Dabei wird deutlich, wie sehr Kants Freiheitsantinomie in ihrer Formulierung von den Diskussionen abhangt, die in dem Zeitraum zwischen Wolff und Tetens gefuhrt worden sind. Auch Kants beruhmte Dissertation des Jahres 1770 erscheint so in neuem Licht. Kants Freiheitsantinomie erweist sich als Antwort auf Fragen seiner unmittelbaren Vorganger. This work combines issues pertaining (...) to the history of concepts, historical sources, context analysis and composition analysis in order to try to solve the problems posed by the antinomy of freedom in the Critique of Pure Reason. The study makes it clear how much the wording of Kant's antinomy of freedom depends on the discussions held during the time between Wolff and Tetens. Kant's famous dissertation of 1770 is thus also seen in a new light. Kant's antinomy of freedom is shown to be the answer to the questions posed by his direct predecessors. (shrink)

Der Leipziger Pietist Chr. A. Crusius setzt sich mit dem von Leibniz und Wolff festgelegten „Satz vom zureichenden Grund“ auseinander, nach dem nicht nur jedes Naturgeschehnis, sondern auch jede Handlung des Menschen a priori determiniert zu verstehen ist. Zunächst kritisiert Crusius die Vieldeutigkeit des Begriffs „Grund“, wo er zunächst zwischen „Realgrund“ und „Erkenntnisgrund“ unterscheidet, und weiterhin ersteren in „wirkende Ursache“ und „Existentialgrund“, und letzteren in „Erkenntnisgrund a priori“ und „Erkenntnisgrund a posteriori“ einteilt. Nach Crusius hat menschliche freie Handlung keinen eindeutig (...) determinierenden Grund, sondern nur wirkende Ursache, die jeder seinerseits ablehnen kann. Crusius gründet seinen Freiheitsbegriff auf die Wahrscheinlichkeitslehre, nach der freie Handlungen wegen der Endlichkeit des Menschen nur a posteriori erkannt werden. In meinem Beitrag versuche ich zu zeigen, dass im Freiheitsbegriff von Crusius, der „Grundtätigkeit der Freiheit“, ein Muster der Vereinbarkeit von der empirisch orientierten Freiheit und dem Determinismus einzusehen ist. (shrink)

We discuss the work of Paul Cohen in set theory and its influence, especially the background, discovery, development of forcing.

Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions cast in set-theoretic terms and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by some of its great developers. This has encouraged the exaggeration of crises in foundations and of metaphysical doctrines in general. However, (...) set theory has proceeded in the opposite direction, from a web of intensions to a theory of extensionpar excellence, and like other fields of mathematics its vitality and progress have depended on a steadily growing core of mathematical structures and methods, problems and results. There is also the stronger contention that from the beginning set theory actually developed through a progression ofmathematicalmoves, whatever and sometimes in spite of what has been claimed on its behalf.What follows is an account of the development of set theory from its beginnings through the creation of forcing based on these contentions, with an avowedly Whiggish emphasis on the heritage that has been retained and developed by current set theory. The whole transfinite landscape can be viewed as the result of Cantor's attempt to articulate and solve the Continuum Problem. (shrink)

For the modern set theorist the empty set Ø, the singleton {a}, and the ordered pair 〈x, y〉 are at the beginning of the systematic, axiomatic development of set theory, both as a field of mathematics and as a unifying framework for ongoing mathematics. These notions are the simplest building locks in the abstract, generative conception of sets advanced by the initial axiomatization of Ernst Zermelo [1908a] and are quickly assimilated long before the complexities of Power Set, Replacement, and Choice (...) are broached in the formal elaboration of the ‘set of’f {} operation. So it is surprising that, while these notions are unproblematic today, they were once sources of considerable concern and confusion among leading pioneers of mathematical logic like Frege, Russell, Dedekind, and Peano. In the development of modern mathematical logic out of the turbulence of 19th century logic, the emergence of the empty set, the singleton, and the ordered pair as clear and elementary set-theoretic concepts serves as amotif that reflects and illuminates larger and more significant developments in mathematical logic: the shift from the intensional to the extensional viewpoint, the development of type distinctions, the logical vs. the iterative conception of set, and the emergence of various concepts and principles as distinctively set-theoretic rather than purely logical. Here there is a loose analogy with Tarski's recursive definition of truth for formal languages: The mathematical interest lies mainly in the procedure of recursion and the attendant formal semantics in model theory, whereas the philosophical interest lies mainly in the basis of the recursion, truth and meaning at the level of basic predication. Circling back to the beginning, we shall see how central the empty set, the singleton, and the ordered pair were, after all. (shrink)

Ernst Friedrich Ferdinand Zermelo transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framework for the development of modern set theory. Two (...) decades later Zermelo promoted a distinctive cumulative hierarchy view of models of set theory and championed the use of infinitary logic, anticipating broad modern developments. In this paper Zermelo's published mathematical work in set theory is described and analyzed in its historical context, with the hindsight afforded by the awareness of what has endured in the subsequent development of set theory. Elaborating formulations and results are provided, and special emphasis is placed on the to and fro surrounding the Schröder-Bernstein Theorem and the correspondence and comparative approaches of Zermelo and Gödel. Much can be and has been written about philosophical and biographical issues and about the reception of the Axiom of Choice, and we will refer and defer to others, staying the course through the decidedly mathematical themes and details. (shrink)

Kurt Gödel with his work on the constructible universeLestablished the relative consistency of the Axiom of Choice and the Continuum Hypothesis. More broadly, he ensured the ascendancy of first-order logic as the framework and a matter of method for set theory and secured the cumulative hierarchy view of the universe of sets. Gödel thereby transformed set theory and launched it with structured subject matter and specific methods of proof. In later years Gödel worked on a variety of set theoretic constructions (...) and speculated about how problems might be settled with new axioms. We here chronicle this development from the point of view of the evolution of set theory as a field of mathematics. Much has been written, of course, about Gödel's work in set theory, from textbook expositions to the introductory notes to his collected papers. The present account presents an integrated view of the historical and mathematical development as supported by his recently published lectures and correspondence. Beyond the surface of things we delve deeper into the mathematics. What emerges are the roots and anticipations in work of Russell and Hilbert, and most prominently the sustained motif of truth as formalizable in the “next higher system”. We especially work at bringing out how transforming Gödel's work was for set theory. It is difficult now to see what conceptual and technical distance Gödel had to cover and how dramatic his re-orientation of set theory was. (shrink)

Set theory, it has been contended, developed from its beginnings through a progression ofmathematicalmoves, despite being intertwined with pronounced metaphysical attitudes and exaggerated foundational claims that have been held on its behalf. In this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership (...) distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his well-known paradox, an early expression of our motif. The motif becomes fully manifest through the study of functionsof the power set of a set into the set in the fundamental work of Zermelo on set theory. His first proof in 1904 of his Well-Ordering Theoremis a central articulation containing much of what would become familiar in the subsequent development of set theory. Afterwards, the motif is cast by Kuratowski as a fixed point theorem, one subsequently abstracted to partial orders by Bourbaki in connection with Zorn's Lemma. Migrating beyond set theory, that generalization becomes cited as the strongest of fixed point theorems useful in computer science.Section 1 describes the emergence of our guiding motif as a line of development from Cantor's diagonal proof to Russell's Paradox, fueled by the clarification of the inclusion vs. membership distinction. Section 2 engages the motif as fully participating in Zermelo's work on the Well-Ordering Theorem and as newly informing on Cantor's basic result that there is no bijection. Then Section 3 describes in connection with Zorn's Lemma the transformation of the motif into an abstract fixed point theorem, one accorded significance in computer science. (shrink)

On the occasion of his 70th birthday, the work of Adrian Mathias in set theory is surveyed in its full range and extent.

We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higher-order reflection principles.

This article serves to present a large mathematical perspective and historical basis for the Axiom of Replacement as well as to affirm its importance as a central axiom of modern set theory.

Azriel Levy did fundamental work in set theory when it was transmuting into a modern, sophisticated field of mathematics, a formative period of over a decade straddling Cohen’s 1963 founding of forcing. The terms “Levy collapse”, “Levy hierarchy”, and “Levy absoluteness” will live on in set theory, and his technique of relative constructibility and connections established between forcing and definability will continue to be basic to the subject. What follows is a detailed account and analysis of Levy’s work and contributions (...) to set theory. (shrink)

(2005). The Problem of Vitalism Revisited. Angelaki: Vol. 10, continental philosophy and the sciences the french tradition issue editor: andrew aitken, pp. 13-26.