Leibniz was an outstanding mathematician of the 17th century and one of the most original philosophers of European history. Against this background it is astonishing that the ideas of Leibniz concerning probability have to date not been appreciated by mathematicians and philosophers. In this article the most important work of Leibniz with respect to probability theory, his De incerti aestimatione , is analysed. Here Leibniz deals with the 'problem of points', the then famous problem as to how to divide justly (...) the stake when two players have to break off a number of prearranged games. The correspondence between Fermat and Pascal about this problem is regarded as the birth of probability theory. Yet, Leibniz favoured another solution to both of these. We reconstruct the underlying normative ideas of Leibniz and of Fermat and Pascal and show that they are equally sound and justifiable. (shrink)

Probability theory developed in history from problems concerning the fairness of games. The historical development of the associated theory of stochastic fairness is described using concepts embodied in the structuralist meta‐theory. The justification of the theory is discussed using an approach derived from J. Rawls.

Are empirical theories empirically testable? In this article Theoretische Begriffe und die Prüfbarkeit von Theorien V. Gadenne comes to the conclusion that theories are testable. On this basis he criticizes the non-statement view which asserts the contrary. It is shown that this criticism, however, is erroneous.

One of the most famous critiques of the Leibnitian calculus is contained in the essay “The Analyst” written by George Berkeley in 1734. His key argument is those on compensating errors. In this article, we reconstruct Berkeley's argument from a systematical point of view showing that the argument is neither circular nor trivial, as some modern historians think. In spite of this well-founded argument, the critique of Berkeley is with respect to the calculus not a fundamental one. Nevertheless, it highlights (...) central aspects of the calculus that are characteristic of modern scientific theories. (shrink)

A main subject of philosophy of science is the reconstruction of scientific theories. Not only scientists are holding theories but everybody else, namely theories about everyday knowledge. In this article two geometric theories of this kind are reconstructed. The reconstruction is performed under the structuralist view of theories. It turns out that there are important differences between scientific theories and everyday theories, concerning the intended applications as well as the logical status of the concepts.

Leibniz is one of the founders of calculus, a starting point of modern mathematics. A crucial point in the understanding of Leibniz' calculus is the concept of differential, especially differential of higher order. In this article we discuss the first successful application of differentials of higher order, namely the determination of the radius of curvature. 1692 Jakob Bernoulli determined three formulas for this radius. Leibniz was not satisfied with the proofs of Bernoulli and published two years later a new elegant (...) deduction. The article is a reconstruction of Bernoulli's and Leibniz' approaches showing the ingenious work of Leibniz in this field. (shrink)

In the history of mathematics Leibniz as one of the scientists who developed the calculus of differentials has an outstanding position. However, it is difficult to reconstruct his theory in a consistent way. The main problem is the concept of differential. For an adequate understanding of this concept it is necessary to analyze how it is used. In this article we deal with the first systematic formulation of Leibniz' calculus, the Lectiones de calculo differentialium of Johann Bernoulli from 1691/92. It (...) will be proved that Leibniz's theory is consistent and can be reconstructed as an empirical theory - concerning physical curves - within the structuralist metatheory. The concept of differential is a theoretical one in respect to this theory. (shrink)

For an appropriate understanding of Leibniz's calculus the concept of differential is a crucial one. In Die Differentialrechnung nach Leibniz -eine Rekonstruktion (published in this journal in 2001) the calculus differentialis of Leibniz was analysed. In this paper we deal with the first systematic formulation of the calculus integralis, the Lectiones mathematicae de methodo integralium aliisque of Johann Bernoulli from 1691/92. It will be pointed out that Leibniz's theory is consistent and can be reconstructed as an empirical theory within the (...) structuralist metatheory. (shrink)

The following article is a response to K. Mainzer's ‘Knowledge-Based Systems; Remarks on the Philosophy of Technology and Artificial Intelligence’. We show, that Mainzer does not reach any of his aimsto analyse the possibilities and limits of AI-technology.to reduce anxiousness and hostility against AI, which is motivated by phantastic speculations.to evaluate the factual impact of AI on our lives and on society.His article contributes on the contrary to phantastic speculations, which are not technologically justified in any way. There are two (...) main reasons for his misleading view: (a) the state of the art of knowledge-based systems is incorrectly described; (b) the roots, paradigms and alternatives to AI are not in the least sufficiently analysed. We examine issues (a) and (b) in Chapter 1 and Chapter 2. In Chapter 3 we discuss, how the conclusions, which Mainzer draws, have to be modified. In analysing the lines of argumentation of Mainzer we try to clarify the methodological errors and the philosophical attitude of Mainzer, which is in many respects not adequate to the subject of the article. (shrink)

Fifty years ago Hartman studied the barrier transmission time of wave packets (J Appl Phys 33:3427–3433, 1962). He was inspired by the tunneling experiments across thin insulating layers at that time. For opaque barriers he calculated faster than light propagation and a transmission time independent of barrier length, which is called the Hartman effect. A faster than light (FTL or superluminal) wave packet velocity was deduced in analog tunneling experiments with microwaves and with infrared light thirty years later. Recently, the (...) conjectured zero time of electron tunneling was claimed to have been observed in ionizing helium inside the barrier. The calculated and measured short tunneling time arises at the barrier front. This tunneling time was found to be universal for elastic fields as well as for electromagnetic fields. Remarkable is that the delay time is the same for the reflected and the transmitted waves in the case of symmetric barriers. Several theoretical physicists predicted this strange nature of the tunneling process. However, even with this background many members of the physics community do not accept a FTL signal velocity interpretation of the experimental tunneling results. Instead a luminal front velocity was calculated to explain the FTL experimental results frequently. However, Brillouin stated in his book on wave propagation and group velocity that the front velocity is given by the group velocity of wave packets in the case of physical signals, which have only finite frequency bandwidths. Some studies assumed barriers to be cavities and the observed tunneling time does represent the cavity lifetime. We are going to discus these continuing misleading interpretations, which are found in journals and in textbooks till today. (shrink)

Sein und Bewußtsein, zwei Kernbegriffe der modernen Bewußtseinsphilosophien, vor allem seit Kant, werden von diesen immer im Gegensatz zur traditionellen Metaphysik bestimmt, obwohl sie ihr der Sache nach entstammen. Die vorliegende Untersuchung beabsichtigt, in einer Gegenüberstellung von Aristoteles und Kant neben dem Verschiedenen auch das Gemeinsame zwischen den traditionellen und den modernen Auffassungen der beiden Begriffe herauszustellen und zu erörtern. Im Ergebnis finden sich Gesichtspunkte, wonach sich die beiden Auffassungen gwissermaßen ergänzen könnten: Die modernen gehen mit dem Bewußtsein auf eine (...) subjektive Erkenntnisbedingung, die traditionellen mit dem Sein der Dinge auf eine objektive reale Erkenntnisvoraussetzung. Die Untersuchung berücksichtigt auch nachkantianische Bewußtseinstheorien (Reinhold, Brentano, Husserl) sowie gegenwärtige Spezialliteratur, in der Absicht, etwas zur Klärung der beiden Begriffe Sein und Bewußtsein beizutragen: Sie erweisen sich als unlösbar aufeinander bezogen. (shrink)

“Analytical construct. The Culture as construct and the constitution of the social – fallowing Max Weber”. The key of this paper is the chalange to determinate theplace of the cultural sociology in the context of the general sociology and of the other cultural sciences, like cultural anthropology and ethnology. For doing that it is necessary to analize Max Weber’s concept: Gedankenbild.

Seit dem byzantinischen Bilderstreit und dem Bildersturm der Reformation ist nicht mehr in solcher Intensität über Bilder nachgedacht worden wie in den letzten Jahrzehnten. Neben der Archäologie und der Kunstgeschichte haben sich zahlreiche weitere Fächer an Fragestellungen rund um das Bild geradezu festgebissen. Angesichts dessen geht einer der bedeutendsten Kunsthistoriker der Gegenwart der Frage nach, warum Begriff und Geltung sowie Macht und Ohnmacht von Bildern so hartnäckig verfolgte Themen unserer Tage geworden sind.

Aufgrund sorgfältiger Untersuchung in phänomenologischer Erkenntnishaltung können die Struktur des Lysis, die künstlerisch-ideelle Gedankenbewegung und damit die Einheit von philosophisch-künstlerischer Gestalt und philosophischem Gehalt des Dialoges in einer strengeren Weise erfasst werden als bisher. Dadurch werden ganz neue Beziehungen zu Gestalt und Gehalt der Politeia sichtbar. Sie erlauben im Verein mit grundsätzlichen Überlegungen zur Methode der datierenden Sprachstatistik und weiteren Beobachtungen, den Lysis chronologisch nach der Politeia anzusetzen - in der Trilogie Phaidros - Lysis - Euthydemos. So können die interpretatorischen (...) Einschränkungen durch das Vorurteil, der Lysis sei ein Frühdialog, überwunden werden. Die positive Interpretation des Dialoges und ihre Vertiefung durch die platonische Prinzipienlehre werden damit auf ungewohnte Weise stärker begründet. (shrink)

This accessible and highly readable book is the first full-length biography of Hegel to be published since the largely outdated treatments of the nineteenth century. Althaus draws on new historical material and scholarly sources about the life and times of this most enigmatic and influential of modern philosophers. He paints a living portrait of a thinker whose personality was more complex than is often imagined, and shows that Hegel's relation to his revolutionary times was also more ambiguous than is usually (...) accepted. Althaus presents a broad chronological narrative of Hegel's development from his early theological studies in Tubingen and the associated unpublished writings, profoundly critical of the established religious orthodoxies. He traces Hegel's years of philosophical apprenticeship with Schelling in Jena as he struggled for an independent intellectual position, up to the crowning period of influence and success in Berlin where Hegel appeared as the advocate of the modern Prussian state. Althaus tells a vivid story of Hegel's life and his intellectual and personal crises, drawing generously on the philosopher's own words from his extensive correspondence. His central role in the cultural and political life of the time is illuminated by the impressions and responses of his contemporaries, such as Schelling, Schleiermacher and Goethe. This panoramic introduction to Hegel's life, work and times will be a valuable resource for scholars, students and anyone interested in this towering figure of philosophy. (shrink)

Die vorliegenden Untersuchungen zu Aristoteles' Naturphilosophie interpretieren Haupttexte aus seinen Schriften Physik, Über Entstehen und Vergehen, Über die Entstehung der Lebewesen, Über die Seele. Sie führen zu einigen wichtigen Einsichten über die Natur, die Materie, die Zeit, die Bewegungs- und Zweckursache u.a. und erheben ihre aktuelle Bedeutung für die gegenwärtigen interdisziplinären Diskussionen zwischen Naturphilosophie, Physik, Biologie, Psychologie und Anthropologie.