Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...) in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body. (shrink)

In Homer’s account of the adventurous journey of Odysseus, the song of the sirens was so appealing and tempting that it lured sailors to their deaths. Warned by the goddess Kirke, Odysseus overcame the trap by plugging his crew’s ears with wax. An archaeo-acoustical research expedition undertaken by members of Humboldt University Berlin made sound propagation experiments at the supposedly historical scene at the Galli Islands where it’s said that the sirens originally sung. At the site we broadcasted both synthetic (...) signals and natural voices via loudspeakers in the direction Odysseus most probably should have approached the Siren’s island. Subjective listening as well as objective acoustic analysis of the recorded signals revealed evidence for a combination of site-specific acoustic effects, which may explain the nature and origin of the song of the sirens in Homer. The local arrangement of the three islands deforms the acoustic signals by amplification and by changes in timbre. Two female singers from the Berlin State Opera were asked to sing differently pitched musical intervals to be tested in the Li Galli environment. The experiment evinced that the first overtones would be merged by the echo of the rocks; yet when singing pure thirds and less consonant intervals, which yield higher orders in the overtone series, the voices appear recognisable as being two. As a result, and particularly because Homer stresses the number of exactly two sirens several times, the evidence of our research supports the musicological theory for a rather early existence of enharmonic tunings and most prominently a two-part polyphonic singing of Greek songs. Given that the rocky formation of the Galli Islands most likely didn’t change during the geological tick of just 2,700 years, we conclude that there has been a real acoustic basis for the myth reported by Homer and that a “song of the Sirens”, most probably based on natural voices, was transformed by the particular acoustic conditions of the landscape in such a way that signals were amplified and sent out in one concrete direction. Based on these results, we continue to discuss further leading acoustic theories that offer new insights into the mythology and which were essential to motivate our expedition in the first place. After all, the question remains open what kind of beings the first emitters of the song might have been. (shrink)

This book presents a range of essays on the conceptual foundations of physicalism, mental causation and human agency, written by established and leading authors ...

Die Krisenerfahrungen der Moderne führen zum Rückgriff auf vormoderne Ordnungsvorstellungen, die jene Legitimationsdefizite kompensieren sollen, die im Zuge einer Dialektik der Aufklärung entstanden sind: die emanzipatorische Kraft der Vernunft scheint sich in eine Instanz neuer Herrschaft zu verkehren, als deren Organ die als repressiv erfahrenen Ordnungsleistungen des Staates begriffen werden. Diese Situation begünstigt die Suche nach Kräften, die menschlichem Eingriff entzogen sind, und kommt der Rehabilitierung von Naturvorstellungen entgegen, die sich der Welt des Menschen als normative Ordnungsquelle anbieten. Inwieweit sich (...) gerade die Geschlechterbeziehungen als Ausdruck solch natürlicher Ordnung verstehen lassen, ist eine der zentralen Fragen einer kritischen feministischen Philosophie. Die Untersuchungen, die die AutorInnen dieses Bandes vorlegen, bewegen sich im thematischen Umkreis dieser Fragestellung: in der Art eines Kompendiums werden in Interpretationen von Texten der politischen Philosophie, die in der Epoche von 1600-1850 entstanden sind, paradigmatische Legitimationsfiguren herausgearbeitet und der feministischen Ideologiekritik zugänglich gemacht. (shrink)

Wie verhalten sich Ideen zu der materiellen Wirklichkeit, die sie abbilden wollen? In der Strukturanalyse der Platonschen Spiegel-Metapher findet der Autor den Schlüssel, um den Zusammenhang der materiellen Vielheit als universelles Reflexionssystem darstellen zu können und das menschliche In-der-Welt-sein als Moment des Naturverhältnisses zu begründen.

On the occasion of the 100th birthday of the physical chemist Kurt Schwabe the article presents an overview about Schwabe’s activities as president of the Saxon Academy of Science from 1965 to 1980. Main topics of this time which has to be solved by Schwabe were to ensure the further existence of the academy and to reach an agreement about the principles of cooperation between the Saxon Academy of Science and the Berlin Academy of Science as an agreement of equals.

Habermas' discourse theory stresses the autonomy of public deliberation transcending the spontaneous emergence of private networks of legal relationships between individuals. Only the public discourse which is detached from the inertia of overlapping practical forms of coordination can refer to the ideally designed social work of legitimated interpersonal relationships. The democratic constitution is regarded as a legal institutionalization of the priority of the public forum of discourse. Conceptions related to classical liberalism would question the cognitive potential of public deliberation, and (...) even deny its productivity as a normative frame of reference for (post‐)modern societies which are confronted with the challenge of uncertainty and the continuous process of self‐transformation. (shrink)

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