In the above mentioned article [1] unfortunately the names of the translators of Toeplitz's lecture were omitted. The correct title is:The Problem of University Courses on Infinitesimal Calculus and TheirDemarcation from Infinitesimal Calculus in High SchoolsOtto ToeplitzTranslated into English by Michael N. Fried and Hans Niels Jahnke.

When the Association of German Scientists and Physicians last met in Düsseldorf exactly twenty-eight years ago on September 24, a debate took place following lectures by Felix Klein and Alfred Pringsheim on roughly the same topic to which I would like to direct your attention today. The printed report of the Düsseldorf debate only remarked that, “It is not possible to go into details here,” so one can only guess how two of the most powerful teacher personalities among German mathematicians (...) of that time had confronted one another with their diametrically opposed views on this topic and how they did so with their characteristically lively spirit. (shrink)

Argument“The problem of university courses on infinitesimal calculus and their demarcation from infinitesimal calculus in high schools” is the published version of an address Otto Toeplitz delivered at a meeting of the German Mathematical Society held in Düsseldorf in 1926. It contains the most detailed exposition of Toeplitz's ideas about mathematics education, particularly his thinking about the role of the history of mathematics in mathematics education, which he called the “genetic method” to teaching mathematics. The tensions and (...) assumptions about mathematics, history of mathematics, and historiography revealed in this piece dedicated to educational ideas are what make Toeplitz's text interesting in the study of historiography of mathematics. In general, the ways historiography of mathematics and teaching of mathematics, even without an immediate concern for history, are deeply entangled and, in our view, worth attention both in historical and educational research. (shrink)

Um den geschichtlich maßgebenden Horizont zu streifen, in den das zu besprechende Buch von Stenzel gehört, sollten zunächst Paul Natorps „Platos Ideenlehre“ und Nicolai Hartmanns „Platos Logik des Seins“ als die einfluss¬reichsten neukantianischen Platoarbeiten jener Zeit erwähnt werden. Zur selben Zeit wird das Mathematische bei Platon durch Beiträge von Otto Toeplitz und Oskar Becker sehr stark in den Vordergrund gerückt und ertragreich ausgearbeitet. In diesem geistigen Klima der 1930er Jahre, werden die um drei Aufsätze erweiterten Studien Stenzels veröffentlicht.

The movement for the Unity of Science has been making headway for a number of years, and each year more workers in the various scientific domains have expressed their interest in it by participating in the discussion of its aims and its specific problems. A characteristic feature of this movement which explains this growing interest is that it does not propose a “super-science” which is to legislate to the special sciences. Its proposal of a Unity of Science is of a (...) different kind, not based upon some grand metaphysical view of any sort. Those who are active within this movement are emphatic in their insistence that instead of aiming at a synthesis of the different sciences on the basis of a prior and independent philosophy, the special sciences will themselves supply their own synthesizing glue. For appreciating the significance of this movement it is therefore necessary to keep in mind that its tendency is toward a unified science, departmentalized into special sciences, and not toward an artificial and speculative juxtaposition of an autonomous philosophy and an autonomous group of sciences. (shrink)

This paper puts forward the hypothesis that consciousness might be linked to matter in a way which is more sophisticated than the traditional macroscopic Cartesian hypothesis suggests.Advances in the biophysics of the nervous system, not only on the level of its macroscopic functioning but also on the level of individual ion channels, have made the question of how finely consciousness is tied to matter and its dynamics more important. Quantum mechanics limits the attainable resolution and puts into doubt the idea (...) of an infinitely fine-woven attachment. A recent approach to physics rekindles such a rationalist hope. Endophysics focuses on the global implications of microscopic computer simulations of chemical and biophysical processes. A complete artificial universe can be set up in the computer. It produces non-classical and nonlocal effects inside — on the interface that exists between an internal observer (fluid neuron) and the rest of the world. This interface is finer than any brain property to which the status of the mind-body interface has been attributed hitherto. A new class of experiments becomes possible in the artificial world and, by analogy, in the real world. Magnetic resonance imaging experiments, routinely performed under open-loop conditions, can be repeated under psychophysical (closed-loop) conditions — in search for microscopically induced changes in the perceived and measured structure of the world. (shrink)

This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our (...) continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. (shrink)

This text presents a broad scope of philosophical issues and primary sources from the history of philosophy with the intent of providing students with a general introduction to significant and relevant questions in philosophy, the humanities, and the history of thought.

Abzj proposed, in a fragment established and translated herein, two methods to build a parabolic mirror. The lack of demonstration, particularly for the first method, raises a difficult question of interpretation. To understand this method, O. Neugebauer used, in an unpublished article translated herein, concepts of descriptive geometry. He then eliminated the space construction used, to keep only simple geometrical considerations known by the Greeks. The second interpretation, given by R. Rashed, is based on the geometrical practices of al-Bnhzj from (...) Ibn Sinān seems to support this last interpretation. (shrink)

Ausgangspunkt des zum Spätwerk zählenden Dialogs ist die Fragestellung nach einer Wesensbestimmung des Sophisten, des Staatsmannes und des Philosophen. Im Verlauf steht jedoch die Frage nach dem Wesen der Philosophie im Vordergrund.

Platons Politeia (347 v. Chr.), der utopische Entwurf eines gerechten Staats, gilt nicht nur als sein "Hauptwerk", sondern auch als das wirkungsgeschichtlich bedeutendste Werk der politischen Philosophie in der Geschichte des europäischen Denkens. Für die 11. Auflage überarbeitete K. Bormann die Apeltsche Übersetzung anhand der Oxforder Ausgabe von Burnet und anderen. Beigegeben wurde eine ausführliche Literaturübersicht, Anmerkungen und Register sowie eine Einleitung.

Der Dialog »Menon« (399 v. Chr.) handelt von der Erkennbarkeit und Lehrbarkeit der Tugend. Ausgehend von dieser Fragestellung begründet und entwickelt Platon die Form und Methode hypothetischer Erkenntnis; der Dialog bietet daher auch eine gute Einführung in die Philosophie Platons.