We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind,and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our (...) main thesis is that Marburg neo-Kantian philosophy formulated a sophisticated position towards the problems raised by the concepts of limits and infinitesimals. The Marburg school neither clung to the traditional approach of logically and metaphysically dubious infinitesimals, nor whiggishly subscribed to the new orthodoxy of the “great triumvirate” of Cantor, Dedekind, and Weierstrass that declared infinitesimals conceptus nongrati in mathematical discourse. Rather, following Cohen’s lead, the Marburg philosophers sought to clarify Leibniz’s principle of continuity, and to exploit it in making sense of infinitesimals and related concepts. (shrink)

One of the most important philosophical topics in the early twentieth century and a topic that was seminal in the emergence of analytic philosophy was the relationship between Kantian philosophy and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but instead develops a kind of (...) logicism modeled on Richard Dedekind's foundations of arithmetic. Further, because he shared with other Neo-Kantians an appreciation of the developmental and historical nature of mathematics, Cassirer developed a philosophical account of the unity and methodology of mathematics over time. With its impressive attention to the detail of contemporary mathematics and its exploration of philosophical questions to which other philosophers paid scant attention, Cassirer's philosophy of mathematics surely deserves a place among the classic works of twentieth century philosophy of mathematics. Though focused on Cassirer's philosophy of geometry, this paper also addresses both Cassirer's general philosophical orientation and his reading of Kant. (shrink)

These essays bring Neo-Kantianism back into contemporary philosophical discourse.

Various contributors to recent philosophy of mathematics havetaken Richard Dedekind to be the founder of structuralismin mathematics. In this paper I examine whether Dedekind did, in fact, hold structuralist views and, insofar as that is the case, how they relate to the main contemporary variants. In addition, I argue that his writings contain philosophical insights that are worth reexamining and reviving. The discussion focusses on Dedekind''s classic essay Was sind und was sollen die Zahlen?, supplemented by evidence from Stetigkeit und (...) irrationale Zahlen, his scientific correspondence, and his Nachlaß. (shrink)

: Few texts summarize and at the same time compound the challenges of their author's philosophy so sharply as Hermann Cohen's Das Prinzip der Infinitesimalmethode und seine Geschichte (1883). The book's meaning and style are greatly illuminated by placing it in the scientific, political, and academic context of late-nineteenth century Germany. As this context changed, so did both the reception of the philosophy of the infinitesimal and of the Marburg school more generally. A study of this transformation casts significant light (...) on the political relevance of the philosophy of science in theWilhelmine era. As a means of following this development across time, Cohen's text is read through its changing reception in the philosophy of his closest disciple, Ernst Cassirer. (shrink)

Michael Heidelberger's exhaustive exploration of Fechner's writings, in relation to current issues in the field, successfully reestablishes Fechner'...

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Die von Jens Timmermann besorgte Neuausgabe innerhalb der Philosophischen Bibliothek bietet den vollständigen Wortlaut der beiden Originalausgaben von 1781 und 1787. Der Kantische Text wurde unter Wahrung der Interpunktion und sprachlicher Eigenheiten sehr behutsam an die heutigen orthographischen Regeln angeglichen. Die semantisch bedeutenden Korrekturvorschläge späterer Herausgeber (nicht nur der Akademie-Ausgabe) sind, wo sie nicht in den Text Aufnahme gefunden haben, am Fuß der Seite verzeichnet. Alle wesentlichen Unterschiede zwischen den Originalausgaben sind durch Kursivdruck hervorgehoben, größere Abweichungen ganzer Textstücke - etwa (...) in der Einleitung und im Kapitel über Phaenomena und Noumena - wurden synoptisch gegenübergestellt, so daß Art und Umfang der Umarbeitung unmittelbar abgelesen werden können. Die durchgängig neu bearbeitete Studienausgabe folgt in den Grundprinzipien der seit 1926 in Forschung und Lehre maßgeblichen Ausgabe von Raymund Schmidt, die hiermit abgelöst wird. Sie wird ergänzt durch eine umfangreiche Bibliographie von Heiner Klemme sowie durch einen ausführlichen Personen- und Sachindex. (shrink)

In this collection of essays one of the preeminent philosophers of science writing offers a reinterpretation of the enduring significance of logical positivism, the revolutionary philosophical movement centered around the Vienna Circle in the 1920s and 30s. Michael Friedman argues that the logical positivists were radicals not by presenting a new version of empiricism but rather by offering a new conception of a priori knowledge and its role in empirical knowledge. This collection will be mandatory reading for any philosopher or (...) historian of science interested in the history of logical positivism in particular or the evolution of modern philosophy in general. (shrink)

Inhalt: Zur Metaphysik der symbolischen Formen (1928); Über Basisphänomene (ca. 1940); Symbolische Formen. Zu Band 4 (ca. 1928); Beilage: Symbolbegriff: Metaphysik des Symbolischen (ca. 1928).

Husserls Briefwechsel is von entscheidender Bedeutung für das Verständnis seiner philosophischen Entwicklung, seiner wissenschaftlichen Arbeit und Publikationsvorhaben. Er nimmt darin Stellung zu den politischen Entwicklungen in Deutschland und spricht sich aus über weltanschaulich-religiöse Fragen. Außerdem bestimmt er sein Verhältnis zu anderen Philosophen und Schulen. Die vorliegende, textkritisch konstituierte und reich kommentierte Gesamtausgabe ist nicht nur für Philosophen, Wissenschaftshistoriker und Zeitgeschichtlicher von hohem Interesse. Die Ausgabe umfaßt in sachlicher Gliederung Husserls Korrespondenz (ca. 1300 Einzelstücke) mit über 250 Personen und Instanzen, wobei (...) neben den Briefen Husserls - und, in großzügiger Auswahl, seiner Frau Malvine - auch alle erhaltenen Briefe an Husserl aufgenommen sind (ca. 700 Einzelstücke). Die Bände I--IV orientieren sich an der chronologischen Entwicklung der Husserlschen Philosophie, die Bände V--IX an der sachlichen Nähe der Korrespondenzpartner zu Husserls Philosophie. Band X enthält neben der Einführung in die Ausgabe verschiedene Register zur differenzierten Aufschlüsselung der Ausgabe. Edmund Husserl's correspondence is of eminent importance for a clear understanding of his philosophical development, his scientific work, and his publications. In his letters, he reacts on the political developments in Germany and ponders on the philosophy of life and on religious questions. He also clearly defines his relationships with other philosophers and schools of philosophy. This annotated and richly commented correspondence edition is of vital interest to philosophers, researchers and historians. The ten volumes consist of Husserl's correspondence (about 1300 letters) with more than 250 institutes and persons, and in addition to his letters, the letters of his wife Malvine and those received by both (about 700) are also included. Volumes I--IV present a chronological development of Husserl's philosophical system, Volumes V--IX are devoted to the correspondence partners in philosophy. The last volume consists of an extensive Introduction and a variety of indexes to all volumes in the set. (shrink)

Buch 1. Geschichte des Materialismus bis auf Kant.--Buch 2. Geschichte des Materialismus seit Kant.

This is a reproduction of a book published before 1923. 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)

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)

Kants Metaphysische Anfangsgründe der Naturwissenschaft von 1786 stehen ihrem Anspruch nach zwischen einer transzendentalen Kritik der Vernunft - Kant bereitete zur selben Zeit die in wesentlichen Stücken umgearbeitete zweite Auflage der KrV vor - und der Physik als empirischer Wissenschaft. Die Notwendigkeit einer Reflexion über die Naturwissenschaft verhilft dieser Schrift heute wieder zu systematischer Relevanz, nachdem sie lange Zeit nur aus dem Blickwinkel ihrer Bedeutsamkeit für die empirische Naturwissenschaft betrachtet und infolgedessen allenfalls aus wissenschaftshistorischem Interesse rezipiert wurde.

Neo-Kantianism was an important movement in German philosophy of the late 19th century: Frederick Beiser traces its development back to the late 18th century, and explains its rise as a response to three major developments in German culture: the collapse of speculative idealism; the materialism controversy; and the identity crisis of philosophy.

Few texts summarize and at the same time compound the challenges of their author's philosophy so sharply as Hermann Cohen's Das Prinzip der Infinitesimalmethode und seine Geschichte . The book's meaning and style are greatly illuminated by placing it in the scientific, political, and academic context of late-nineteenth century Germany. As this context changed, so did both the reception of the philosophy of the infinitesimal and of the Marburg school more generally. A study of this transformation casts significant light on (...) the political relevance of the philosophy of science in theWilhelmine era. As a means of following this development across time, Cohen's text is read through its changing reception in the philosophy of his closest disciple, Ernst Cassirer. (shrink)

La logique de Leibniz: d'apres des documents inedits / par Louis Couturat,...Date de l'edition originale: 1901Sujet de l'ouvrage: Leibniz, Gottfried Wilhelm (1646-1716)Logique moderneCollection: Collection historique des grands philosophesCe livre est la reproduction fidele d'une oeuvre publiee avant 1920 et fait partie d'une collection de livres reimprimes a la demande editee par Hachette Livre, dans le cadre d'un partenariat avec la Bibliotheque nationale de France, offrant l'opportunite d'acceder a des ouvrages anciens et souvent rares issus des fonds patrimoniaux de la BnF.Les (...) oeuvres faisant partie de cette collection ont ete numerisees par la BnF et sont presentes sur Gallica, sa bibliotheque numerique.En entreprenant de redonner vie a ces ouvrages au travers d'une collection de livres reimprimes a la demande, nous leur donnons la possibilite de rencontrer un public elargi et participons a la transmission de connaissances et de savoirs parfois difficilement accessibles.Nous avons cherche a concilier la reproduction fidele d'un livre ancien a partir de sa version numerisee avec le souci d'un confort de lecture optimal. Nous esperons que les ouvrages de cette nouvelle collection vous apporteront entiere satisfaction.Pour plus d'informations, rendez-vous sur www.hachettebnf.frhttp: //gallica.bnf.fr/ark: /12148/bpt6k110843d. (shrink)

This comprehensive treatment of Neo-Kantianism discusses the main topics and key figures of the movement and their intersection with other 20th-century philosophers. With the advent of phenomenology, existentialism, and the Frankfurt School, Neo-Kantianism was deemed too narrowly academic and science-oriented to compete with new directions in philosophy. These essays bring Neo-Kantianism back into contemporary philosophical discourse. They expand current views of the Neo-Kantians and reassess the movement and the philosophical traditions emerging from it. This groundbreaking volume provides new and important (...) insights into the history of philosophy, the scope of transcendental thought, and Neo-Kantian influence on the sciences and intellectual culture. (shrink)