This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the formal sciences. (...) We also discuss the second, unfinished and unpublished issue, where Bolzano develops his views on universal mathematics. Here we find the beginnings of his theory of collections, for him the most fundamental of the mathematical disciplines. Though not exactly the same as the later Cantorian set theory, Bolzano's theory of collections was used in very similar ways in mathematics, notably in analysis. In retrospect, Bolzano's debut in philosophy was a remarkably successful one, though its fruits would only become generally known much later. (shrink)

Ce dialogue confronte deux conceptions qui dominent jusqu’à nos jours la philosophie des mathématiques : d’un côté la conception kantienne qui souligne l’irréductible apport de l’intuition dans la formulation des axiomes, ainsi que l’effectivité des procédés de construction ; de l’autre côté la conception bolzanienne qui s’efforce d’éliminer toute intervention de l’intuition au profit des démonstrations et des procédés purement conceptuels.In this dialogue, two opposed conceptions, which dominate the philosophy of mathematics till today, are confronted. Kant’s account of mathematics is (...) based upon the activity of constructing mathematical objects in pure intuition . In yielding objects for mathematics, our intuition contributes in an essential way to the formulation of mathematical truths. Against Kant, Bolzano argues that intuition has place neither in arithmetic nor in geometry and that mathematical existence consists in the possibility of the defined objects. i.e. in non-contradiction. For Bolzano, the central idea of mathematics is that of rigorous proof. (shrink)

[A dialogue between Kant and Bolzano on mathematical knowledge.].

Bernard Bolzano is increasingly recognized as one of the greatest nineteenth-century philosophers. A philosopher and mathematician of rare talent, he made ground-breaking contributions to logic, the foundations and philosophy of mathematics, metaphysics, and the philosophy of religion. Many of the larger features of later analytic philosophy first appear in his work: for example, the separation of logic from psychology, his sophisticated understanding of mathematical proof, his definition of logical consequence, his work on the semantics of natural kind terms, or his (...) anticipations of Cantor's set theory, to name but a few. To his contemporaries, however, he was best known as an intelligent and determined advocate for reform of Church and State. Based in large part on a carefully argued utilitarian practical philosophy, he developed a program for the non-violent reform of the authoritarian institutions of the Hapsburg Empire, a program which he himself helped to set in motion through his teaching and other activities. Rarely has a philosopher had such a great impact on the political culture of his homeland. Persecuted in his lifetime by secular and ecclesiastical authorities, long ignored or misunderstood by philosophers, Bolzano's reputation has nevertheless steadily increased over the past century and a half. Much discussed and respected in Central Europe for over a century, he is finally beginning to receive the recognition he deserves in the English-speaking world. This book provides a comprehensive and detailed critical introduction to Bolzano, covering both his life and works. (shrink)

Jean-Paul Coujou a traduit – première en langue française –, commenté et annoté des ouvrages choisis dans l’œuvre monumentale de Francisco Suarez. Avant les trois présents volumes, il avait publié les trois premières Disputes et la XXXIe . Depuis trois..

Analytical philosophy begins with the first mathematical and philosophical works of Bolzano published between 1804 and 1817. There, Bolzano set out a project for the global reform of mathematics by means of the axiomatic method. Having completed the Wissenschaftslehre, Bolzano wrote a summary of his logic for the Größenlehre, which he sent to Exner in 1833. The correspondence between Bolzano and Exner covered some of the main subjects treated by analytical philosophy: the status of abstract objects (propositions and objective ideas), (...) intuitions, objectless ideas, the concept of object and many others. While Bolzano argued in favor of abstract entities independent of mind and of language, Exner considered them as abstractions obtained from the subjective judgments and representations. During the XlXth century, Bolzano's philosophy spread over Bohemia and Austria through manuscripts and through the first edition of Zimmermann's textbook of philosophy. The most important Brentanians, Kerry, Twardowski, Meinong and Husserl, discussed his doctrines which may also have influenced Wittgenstein and the Polish school. (shrink)

Analytical philosophy begins with the first mathematical and philosophical works of Bolzano published between 1804 and 1817. There, Bolzano set out a project for the global reform of mathematics by means of the axiomatic method. Having completed the Wissenschaftslehre, Bolzano wrote a summary of his logic for the Größenlehre, which he sent to Exner in 1833. The correspondence between Bolzano and Exner covered some of the main subjects treated by analytical philosophy: the status of abstract objects (propositions and objective ideas), (...) intuitions, objectless ideas, the concept of object and many others. While Bolzano argued in favor of abstract entities independent of mind and of language, Exner considered them as abstractions obtained from the subjective judgments and representations. During the XlXth century, Bolzano's philosophy spread over Bohemia and Austria through manuscripts and through the first edition of Zimmermann's textbook of philosophy. The most important Brentanians, Kerry, Twardowski, Meinong and Husserl, discussed his doctrines which may also have influenced Wittgenstein and the Polish school. (shrink)

Bernard Bolzano was born in Prague in 1781 and died in 1848 in the same city1. His major work Wissenschaftslehre was published in 1837 in Sulzbach, Germany.Since the publication of Jan Berg’s Bolza...

« Pour la première fois peut-être la science n’est plus considérée comme simple intermédiaire entre l’esprit humain et l’être en soi, dépendant autant de l’un que de l’autre et n’ayant pas de réalité propre, mais comme un objet sui generis, original dans son essence, autonome dans son mouvement ». En écoutant les différentes contributions à ce colloque, je me suis retrouvé sur un terrain familier. Presque tous les noms des auteurs des xviie et xviiie siècles m’étaient bien connus : ceux (...) de La... (shrink)

Les origines grecques de la conception d'harmonie (H. Dufourt) - Du monde au matériau : le devenir-musical du timbre (A. Soulez) - La musique est-elle un langage? (R. Casati et J. Dokic) - Le devenir du matériau musical au XXe siècle (M. Solomos) - Hauteur, timbre, harmonie, synthèse (J.C. Risset) et d'autres articles...

Review of S. Lapointe: Bolzano’s Theoretical Philosophy, An Introduction.