The Mathematical Works of Bernard Bolzano

The Mathematical Works of Bernard Bolzano
Title The Mathematical Works of Bernard Bolzano PDF eBook
Author Bernard Bolzano
Publisher Oxford University Press
Pages 729
Release 2004-12-09
Genre Mathematics
ISBN 0198539304

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Bernard Bolzano (1781-1848, Prague) was an outstanding thinker and reformer, far ahead of his times in many areas, including philosophy, ethics, politics, logic, theology and physics, and mathematics. Aimed at historians of mathematics, philosophy, ethics and logic, this volume contains the first English translations of some of his most significant mathematical writings, which contain the details of many celebrated insights and anticipations: clear topological definitions of various geometric extensions, an effective statement and use of the Cauchy convergence before it appears in Cauchy's work, remarkable results on measurable numbers (a version of real numbers), on functions (the construction of a continuous, non-differentiable function around 1830) and on infinite collections.

Bernard Bolzano

Bernard Bolzano
Title Bernard Bolzano PDF eBook
Author Paul Rusnock
Publisher
Pages 702
Release 2019
Genre Biography & Autobiography
ISBN 0198823681

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The majority of histories of nineteenth-century philosophy overlook Bernard Bolzano of Prague (1781-1848), a systematic philosopher-mathematician whose contributions extend across the entire range of philosophy. This book, the first of its kind to be published in English, gives a detailed and comprehensive introduction to Bolzano's life and work.

Paradoxes of the Infinite (Routledge Revivals)

Paradoxes of the Infinite (Routledge Revivals)
Title Paradoxes of the Infinite (Routledge Revivals) PDF eBook
Author Bernard Bolzano
Publisher Routledge
Pages 202
Release 2014-03-18
Genre Philosophy
ISBN 1317748581

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Paradoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19th century: Dr Bernard Bolzano’s Paradoxien. This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.

On the Mathematical Method and Correspondence with Exner

On the Mathematical Method and Correspondence with Exner
Title On the Mathematical Method and Correspondence with Exner PDF eBook
Author Bernard Bolzano
Publisher Rodopi
Pages 208
Release 2004
Genre Logic
ISBN 9789042017818

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The Prague Philosopher Bernard Bolzano (1781-1848) has long been admired for his groundbreaking work in mathematics: his rigorous proofs of fundamental theorems in analysis, his construction of a continuous, nowhere-differentiable function, his investigations of the infinite, and his anticipations of Cantor's set theory. He made equally outstanding contributions in philosophy, most notably in logic and methodology. One of the greatest mathematician-philosophers since Leibniz, Bolzano is now widely recognised as a major figure of nineteenth-century philosophy. Praised by Husserl as "one of the greatest logicians of all times," he has also been recognised by Michael Dummett as one of the first modern analytic philosophers and by Alberto Coffa as the founder of the "semantic tradition." This volume contains English translations of the essay "On the Mathematical Method," a concise introduction to Bolzano's logic and philosophy of mathematics, as well as substantial selections from his correspondence with Franz Exner, Professor of Philosophy at the Charles University in Prague in the 1830s and 40s. It will be of interest to students of Austrian philosophy, the development of analytic philosophy, the philosophy of language, and the history and philosophy of logic and mathematics.

The Theory of Science

The Theory of Science
Title The Theory of Science PDF eBook
Author Bernard Bolzano
Publisher Univ of California Press
Pages 454
Release 1972-01-01
Genre Philosophy
ISBN 9780520017870

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The Mathematical Works of Bernard Bolzano

The Mathematical Works of Bernard Bolzano
Title The Mathematical Works of Bernard Bolzano PDF eBook
Author Steve Russ
Publisher OUP Oxford
Pages 742
Release 2004-12-09
Genre Mathematics
ISBN 9780191513701

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Bernard Bolzano (1781-1848, Prague) was a remarkable thinker and reformer far ahead of his time in many areas, including philosophy, theology, ethics, politics, logic, and mathematics. Aimed at historians and philosophers of both mathematics and logic, and research students in those fields, this volume contains English translations, in most cases for the first time, of many of Bolzano's most significant mathematical writings. These are the primary sources for many of his celebrated insights and anticipations, including: clear topological definitions of various geometric extensions; an effective statement and use of the Cauchy convergence criterion before it appears in Cauchy's work; proofs of the binomial theorem and the intermediate value theorem that are more general and rigorous than previous ones; an impressive theory of measurable numbers (a version of real numbers), a theory of functions including the construction of a continuous, non-differentiable function (around 1830); and his tantalising conceptual struggles over the possible relationships between infinite collections. Bolzano identified an objective and semantic connection between truths, his so-called 'ground-consequence' relation that imposed a structure on mathematical theories and reflected careful conceptual analysis. This was part of his highly original philosophy of mathematics that appears to be inseparable from his extraordinarily fruitful practical development of mathematics in ways that remain far from being properly understood, and may still be of relevance today.

Bolzano's Theoretical Philosophy

Bolzano's Theoretical Philosophy
Title Bolzano's Theoretical Philosophy PDF eBook
Author S. Lapointe
Publisher Springer
Pages 194
Release 2011-01-28
Genre Philosophy
ISBN 0230308643

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The first book in English to offer a systematic survey of Bolzano's philosophical logic and theory of knowledge, it offers a reconstruction of Bolzano's views on a series of key issues: the analysis of meaning, generality, analyticity, logical consequence, mathematical demonstration and knowledge by virtue of meaning.