Download or read book The Mathematical Works of Bernard Bolzano written by Bernard Bolzano and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an English translation of the key mathematical and philosophical works of Bernard Bolzano (1781-1848).
Download or read book The Mathematical Works of Bernard Bolzano written by Bernard Bolzano and published by Oxford University Press on Demand. This book was released on 2004-12-09 with total page 729 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 theconstruction 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.
Download or read book The Mathematical Works of Bernard Bolzano written by Steve Russ and published by OUP Oxford. This book was released on 2004-12-09 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bernard Bolzano written by Paul Rusnock and published by Oxford University Press, USA. This book was released on 2019-03-15 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bernard Bolzano (1781-1850) 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 (but also many of the details) 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.
Download or read book Paradoxes of the Infinite Routledge Revivals written by Bernard Bolzano and published by Routledge. This book was released on 2014-03-18 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Theory of Science written by Bernard Bolzano and published by Univ of California Press. This book was released on 1972-01-01 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Mathematical Method and Correspondence with Exner written by Bernard Bolzano and published by BRILL. This book was released on 2021-10-25 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bolzano s Philosophy and the Emergence of Modern Mathematics written by Paul Rusnock and published by BRILL. This book was released on 2022-06-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bernard Bolzano written by Paul Rusnock and published by . This book was released on 2019 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: The majority of histories of 19th-century philosophy overlook Bernard Bolzano of Prague (1781-1848), a systematic philosopher-mathematician whose contributions extend across the entire range of philosophy. This text gives a detailed and comprehensive introduction to Bolzano's life and work.
Download or read book Bolzano s Logical System written by Ettore Casari and published by Oxford University Press. This book was released on 2016 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is focused on the first three parts of Bolzano's Theory of Sciene and introduces a more systematic reconsideration of Bolzano's logial thought. In undertaking this task, the book is intended as an exploration, not so much of the more specifically discursive aspects of Bolzano's logial thought - already amply studied - as muh as on identifying the singularly coherent and systematic nature of the logic presented in Bolzano's work. Casari presents this within a formal system and adopts the approach of the predicate calculus with identity and choice operator by using Hilbert's epsilon calculus (the logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics).
Download or read book Paradoxes of the Infinite Routledge Revivals written by Bernard Bolzano and published by Routledge. This book was released on 2014-03-18 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Mathematical Theory of Turbulence written by M.M. Stanisic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: "I do not think at all that I am able to present here any procedure of investiga tion that was not perceived long ago by aZl men of talent; and I do not promise at all that you can find here anything quite new of this kind. But I shall take pains to state in clear words the pules and ways of investigation which are followed by able men, who in most cases are not even conscious of follow ing them. Although I am free from illusion that I shall fully succeed even in doing this, I stiZl hope that the little that is present here may please some people and have some application afterwards. " Bernard Balzano (Wissenschaftslehre, 1929) The following book results from a series of lectures on the mathematical theory of turbulence delivered by the author at the Purdue University School of Aeronautics and Astronautics during the past several years, and represents, in fact, a comprehensive account of the author's work with his graduate students in this field. It was my aim in writing this book to give engineers and scientists a mathematical feeling for a subject, which because of its nonlinear character has resisted mathematical analysis for many years. On account viii of its refractory nature this subject was categorized as one of seven "elementary catastrophes". The material presented here is designed for a first graduate course in turbulence. The complete course has been taught in one semester.
Download or read book Bolzano and the Foundations of Mathematical Analysis written by Vojtěch Jarník and published by . This book was released on 1981 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bolzano s Philosophy of Grounding written by Stefan Roski and published by Oxford University Press. This book was released on 2022 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Provides translations of Bolzano's most important work on grounding, including previously untranslated material"--
Download or read book A Treatise on the Binomial Theorem written by Craig Smorynski and published by Texts in Mathematics. This book was released on 2012 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The binomial theorem is usually quite rightly considered as one of the most important theorems in the whole of analysis." Thus wrote Bernard Bolzano in 1816 in introducing the first correct proof of Newton's generalisation of a century and a half earlier of a result familiar to us all from elementary algebra. Bolzano's appraisal may surprise the modern reader familiar only with the finite algebraic version of the Binomial Theorem involving positive integral exponents, and may also appear incongruous to one familiar with Newton's series for rational exponents. Yet his statement was a sound judgment back in the day. Here the story of the Binomial Theorem is presented in all its glory, from the early days in India, the Moslem world, and China as an essential tool for root extraction, through Newton's generalisation and its central role in infinite series expansions in the 17th and 18th centuries, and to its rigorous foundation in the 19th. The exposition is well-organised and fairly complete with all the necessary details, yet still readable and understandable for those with a limited mathematical background, say at the Calculus level or just below that. The present book, with its many citations from the literature, will be of interest to anyone concerned with the history or foundations of mathematics.
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Science written by Bernard Bolzano and published by Oxford University Press, USA. This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Original work first published: Sulzbach: Seidel, 1837.
