From Kant to Hilbert Volume 1

A Source Book in the Foundations of Mathematics

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Author: William Bragg Ewald

Publisher: OUP Oxford

ISBN: 9780191523090

Category: Mathematics

Page: 678

View: 9242

Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics—algebra, geometry, number theory, analysis, logic and set theory—with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecker and Zermelo are here translated for the first time. The collection is an invaluable source for anyone wishing to gain an understanding of the foundation of modern mathematics.

From Kant to Hilbert Volume 1

A Source Book in the Foundations of Mathematics

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Author: William Ewald

Publisher: Oxford University Press on Demand

ISBN: 0198505353

Category: Mathematics

Page: 1340

View: 4339

This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume.

From Kant to Hilbert

a source book in the foundations of mathematics

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Author: William Bragg Ewald

Publisher: Oxford University Press, USA

ISBN: 9780198532712

Category: Mathematics

Page: 1408

View: 2204

This two-volume set contains extracts from principal texts on the foundations of mathematics, written from the late 18th to the early 20th centuries. Much of the work has been translated into English for the first time

From Kant to Hilbert

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Author: William Ewald

Publisher: Oxford University Press on Demand

ISBN: 0198505361

Category: Mathematics

Page: 1340

View: 5801

This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume.

Internal Logic

Foundations of Mathematics from Kronecker to Hilbert

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Author: Y. Gauthier

Publisher: Springer Science & Business Media

ISBN: 9401700834

Category: Mathematics

Page: 251

View: 4840

Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer. The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.

The Kantian Legacy in Nineteenth-century Science

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Author: Michael Friedman,Alfred Nordmann

Publisher: MIT Press

ISBN: 0262062542

Category: Philosophy

Page: 370

View: 1156

Historians of philosophy, science, and mathematics explore the influence of Kant'sphilosophy on the evolution of modern scientific thought.

Logic from Kant to Russell

Laying the Foundations for Analytic Philosophy

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Author: Sandra Lapointe

Publisher: Routledge

ISBN: 1351182226

Category: Philosophy

Page: 256

View: 5352

The scope and method of logic as we know it today eminently reflect the ground-breaking developments of set theory and the logical foundations of mathematics at the turn of the 20th century. Unfortunately, little effort has been made to understand the idiosyncrasies of the philosophical context that led to these tremendous innovations in the 19thcentury beyond what is found in the works of mathematicians such as Frege, Hilbert, and Russell. This constitutes a monumental gap in our understanding of the central influences that shaped 19th-century thought, from Kant to Russell, and that helped to create the conditions in which analytic philosophy could emerge. The aim of Logic from Kant to Russell is to document the development of logic in the works of 19th-century philosophers. It contains thirteen original essays written by authors from a broad range of backgrounds—intellectual historians, historians of idealism, philosophers of science, and historians of logic and analytic philosophy. These essays question the standard narratives of analytic philosophy’s past and address concerns that are relevant to the contemporary philosophical study of language, mind, and cognition. The book covers a broad range of influential thinkers in 19th-century philosophy and analytic philosophy, including Kant, Bolzano, Hegel, Herbart, Lotze, the British Algebraists and Idealists, Moore, Russell, the Neo-Kantians, and Frege.

Realizing Reason

A Narrative of Truth and Knowing

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Author: Danielle Macbeth

Publisher: OUP Oxford

ISBN: 0191022756

Category: Philosophy

Page: 496

View: 2094

Realizing Reason pursues three interrelated themes. First, it traces the essential moments in the historical unfolding—from the ancient Greeks, through Descartes, Kant, and developments in the nineteenth century, to the present—that culminates in the realization of pure reason as a power of knowing. Second, it provides a cogent account of mathematical practice as a mode of inquiry into objective truth. And finally, it develops and defends a new conception of our being in the world, one that builds on and transforms the now standard conception according to which our experience of reality arises out of brain activity due, in part, to merely causal impacts on our sense organs. Danielle Macbeth shows that to achieve an adequate understanding of the striving for truth in the exact sciences we must overcome this standard conception and that the way to do that is through a more adequate understanding of the nature of mathematical practice and the profound transformations it has undergone over the course of its history, the history through which reason is first realized as a power of knowing. Because we can understand mathematical practice only if we attend to the systems of written signs within which to do mathematics, Macbeth provides an account of the nature and role of written notations, specifically, of the principal systems that have been developed within which to reason in mathematics: Euclidean diagrams, the symbolic language of arithmetic and algebra, and Frege's concept-script, Begriffsschrift.

A History of Abstract Algebra

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Author: Israel Kleiner

Publisher: Springer Science & Business Media

ISBN: 081764685X

Category: Mathematics

Page: 168

View: 470

This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.