From Kant To Hilbert Volume 1

Author : William Bragg Ewald,William Ewald
Publisher : Oxford University Press, USA
Page : 695 pages
File Size : 52,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9780198505358

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From Kant to Hilbert Volume 1 by William Bragg Ewald,William Ewald Pdf

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.

Author : William Bragg Ewald,William Ewald
Publisher : Oxford University Press
Page : 709 pages
File Size : 55,8 Mb
Release : 1999
Category : Mathematics
ISBN : 9780198505365

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From Kant to Hilbert Volume 2 by William Bragg Ewald,William Ewald Pdf

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.

Author : William Bragg Ewald
Publisher : OUP Oxford
Page : 710 pages
File Size : 42,5 Mb
Release : 2005-04-21
Category : Mathematics
ISBN : 9780191523106

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From Kant to Hilbert Volume 2 by William Bragg Ewald Pdf

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.

Author : William Ewald
Publisher : Unknown
Page : 128 pages
File Size : 52,7 Mb
Release : 1996
Category : Electronic
ISBN : 019850537X

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From Kant to Hilbert: a Source Book in the Foundations of Mathematics by William Ewald Pdf

Author : Sandra Lapointe
Publisher : Routledge
Page : 256 pages
File Size : 45,8 Mb
Release : 2020-09-30
Category : Analysis (Philosophy)
ISBN : 0367663341

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Logic from Kant to Russell by Sandra Lapointe Pdf

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.

Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 55,7 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X

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Principia Mathematica by Alfred North Whitehead,Bertrand Russell Pdf

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

Author : Øystein Linnebo
Publisher : Princeton University Press
Page : 214 pages
File Size : 55,7 Mb
Release : 2020-03-24
Category : Mathematics
ISBN : 9780691202297

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Philosophy of Mathematics by Øystein Linnebo Pdf

A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.

Author : Paolo Mancosu,Benito Miller,Amy Rocha,Walter Van Stigt
Publisher : Oxford University Press, USA
Page : 337 pages
File Size : 49,5 Mb
Release : 1998
Category : Mathematics
ISBN : 0195096312

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From Brouwer to Hilbert by Paolo Mancosu,Benito Miller,Amy Rocha,Walter Van Stigt Pdf

From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays inproof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors and many others. The articleshave been translated for the first time from Dutch, French, and German, and the volume is divided into four sections devoted to (1) Brouwer, (2) Weyl, (3) Bernays and Hilbert, and (4) the emergence of intuitionistic logic. Each section opens with an introduction which provides the necessaryhistorical and technical context for understanding the articles. Although most contemporary work in this field takes its start from the groundbreaking contributions of these major figures, a good, scholarly introduction to the area was not available until now. Unique and accessible, From Brouwer ToHilbert will serve as an ideal text for undergraduate and graduate courses in the philosophy of mathematics, and will also be an invaluable resource for philosophers, mathematicians, and interested non-specialists.

Author : Jeremy Gray
Publisher : Princeton University Press
Page : 528 pages
File Size : 45,7 Mb
Release : 2008-09-02
Category : Mathematics
ISBN : 9781400829040

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Plato's Ghost by Jeremy Gray Pdf

Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 51,8 Mb
Release : 1966
Category : Electronic
ISBN : OCLC:473160649

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From Kant to Hilbert by Anonim Pdf

Author : Reuben Hersh
Publisher : Oxford University Press
Page : 368 pages
File Size : 51,9 Mb
Release : 1997-08-21
Category : Mathematics
ISBN : 9780198027362

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What Is Mathematics, Really? by Reuben Hersh Pdf

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

Author : Hermann Weyl
Publisher : Princeton University Press
Page : 338 pages
File Size : 51,6 Mb
Release : 2009-05-17
Category : Mathematics
ISBN : 0691141207

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Philosophy of Mathematics and Natural Science by Hermann Weyl Pdf

History of mathematics.

Author : William Ewald
Publisher : Unknown
Page : 128 pages
File Size : 53,9 Mb
Release : 1999
Category : Electronic
ISBN : OCLC:1146496526

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From Kant to Hilbert by William Ewald Pdf

Author : Jaakko Hintikka
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 53,8 Mb
Release : 2013-03-09
Category : Philosophy
ISBN : 9789401584784

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From Dedekind to Gödel by Jaakko Hintikka Pdf

Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either. Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.

Author : Roman Kossak,Philip Ording
Publisher : Springer
Page : 305 pages
File Size : 47,8 Mb
Release : 2017-06-28
Category : Mathematics
ISBN : 9783319533858

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Simplicity: Ideals of Practice in Mathematics and the Arts by Roman Kossak,Philip Ording Pdf

To find "criteria of simplicity" was the goal of David Hilbert's recently discovered twenty-fourth problem on his renowned list of open problems given at the 1900 International Congress of Mathematicians in Paris. At the same time, simplicity and economy of means are powerful impulses in the creation of artworks. This was an inspiration for a conference, titled the same as this volume, that took place at the Graduate Center of the City University of New York in April of 2013. This volume includes selected lectures presented at the conference, and additional contributions offering diverse perspectives from art and architecture, the philosophy and history of mathematics, and current mathematical practice.