國立高雄大學圖資館 |

Language: English

Back

The continuous, the discrete and the...

Bell, John L.

The continuous, the discrete and the infinitesimal in philosophy and mathematics

Record Type:	Electronic resources : Monograph/item
Title/Author:	The continuous, the discrete and the infinitesimal in philosophy and mathematicsby John L. Bell.
Author:	Bell, John L.
Published:	Cham :Springer International Publishing :2019.
Description:	xvii, 313 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	MathematicsPhilosophy.
Online resource:	https://doi.org/10.1007/978-3-030-18707-1
ISBN:	9783030187071$q(electronic bk.)

The continuous, the discrete and the infinitesimal in philosophy and mathematics
Bell, John L.

The continuous, the discrete and the infinitesimal in philosophy and mathematics[electronic resource] /by John L. Bell. - Cham :Springer International Publishing :2019. - xvii, 313 p. :ill., digital ;24 cm. - The Western Ontario series in philosophy of science ;v.82. - Western Ontario series in philosophy of science ;v.81..

Part I: The Continuous, the Discrete, and the Infinitesimal in the History of Thought -- Chapter 1. The Continuous and the Discrete in Ancient Greece, the Orient, and the European Middle Ages -- Chapter 2. The 16th and 17th Centuries: The Founding of the Infinitesimal Calculus -- Chapter 3. The 18th and Early 19th Centuries: The Age of Continuity -- Chapter 4. The Reduction of the Continuous to the Discrete in the 19th and early 20th Centuries -- Chapter 5. Dissenting Voices: Divergent Conceptions of the Continuum in the 19th and Early 20th Centuries -- Part II: Continuity and Infinitesimals in Today's Mathematics -- Chapter 6. Topology -- Chapter 7. Category/Topos Theory -- Chapter 8. Nonstandard Analysis -- Chapter 9. The Constructive and Intuitionistic Continua -- Chapter 10. Smooth Infiniteimal Analysis/Synthetic Geometry.

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled 'The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,' reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,' discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincare, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.

ISBN: 9783030187071$q(electronic bk.)

Standard No.: 10.1007/978-3-030-18707-1doiSubjects--Topical Terms:

187658
Mathematics
--Philosophy.

LC Class. No.: QA8.4 / .B455 2019

Dewey Class. No.: 510.1

The continuous, the discrete and the infinitesimal in philosophy and mathematics
LDR:03723nmm a2200337 a 4500 001 566558
003 DE-He213
005 20191225095256.0
006 m d
007 cr nn 008maaau
008 200429s2019 gw s 0 eng d
020 $a 9783030187071$q(electronic bk.)
020 $a 9783030187064$q(paper)
024 7 $a 10.1007/978-3-030-18707-1 $2 doi
035 $a 978-3-030-18707-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA8.4 $b .B455 2019
072 7 $a PBB $2 bicssc
072 7 $a MAT015000 $2 bisacsh
072 7 $a PBB $2 thema
082 0 4 $a 510.1 $2 23
090 $a QA8.4 $b .B433 2019
100 1 $a Bell, John L. $3 272552
245 1 4 $a The continuous, the discrete and the infinitesimal in philosophy and mathematics $h [electronic resource] / $c by John L. Bell.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xvii, 313 p. : $b ill., digital ; $c 24 cm.
490 1 $a The Western Ontario series in philosophy of science ; $v v.82
505 0 $a Part I: The Continuous, the Discrete, and the Infinitesimal in the History of Thought -- Chapter 1. The Continuous and the Discrete in Ancient Greece, the Orient, and the European Middle Ages -- Chapter 2. The 16th and 17th Centuries: The Founding of the Infinitesimal Calculus -- Chapter 3. The 18th and Early 19th Centuries: The Age of Continuity -- Chapter 4. The Reduction of the Continuous to the Discrete in the 19th and early 20th Centuries -- Chapter 5. Dissenting Voices: Divergent Conceptions of the Continuum in the 19th and Early 20th Centuries -- Part II: Continuity and Infinitesimals in Today's Mathematics -- Chapter 6. Topology -- Chapter 7. Category/Topos Theory -- Chapter 8. Nonstandard Analysis -- Chapter 9. The Constructive and Intuitionistic Continua -- Chapter 10. Smooth Infiniteimal Analysis/Synthetic Geometry.
520 $a This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled 'The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,' reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,' discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincare, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
650 0 $a Mathematics $x Philosophy. $3 187658
650 1 4 $a Philosophy of Mathematics. $3 745264
650 2 4 $a History of Philosophy. $3 274764
650 2 4 $a Mathematical Logic and Formal Languages. $3 275383
650 2 4 $a Analysis. $3 273775
650 2 4 $a Differential Geometry. $3 273785
650 2 4 $a History of Mathematical Sciences. $3 511733
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Western Ontario series in philosophy of science ; $v v.81. $3 776367
856 4 0 $u https://doi.org/10.1007/978-3-030-18707-1
950 $a Religion and Philosophy (Springer-41175)