國立虎尾科技大學 |

Logos and Alogon = thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Logos and Alogon/ by Arkady Plotnitsky.
Reminder of title:	thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns /
Author:	Plotnitsky, Arkady.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xvi, 294 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Mathematics - Philosophy. -
Online resource:	https://doi.org/10.1007/978-3-031-13678-8
ISBN:	9783031136788

Logos and Alogon = thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns /
Plotnitsky, Arkady.

Logos and Alogonthinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns /[electronic resource] :by Arkady Plotnitsky. - Cham :Springer International Publishing :2022. - xvi, 294 p. :ill., digital ;24 cm.

1 The Ghost and the Spirit of Pythagoras in Modern and Modernist Mathematics -- 2 Plato's Ghosts: Pythagorean Mathematics, Socratic Philosophy, and Tragic Art -- 3 'Comprehending the Connection of Things': Bernhard Riemann and the Architecture of Mathematical Concepts -- 4 What is a Curve?: From Geometry to Algebra, from Modern to Modernist Mathematics -- 5 Returns of Geometry: From the Pythagoreans to Mathematical Modernism and Beyond -- 6 Who Thinks Abstractly: Emmy Noether and Modernist Mathematics -- 7 Mathematical Practice as Philosophy, with Galois, Riemann, Poincaré, and Grothendieck.

This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book's title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields.

ISBN: 9783031136788

Standard No.: 10.1007/978-3-031-13678-8doiSubjects--Topical Terms:

575254
Mathematics
--Philosophy.

LC Class. No.: QA8.4 / .P56 2022

Dewey Class. No.: 510.1

Logos and Alogon = thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns /
LDR:02907nam a2200325 a 4500 001 1105454
003 DE-He213
005 20230116122221.0
006 m d
007 cr nn 008maaau
008 231013s2022 sz s 0 eng d
020 $a 9783031136788 $q (electronic bk.)
020 $a 9783031136771 $q (paper)
024 7 $a 10.1007/978-3-031-13678-8 $2 doi
035 $a 978-3-031-13678-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA8.4 $b .P56 2022
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 .P729 2022
100 1 $a Plotnitsky, Arkady. $3 1114013
245 1 0 $a Logos and Alogon $h [electronic resource] : $b thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns / $c by Arkady Plotnitsky.
260 $a Cham : $c 2022. $b Springer International Publishing : $b Imprint: Springer,
300 $a xvi, 294 p. : $b ill., digital ; $c 24 cm.
505 0 $a 1 The Ghost and the Spirit of Pythagoras in Modern and Modernist Mathematics -- 2 Plato's Ghosts: Pythagorean Mathematics, Socratic Philosophy, and Tragic Art -- 3 'Comprehending the Connection of Things': Bernhard Riemann and the Architecture of Mathematical Concepts -- 4 What is a Curve?: From Geometry to Algebra, from Modern to Modernist Mathematics -- 5 Returns of Geometry: From the Pythagoreans to Mathematical Modernism and Beyond -- 6 Who Thinks Abstractly: Emmy Noether and Modernist Mathematics -- 7 Mathematical Practice as Philosophy, with Galois, Riemann, Poincaré, and Grothendieck.
520 $a This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book's title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields.
650 0 $a Mathematics $x Philosophy. $3 575254
650 1 4 $a Philosophy of Mathematics. $3 1108410
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-13678-8
950 $a Mathematics and Statistics (SpringerNature-11649)