| The Growth of Mathematical Knowledge 2000 Edition Contributor(s): Grosholz, Emily (Editor), Breger, Herbert (Editor) |
|
 |
ISBN: 0792361512 ISBN-13: 9780792361510 Publisher: Springer OUR PRICE: $237.49 Product Type: Hardcover - Other Formats Published: January 2000 Annotation: This book draws its inspiration from Hilbert, Wittgenstein, Cavailles and Lakatos and is designed to reconfigure contemporary philosophy of mathematics by making the growth of knowledge rather than its foundations central to the study of mathematical rationality, and by analyzing the notion of growth in historical as well as logical terms. Not a mere compendium of opinions, it is organised in dialogical forms, with each philosophical thesis answered by one or more historical case studies designed to support, complicate or question it. The first part of the book examines the role of scientific theory and empirical fact in the growth of mathematical knowledge. The second examines the role of abstraction, analysis and axiomatization. The third raises the question of whether the growth of mathematical knowledge constitutes progress, and how progress may be understood. Readership: Students and scholars concerned with the history and philosophy of mathematics and the formal sciences. |
| Additional Information |
| BISAC Categories: - Mathematics |
| Dewey: 510.1 |
| LCCN: 99089023 |
| Series: Synthese Library (Hardcover) |
| Physical Information: 1.06" H x 6.14" W x 9.21" (1.85 lbs) 416 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics. |