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The Nature Of Mathematical Knowledge

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The Nature Of Mathematical Knowledge

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Author : San Diego Philip Kitcher Professor of Philosophy University of California
language : en
Publisher: Oxford University Press, USA
Release Date : 1983-04-21

The Nature Of Mathematical Knowledge written by San Diego Philip Kitcher Professor of Philosophy University of California and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-04-21 with Mathematics categories.

This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.

The Nature Of Mathematical Knowledge

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Author : Philip Kitcher
language : en
Publisher:
Release Date : 1983

The Nature Of Mathematical Knowledge written by Philip Kitcher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

The Nature Of Mathematical Knowledge

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Author : Philip Kitcher
language : en
Publisher:
Release Date : 1984

Mathematical Knowledge

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Author : Mary Leng
language : en
Publisher: OUP Oxford
Release Date : 2007-11-15

Mathematical Knowledge written by Mary Leng and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-15 with Philosophy categories.

What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense of the current state of debate in this fascinating field.

The Nature Of Mathematical Knowledge

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Author : PHILIP. KITCHER
language : en
Publisher:
Release Date : 2011

The Nature Of Mathematical Knowledge written by PHILIP. KITCHER and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

Mathematical Knowledge And The Interplay Of Practices

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Author : José Ferreirós
language : en
Publisher: Princeton University Press
Release Date : 2015-12-22

Mathematical Knowledge And The Interplay Of Practices written by José Ferreirós and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-22 with Science categories.

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

The Growth Of Mathematical Knowledge

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Author : Emily Grosholz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

The Growth Of Mathematical Knowledge written by Emily Grosholz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Philosophy categories.

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.

Mathematical Understanding Of Nature

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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-09-04

Mathematical Understanding Of Nature written by Vladimir Igorevich Arnolʹd and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-04 with Mathematics categories.

"This collection of 39 short stories gives the reader a unique opportunity to take a look at the scientific philosophy of Vladimir Arnold, one of the most original contemporary researchers. Topics of the stories included range from astronomy, to mirages, to motion of glaciers, to geometry of mirrors and beyond. In each case Arnold's explanation is both deep and simple, which makes the book interesting and accessible to an extremely broad readership. Original illustrations hand drawn by the author help the reader to further understand and appreciate Arnold's view on the relationship between mathematics and science."--

Explanation And Proof In Mathematics

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Author : Gila Hanna
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-04

Explanation And Proof In Mathematics written by Gila Hanna and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-04 with Education categories.

In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.

A Mathematical Nature Walk

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Author : John A. Adam
language : en
Publisher: Princeton University Press
Release Date : 2011-09-12

A Mathematical Nature Walk written by John A. Adam and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-12 with Nature categories.

How heavy is that cloud? Why can you see farther in rain than in fog? Why are the droplets on that spider web spaced apart so evenly? If you have ever asked questions like these while outdoors, and wondered how you might figure out the answers, this is a book for you. An entertaining and informative collection of fascinating puzzles from the natural world around us, A Mathematical Nature Walk will delight anyone who loves nature or math or both. John Adam presents ninety-six questions about many common natural phenomena--and a few uncommon ones--and then shows how to answer them using mostly basic mathematics. Can you weigh a pumpkin just by carefully looking at it? Why can you see farther in rain than in fog? What causes the variations in the colors of butterfly wings, bird feathers, and oil slicks? And why are large haystacks prone to spontaneous combustion? These are just a few of the questions you'll find inside. Many of the problems are illustrated with photos and drawings, and the book also has answers, a glossary of terms, and a list of some of the patterns found in nature. About a quarter of the questions can be answered with arithmetic, and many of the rest require only precalculus. But regardless of math background, readers will learn from the informal descriptions of the problems and gain a new appreciation of the beauty of nature and the mathematics that lies behind it.

The Nature Of Mathematical Knowledge

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