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Proof and Other Dilemmas Mathematics and Philosophy~tqw~_darksiderg

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INFO

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Title................: Proof and Other Dilemmas Mathematics and Philosophy

Type.................: Ebook

Reader...............: PDF Reader

Size.................: 24.2 MB

Torrent Hash.........: 5841A0783680CB8F80F4478F7D43DC82F89238A0

Posted by............: ~tqw~



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CONTENTS

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Synopsis:

Has the advent of computers changed the nature of mathematical knowledge?

Should it? Is the importance of proof decreasing? Is there an empirical

aspect to mathematics after all? To what extent is mathematics socially

constructed? Is mathematics the "science of patterns?" Recently emerging

questions like these are discussed in this book along with some recent

thinking about classical questions.



Table Of Contents:

Acknowledgments

Introduction

I. Proof and How it is Changing

1. Proof: Its Nature and Significance

2. Implications of Experimental Mathematics for the Philosophy of Mathematics

3. On the Roles of Proof in Mathematics

II. Social Constructivist Views of Mathematics

4. When Is a Problem Solved?

5. Mathematical Practice as a Scientific Problem

6. Mathematical Domains: Social Constructs?

III. The Nature of Mathematical Objects and Mathematical Knowledge

7. The Existence of Mathematical Objects

8. Mathematical Objects

9. Mathematical Platonism

10. The Nature of Mathematical Objects

11. When is One Thing Equal to Some Other Thing?

IV. The Nature of Mathematics and its Applications

12. Extreme Science: Mathematics as the Science of Relations as Such

13. What is Mathematics? A Pedagogical Answer to a Philosophical Question

14. What Will Count as Mathematics in 2100?

15. Mathematics Applied: The Case of Addition

16. Probability—A Philosophical Overview

Glossary of Common Philosophical Terms



Product Details:

    * ISBN: 0883855674

    * ISBN-13: 9780883855676

    * Format: Hardcover, 350pp

    * Publisher: Mathematical Association of America

    * Pub. Date: February 2008



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