Cover

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Title page, Copyright

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Preface

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pp. v-vi

The chapters of this book were originally separate essays for several purposes, and all but one have been published before, beginning in 1961. The essays have now been revised, and linked up; and an Introduction, and a collection of Biographical Sketches in lieu of an Epilogue, have been added. ...

Contents

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pp. vii-x

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Introduction

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pp. 3-10

The essays of this collection are all concerned with the role of mathematics in the rise and unfolding of Western intellectuality, with the sources and manifestations of the clarity and the mystique of mathematics, and with its ubiquity, universality, and indispensability. ...

Part I. Essays

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1. From Myth to Mathematics to Knowledge

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pp. 13-58

What indeed is mathematics? This question, if asked in earnest, has no answer, not a satisfactory one; only part answers and observations can be attempted. ...

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2. How History of Science Differs from Other History

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pp. 59-130

There are differences of consequence, we contend, between history of science and other history, mainly general (that is, politico-social) history, but also history of literature, and even history of philosophy proper. The differences are differences of degree only, but they are significant. ...

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3. Revolutions in Physics and Crises in Mathematics

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pp. 131-142

We will now deal with two topics which, although separable, are closely connected with each other. The first and larger part of the chapter is concerned with the conception of a revolution in physics, as recently blueprinted in a provocative book by Thomas Kuhn.1 ...

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4. Aristotle's Physics and Today's Physics

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pp. 143-178

In making some observations on the nature of the physics of the Greeks, especially of the physics of Aristotle, our aim will be to point up similarities and dissimilarities, analogies and discrepancies, between the physics of antiquity and the physics of today. ...

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5. The Role of Mathematics in the Rise of Mechanics

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pp. 179-208

Mechanics, as a part of physics, is very mathematical, in imagery, content, and consequences. We will make some observations on the mathematical structure of mechanics during some phases of its development, and we will be concerned with the inward mathematical texture rather than with the outward mathematical setting. ...

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6. The Significance of Some Basic Mathematical Conceptions for Physics

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pp. 209-254

The present chapter supplements and continues the preceding one, and we will again make observations on the relations between mathematics and physics on the level of abstractions and conceptualizations; in the preceding chapter we emphasized mechanics, and at present we will be more concerned with physics in general. ...

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7. The Essence of Mathematics

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pp. 255-274

Mathematics is frequently encountered in association and interaction with Astronomy, Physics, and other branches of Natural Science, and it also has deep-rooted affinities to what are called Humanities nowadays. Actually, it is a realm of knowledge entirely by itself, and one of considerable scope too; ...

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8. The Essence of Analysis

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pp. 275-300

Analysis is one of three main divisions of mathematics, the other two being (i) Geometry and Topology and (ii) Algebra and Arithmetic. In extent, Analysis is the largest; it comprises subdivisions which are nearly autonomous and which are easier to describe than the whole division. ...

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Part II. Biographical Sketches

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pp. 301-372

Aeschylus (525-456 B.C.), Attic Tragedian, the first, and still one of the greatest, tragedians in the "West" of whom entire plays survive. Aeschylus derived from landed aristocracy, and, although a lifelong poet by avocation, he led, as customary with Athenians of his generation, a crowded citizen's life in the service of the polis. ...

Index

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pp. 373-386