Principles of Mathematics

BOOK COVER......Page 1
TITLE......Page 4
COPYRIGHT......Page 5
CONTENTS......Page 6
INTRODUCTION TO THE 1992 EDITION......Page 26
INTRODUCTION TO THE SECOND EDITION......Page 32
PREFACE......Page 44
Part I The Inde.nables of Mathematics......Page 50
1 DEFINITION OF PURE MATHEMATICS......Page 52
2 SYMBOLIC LOGIC......Page 59
3 IMPLICATION AND FORMAL IMPLICATION......Page 83
4 PROPER NAMES, ADJECTIVES AND VERBS......Page 92
5 DENOTING......Page 103
6 CLASSES......Page 116
7 PROPOSITIONAL FUNCTIONS......Page 131
8 THE VARIABLE......Page 138
9 RELATIONS......Page 144
10 THE CONTRADICTION......Page 150
Part II Number......Page 158
11 DEFINITION OF CARDINAL NUMBERS......Page 160
12 ADDITION AND MULTIPLICATION......Page 167
13 FINITE AND INFINITE......Page 171
14 THEORY OF FINITE NUMBERS......Page 174
15 ADDITION OF TERMS AND ADDITION OF CLASSES......Page 179
16 WHOLE AND PART......Page 187
17 INFINITE WHOLES......Page 193
18 RATIOS AND FRACTIONS......Page 199
Part III Quantity......Page 204
19 THE MEANING OF MAGNITUDE......Page 206
20 THE RANGE OF QUANTITY......Page 219
21 NUMBERS AS EXPRESSING MAGNITUDES: MEASUREMENT......Page 225
22 ZERO......Page 233
23 INFINITY, THE INFINITESIMAL AND CONTINUITY......Page 238
Part IV Order......Page 248
24 THE GENESIS OF SERIES......Page 250
25 THE MEANING OF ORDER......Page 258
26 ASYMMETRICAL RELATIONS......Page 269
27 DIFFERENCE OF SENSE AND DIFFERENCE OF SIGN......Page 278
28 ON THE DIFFERENCE BETWEEN OPEN AND CLOSED SERIES......Page 285
29 PROGRESSIONS AND ORDINAL NUMBERS......Page 290
30 DEDEKIND’S THEORY OF NUMBER......Page 296
31 DISTANCE......Page 303
Part V In.nity and Continuity......Page 308
32 THE CORRELATION OF SERIES......Page 310
33 REAL NUMBERS......Page 321
34 LIMITS AND IRRATIONAL NUMBERS......Page 327
35 CANTOR’S FIRST DEFINITION OF CONTINUITY......Page 339
36 ORDINAL CONTINUITY......Page 348
37 TRANSFINITE CARDINALS......Page 356
38 TRANSFINITE ORDINALS......Page 365
39 THE INFINITESIMAL CALCULUS......Page 379
40 THE INFINITESIMAL AND THE IMPROPER INFINITE......Page 385
41 PHILOSOPHICAL ARGUMENTS CONCERNING THE INFINITESIMAL......Page 392
42 THE PHILOSOPHY OF THE CONTINUUM......Page 400
43 THE PHILOSOPHY OF THE INFINITE......Page 409
Part VI Space......Page 424
44 DIMENSIONS AND COMPLEX NUMBERS......Page 426
45 PROJECTIVE GEOMETRY......Page 436
46 DESCRIPTIVE GEOMETRY......Page 448
47 METRICAL GEOMETRY......Page 459
48 RELATION OF METRICAL TO PROJECTIVE AND DESCRIPTIVE GEOMETRY......Page 474
49 DEFINITIONS OF VARIOUS SPACES......Page 484
50 THE CONTINUITY OF SPACE......Page 492
51 LOGICAL ARGUMENTS AGAINST POINTS......Page 500
52 KANT’S THEORY OF SPACE......Page 511
Part VII Matter and Motion......Page 518
53 MATTER......Page 520
54 MOTION......Page 525
55 CAUSALITY......Page 530
56 DEFINITION OF A DYNAMICAL WORLD......Page 536
57 NEWTON’S LAWS OF MOTION......Page 538
58 ABSOLUTE AND RELATIVE MOTION......Page 546
59 HERTZ’S DYNAMICS......Page 551
Appendices......Page 556
LIST OF ABBREVIATIONS......Page 557
Appendix A......Page 558
Appendix B......Page 583
INDEX......Page 590