Index:The Foundations of Science (1913).djvu

Title	The Foundations of Science
Author	Henri Poincaré
Translator	George Bruce Halsted
Year	1913
Publisher	The Science Press
Location	New York
Source	djvu
Progress	To be proofread
Transclusion	Index not transcluded or unreviewed

Pages (key to Page Status)

Cover – – – – – i ii iii iv v vi vii viii ix x xi xii 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 – – – – – – Cover

CONTENTS

PAGE
Henri Poincaré	xi
Author’s Preface to the Translation	3
SCIENCE AND HYPOTHESIS
Introduction by Royce	9
Introduction	27
Part I. Number and Magnitude
CHAPTER I.—On the Nature of Mathematical Reasoning	31
Syllogistie Deduction	31
Verification and Proof	32
Elements of Arithmetic	33
Reasoning by Recurrence	37
Induction	40
Mathematical Construction	41
CHAPTER II.—Mathematical Magnitude and Experience	43
Definition of Incommensurables	44
The Physical Continuum	46
Creation of the Mathematical Continuum	46
Measurable Magnitude	49
Various Remarks (Curves without Tangents)	50
The Physical Continuum of Several Dimensions	52
The Mathematical Continuum of Several Dimensions	58
Part II. Space
CHAPTER III.—The Non-Euclidean Geometries	55
The Bolyai-Lobachevski Geometry	56
Riemann’s Geometry	57
The Surfaces of Constant Curvature	58
Interpretation of Non-Euclidean Geometries	59
The Implicit Axioms	60
The Fourth Geometry	62
Lie’s Theorem	62
Riemann’s Geometries	63
On the Nature-of Axioms	63
CHAPTER IV.—Space and Geometry	66
Geometric Space and Perceptual Space	66
Visual Space	67
Tactile Space and Motor Space	68
Characteristics of Perceptual Space	69
Change of State and Change of Position	70
Conditions of Compensation	72
Solid Bodies and Geometry	73
Law of Homogeneity	74
The Non-Euclidean World	75
The World of Four Dimensions	78
Conclusions	79
Chapter V.—Experience and Geometry	81
Geometry and Astronomy	81
The Law of Relativity	83
Bearing of Experiments	86
Supplement (What is a Point?)	89
Ancestral Experience	91
Part III. Force
Chapter VI.—The Classic Mechanics	92
The Principle of Inertia	93
The Law of Acceleration	97
Anthropomorphic Mechanics	103
The School of the Thread	104
Chapter VII.—Relative Motion and Absolute Motion	107
The Principle of Relative Motion	107
Newton’s Argument	108
Chapter VIII.—Emergy and Thermodynamics	115
Energetics	115
Thermodynamics	119
General Conclusions on Part III	123
Part IV. Nature
Chapter IX.—Hypotheses in Physics	127
The Rôle of Experiment and Generalization	127
The Unity of Nature	130
The Rôle of Hypothesis	133
Origin of Mathematical Physics	136
Chapter X.—The Theories of Modern Physics	140
Meaning of Physical Theories	140
Physics and Mechanism	144
Present State of the Science	148
Chapter XI.—The Caleulus of Probabilities	155
Classification of the Problems of Probability	158
Probability in Mathematics	161
Probability in the Physical Sciences	164
Rouge et noir	167
The Probability of Causes	169
The Theory of Errors	170
Conclusions	172
Chapter XII.—Optics and Electricity	174
Fresnel’s Theory	174
Maxwell’s Theory	175
The Mechanical Explanation of Physical Phenomena	177
Chapter XIII.—Electrodynamics	184
Ampére’s Theory	184
Closed Currents	185
Action of a Closed Current on a Portion of Current	186
Continuous Rotations	187
Mutual Action of Two Open Currents	189
Induction	190
Theory of Helmholtz	191
Difficulties Raised by these Theories	193
Maxwell’s Theory	193
Rowland’s Experiment	194
The Theory of Lorentz	196
THE VALUE OF SCIENCE
Translator’s Introduction	201
Does the Scientist Create Science?	201
The Mind Dispelling Optical Illusions	202
Euclid not Necessary	202
Without Hypotheses, no Science	203
What Outcome?	203
Introduction	205
Part I. The Mathematical Sciences
Chapter I.—Intuition and Logie in Mathematics	210
Chapter II.—The Measure of Time	223
Chapter III.—The Notion of Space	235
Qualitative, Geometry	238
The Physical Continuum of Several Dimensions	240
The Notion of Point	244
The Notion of Displacement	247
Visual Space	252
Chapter IV.—Space and its Three Dimensions	256
The Group of Displacements	256
Identity of Two Points	259
Tactile Space	264
Identity of the Different Spaces	268
Space and Empiricism	271
Rôle of the Semicircular Canals	276
Part II. The Physical Sciences
Chapter V.—Analysis and Physics	279
Chapter VI.—Astronomy	289
Chapter VII.—The History of Mathematical Physics	297
The Physics of Central Forces	297
The Physics of the Principles	299
Chapter VIII.—The Present Crisis in Physics	303
The New Crisis	303
Carnot’s Principle	303
The Principle of Relativity	305
Newton’s Principle	308
Lavoisier’s Principle	310
Mayer’s Principle	312
Chapter IX.—The Future of Mathematical Physies	314
The Principles and Experiment	314
The Role of the Analyst	314
Aberration and Astronomy	315
Electrons and Spectra	316
Conventions preceding Experiment	317
Future Mathematical Physics	319
Part III. The Objective Value of Science
Chapter X.—Is Science Artificial?	321
The Philosophy of LeRoy	321
Science, Rule of Action	323
The Crude Fact and the Scientific Fact	325
Nominalism and the Universal Invariant	333
Chapter XI.—Science and Reality	340
Contingence and Determinism	340
Objectivity of Science	347
The Rotation of the Earth	353
Science for Its Own Sake	354
SCIENCE AND METHOD
Introduction	359
Book I. Science and the Scientist
Chapter I.—The Choice of Facts	362
Chapter II.—The Future of Mathematics	369
Chapter III.—Mathematical Creation	383
Chapter IV.—Chance	395
Book II. Mathematical Reasoning
Chapter I.—The Relativity of Space	413
Chapter II.—Mathematical Definitions and Teaching	430
Chapter III.—Mathematics and Logic	448
Chapter IV.—The New Logics	460
Chapter V.—The Latest Efforts of the Logisticians	472
Book III. The New Mechanics
Chapter I.—Mechanics and Radium	486
Chapter II.—Mechanics and Optics	496
Chapter III.—The New Mechanics and Astronomy	515
Book IV. Astronomic Science
Chapter I.—The Milky Way and the Theory of Gases	522
Chapter I.—French Geodesy	535
General Conclusions	544
Index	547