The Principles of MathematicsPure Mathematics is the class of all propositions of the form p implies q, where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth. |
Contents
III | 3 |
IV | 4 |
V | 5 |
VI | 6 |
VII | 7 |
VIII | 8 |
IX | 10 |
X | 11 |
CCXIX | 271 |
CCXX | 272 |
CCXXI | 274 |
CCXXII | 276 |
CCXXIII | 277 |
CCXXIV | 278 |
CCXXV | 279 |
CCXXVI | 280 |
XII | 13 |
XIII | 14 |
XV | 15 |
XVI | 16 |
XVII | 17 |
XVIII | 18 |
XIX | 19 |
XX | 20 |
XXI | 21 |
XXII | 23 |
XXIV | 24 |
XXV | 25 |
XXVI | 26 |
XXVIII | 27 |
XXIX | 28 |
XXX | 29 |
XXXI | 31 |
XXXII | 32 |
XXXIII | 33 |
XXXIV | 34 |
XXXV | 35 |
XXXVI | 36 |
XXXVII | 38 |
XXXVIII | 39 |
XXXIX | 40 |
XL | 42 |
XLI | 43 |
XLII | 44 |
XLIII | 45 |
XLIV | 46 |
XLV | 47 |
XLVI | 49 |
XLVIII | 50 |
XLIX | 53 |
L | 54 |
LI | 55 |
LII | 56 |
LIII | 58 |
LIV | 59 |
LV | 61 |
LVI | 62 |
LVII | 63 |
LVIII | 64 |
LIX | 66 |
LXI | 67 |
LXII | 68 |
LXIII | 69 |
LXIV | 72 |
LXV | 73 |
LXVI | 76 |
LXVII | 77 |
LXIX | 78 |
LXX | 79 |
LXXI | 80 |
LXXII | 82 |
LXXIII | 83 |
LXXIV | 84 |
LXXV | 86 |
LXXVI | 88 |
LXXVII | 89 |
LXXVIII | 91 |
LXXX | 92 |
LXXXI | 93 |
LXXXII | 95 |
LXXXIII | 96 |
LXXXIV | 97 |
LXXXV | 98 |
LXXXVI | 99 |
LXXXVII | 101 |
LXXXVIII | 102 |
XC | 103 |
XCI | 104 |
XCII | 105 |
XCIII | 106 |
XCIV | 109 |
XCV | 111 |
XCVI | 112 |
XCVII | 114 |
XCVIII | 115 |
XCIX | 117 |
C | 118 |
CI | 119 |
CII | 121 |
CIII | 123 |
CIV | 124 |
CV | 125 |
CVII | 127 |
CVIII | 129 |
CIX | 130 |
CX | 131 |
CXI | 132 |
CXII | 133 |
CXIV | 135 |
CXV | 137 |
CXVI | 138 |
CXVII | 140 |
CXVIII | 141 |
CXIX | 143 |
CXX | 144 |
CXXI | 146 |
CXXIII | 149 |
CXXIV | 150 |
CXXVI | 151 |
CXXVII | 152 |
CXXVIII | 155 |
CXXIX | 157 |
CXXX | 158 |
CXXXI | 159 |
CXXXIII | 160 |
CXXXIV | 162 |
CXXXV | 164 |
CXXXVI | 166 |
CXXXVII | 167 |
CXXXVIII | 170 |
CXXXIX | 171 |
CXL | 173 |
CXLI | 174 |
CXLII | 176 |
CXLIII | 177 |
CXLIV | 178 |
CXLV | 179 |
CXLVI | 181 |
CXLVII | 182 |
CXLVIII | 184 |
CLI | 185 |
CLII | 186 |
CLIII | 187 |
CLIV | 188 |
CLV | 189 |
CLVI | 190 |
CLVII | 192 |
CLIX | 193 |
CLX | 194 |
CLXI | 197 |
CLXII | 199 |
CLXIII | 200 |
CLXIV | 203 |
CLXV | 204 |
CLXVI | 205 |
CLXVIII | 207 |
CLXIX | 208 |
CLXX | 210 |
CLXXI | 211 |
CLXXII | 212 |
CLXXIII | 213 |
CLXXIV | 214 |
CLXXV | 215 |
CLXXVI | 216 |
CLXXVII | 218 |
CLXXVIII | 219 |
CLXXIX | 220 |
CLXXX | 221 |
CLXXXI | 222 |
CLXXXIII | 224 |
CLXXXIV | 226 |
CLXXXV | 227 |
CLXXXVI | 228 |
CLXXXVII | 229 |
CLXXXVIII | 231 |
CLXXXIX | 232 |
CXC | 234 |
CXCI | 236 |
CXCII | 237 |
CXCIII | 238 |
CXCIV | 239 |
CXCV | 240 |
CXCVI | 242 |
CXCVII | 243 |
CXCVIII | 244 |
CXCIX | 245 |
CC | 246 |
CCI | 247 |
CCII | 248 |
CCIV | 249 |
CCV | 252 |
CCVI | 253 |
CCVII | 254 |
CCIX | 255 |
CCX | 257 |
CCXI | 259 |
CCXII | 260 |
CCXIII | 262 |
CCXIV | 263 |
CCXV | 264 |
CCXVI | 267 |
CCXVII | 269 |
CCXVIII | 270 |
CCXXVII | 282 |
CCXXVIII | 283 |
CCXXIX | 285 |
CCXXX | 287 |
CCXXXI | 288 |
CCXXXII | 290 |
CCXXXIII | 291 |
CCXXXIV | 293 |
CCXXXV | 296 |
CCXXXVI | 298 |
CCXXXVII | 299 |
CCXXXVIII | 300 |
CCXXXIX | 303 |
CCXL | 304 |
CCXLI | 306 |
CCXLII | 307 |
CCXLIII | 309 |
CCXLIV | 310 |
CCXLV | 311 |
CCXLVI | 312 |
CCXLVII | 314 |
CCXLVIII | 315 |
CCXLIX | 317 |
CCL | 319 |
CCLI | 320 |
CCLII | 321 |
CCLIV | 322 |
CCLV | 323 |
CCLVI | 325 |
CCLVII | 326 |
CCLVIII | 328 |
CCLIX | 329 |
CCLX | 330 |
CCLXI | 331 |
CCLXII | 332 |
CCLXIII | 334 |
CCLXIV | 335 |
CCLXV | 337 |
CCLXVI | 338 |
CCLXVII | 339 |
CCLXVIII | 340 |
CCLXIX | 341 |
CCLXX | 342 |
CCLXXI | 344 |
CCLXXII | 346 |
CCLXXIII | 347 |
CCLXXIV | 348 |
CCLXXVI | 349 |
CCLXXVII | 350 |
CCLXXVIII | 351 |
CCLXXIX | 352 |
CCLXXX | 353 |
CCLXXXII | 355 |
CCLXXXIII | 356 |
CCLXXXIV | 357 |
CCLXXXV | 358 |
CCLXXXVI | 359 |
CCLXXXVII | 360 |
CCLXXXVIII | 361 |
CCLXXXIX | 362 |
CCXC | 363 |
CCXCI | 364 |
CCXCII | 366 |
CCXCIV | 367 |
CCXCV | 368 |
CCXCVI | 369 |
CCXCVII | 371 |
CCXCVIII | 372 |
CCC | 374 |
CCCI | 375 |
CCCII | 376 |
CCCIV | 377 |
CCCV | 378 |
CCCVI | 379 |
CCCVII | 381 |
CCCVIII | 382 |
CCCIX | 384 |
CCCX | 385 |
CCCXI | 386 |
CCCXII | 388 |
CCCXIII | 389 |
CCCXIV | 390 |
CCCXVI | 391 |
CCCXVII | 392 |
CCCXVIII | 393 |
CCCXIX | 394 |
CCCXX | 395 |
CCCXXI | 396 |
CCCXXII | 397 |
CCCXXIII | 398 |
CCCXXIV | 399 |
CCCXXV | 400 |
CCCXXVI | 401 |
CCCXXVII | 402 |
CCCXXVIII | 403 |
CCCXXIX | 404 |
CCCXXX | 405 |
CCCXXXI | 406 |
CCCXXXII | 407 |
CCCXXXIII | 408 |
CCCXXXIV | 409 |
CCCXXXV | 410 |
CCCXXXVI | 411 |
CCCXXXVII | 413 |
CCCXXXVIII | 414 |
CCCXXXIX | 415 |
CCCXL | 416 |
CCCXLI | 417 |
CCCXLIII | 419 |
CCCXLIV | 420 |
CCCXLV | 421 |
CCCXLVI | 423 |
CCCXLVII | 425 |
CCCXLVIII | 426 |
CCCXLIX | 427 |
CCCL | 429 |
CCCLI | 430 |
CCCLII | 432 |
CCCLIII | 434 |
CCCLIV | 437 |
CCCLV | 438 |
CCCLVI | 440 |
CCCLVII | 441 |
CCCLVIII | 442 |
CCCLIX | 445 |
CCCLX | 446 |
CCCLXII | 448 |
CCCLXIII | 449 |
CCCLXIV | 451 |
CCCLXV | 452 |
CCCLXVI | 454 |
CCCLXVIII | 456 |
CCCLXIX | 457 |
CCCLXX | 458 |
CCCLXXI | 461 |
CCCLXXII | 463 |
CCCLXXIII | 465 |
CCCLXXIV | 466 |
CCCLXXV | 467 |
CCCLXXVI | 468 |
CCCLXXVII | 469 |
CCCLXXIX | 471 |
CCCLXXX | 472 |
CCCLXXXI | 473 |
CCCLXXXII | 474 |
CCCLXXXIV | 475 |
CCCLXXXV | 476 |
CCCLXXXVI | 477 |
CCCLXXXVII | 478 |
CCCLXXXVIII | 480 |
CCCLXXXIX | 482 |
CCCXC | 483 |
CCCXCII | 485 |
CCCXCIII | 486 |
CCCXCIV | 487 |
CCCXCV | 488 |
CCCXCVI | 489 |
CCCXCVII | 490 |
CCCXCIX | 491 |
CD | 492 |
CDII | 494 |
CDIII | 495 |
CDIV | 496 |
CDVI | 497 |
CDVII | 501 |
CDVIII | 502 |
CDX | 503 |
CDXI | 504 |
CDXII | 505 |
CDXIII | 507 |
CDXIV | 508 |
CDXV | 510 |
CDXVII | 512 |
CDXVIII | 513 |
CDXIX | 514 |
CDXX | 515 |
CDXXI | 516 |
CDXXII | 517 |
CDXXIII | 518 |
CDXXV | 519 |
CDXXVI | 520 |
CDXXVIII | 523 |
CDXXIX | 525 |
CDXXX | 526 |
CDXXXI | 527 |
529 | |
Other editions - View all
Common terms and phrases
argument Arithmetic assertion asymmetrical relation axiom axiom of Archimedes belongs calculus called Cantor cardinal number Chapter class of classes class of terms class-concept collection compact series complex numbers concept concerning considered contained continuity contradiction correlation defined definition denoted descriptive Geometry discussion distance distinction distinguish divisibility entities equal equivalent Euclidean space existence fact false finite number follows formal implication Frege given greater Hence hold ideal points identical indefinable infinite classes infinitesimal infinity integers involved kind Leibniz less limit logical constants logical product magnitude material implication mathematical induction means metrical notion null-class number of terms object obtained one-one relation ordinal Peano philosophical plane possible predicate premisses present presupposed principle projective Geometry projective space properties propositional function prove quantities question rational numbers real numbers regard seems segments sense Socrates straight line stretch supposed Symbolic Logic theory transfinite transitive transitive relation true values variable zero