# The Principles of Mathematics, Volume 1 (Google eBook)

University Press, 1903 - Mathematics - 534 pages

### What people are saying -Write a review

#### Review: The Principles of Mathematics

User Review  - Cayden - Goodreads

Bertrand Russell has always given me a bit of a headache. Read full review

#### Review: The Principles of Mathematics

User Review  - Keshav - Goodreads

Despite its title, this is NOT a math book, at least in the conventional definition of the term. It is indeed true that the subject matter of the book is indeed mathematics, but it neither teaches the ... Read full review

### Contents

 II 3 III 10 IV 33 V 42 VI 53 VII 66 VIII 82 IX 89
 XXXV 252 XXXVI 257 XXXVII 259 XXXVIII 270 XXXIX 276 XL 287 XLI 296 XLII 304

 X 95 XI 101 XII 109 XIII 111 XIV 117 XV 121 XVI 124 XVII 129 XVIII 137 XIX 143 XX 149 XXI 155 XXII 157 XXIII 170 XXIV 176 XXV 184 XXVI 188 XXVII 197 XXVIII 199 XXIX 207 XXX 218 XXXI 227 XXXII 234 XXXIII 239 XXXIV 245
 XLIII 312 XLIV 325 XLV 331 XLVI 338 XLVII 346 XLVIII 355 XLIX 369 L 371 LI 381 LII 393 LIII 404 LIV 419 LV 429 LVI 437 LVII 445 LVIII 456 LIX 463 LX 465 LXI 469 LXII 474 LXIII 480 LXIV 482 LXV 489 LXVI 494

### Popular passages

Page 3 - 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.
Page 459 - It follows that an infinite series already elapsed is impossible and that, consequently, a beginning of the world is a necessary condition of its existence. And this was the first thing to be proved. As regards the second, let us take the opposite for granted.
Page 460 - For let us assume that compound substances did not consist of simple parts, then if all composition is removed in thought, there would be no compound part, and (as no simple parts are admitted) no simple...
Page 168 - greater than" is typical in this respect; it is conventional to argue that if A is greater than B, and B is greater than C, then A is greater than C.
Page 252 - As for the objection that space and time are quantities, or rather things endowed with quantity ; and that situation and order are not so: I answer, that order also has its quantity; there is in it, that which goes before, and that which follows ; there is distance or interval.
Page 222 - The ratio or proportion between two lines L and M, may be conceived three several ways; as a ratio of the greater L, to the lesser M; as a ratio of the lesser M, to the greater L; and lastly, as something abstracted from both, that is, as the ratio between L and M, without considering which is the antecedent, or which the consequent; which the subject, and which the object.
Page 9 - For example, it is always true that if p implies q and q implies r then p implies r, or that, if all a's are j3's and x is an a then x is a j8.
Page 42 - The study of grammar, in my opinion, is capable of throwing far more light on philosophical questions than is commonly supposed by philosophers. Although a grammatical distinction cannot be uncritically assumed to correspond to a genuine philosophical difference, yet the one is prima facie evidence of the other, and may often be most usefully employed as a source of discovery.
Page 469 - Change is the difference, in respect of truth or falsehood, between a proposition concerning an entity and the time T, and a proposition concerning the same entity and the time T', provided that these propositions differ only by the fact that T occurs in the one where T
Page 358 - I maintain that, if he had lived for ever, and had not wearied of his task, then, even if his life had continued as eventfully as it began, no part of his biography would have remained unwritten.