The Principles of Mathematics, Volume 1 (Google eBook)

Front Cover
University Press, 1903 - Mathematics - 534 pages
4 Reviews
  

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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

Common terms and phrases

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.

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