311 records matched your query       

Author:

Whitehead, Alfred North, 1861-1947.

Title:

Principia mathematica / by Alfred North Whitehead and Bertrand Russell.

Publisher:

Rough Draft Printing,

Copyright Date:

2011

Description:

3 volumes ; 24 cm

Subject:

Mathematics.
Mathematics--Philosophy.
Logic, Symbolic and mathematical.
Logic, Symbolic and mathematical.
Mathematics.
Mathematics--Philosophy.

Other Authors:

Russell, Bertrand, 1872-1970.

Notes:

Originally published by Cambridge : University Press, 1910-1913; digitized by Watchmaker Publishing.

Contents:

97. CHAPTER I. Analysis of the Field of a Relation into Families, p.654. CHAPTER II. THE THEORY OF LOGICAL TYPES -- CHAPTER III. INCOMPLETE SYMBOLS -- PART I. MATHEMATICAL LOGIC -- Summary of Part I., p.91 -- SECTION A. THE THEORY OF DEDUCTION, p.94 -- I. Primitive Ideas and Propositions, p.95 -- 2. Immediate Consequences of the Primitive Propositions, p.102 -- 3. The Logical Product of two Propositions, p.114 -- 4. Equivalence and Formal Rules -- 5. Miseellaneous Propositions -- SECTION B. THEORY OF APPARENT VARIABLES, p.132 -- 9. Extension of the Theory of Deduction from Lower to Higher Types of Propositions, p.132 -- 10. Theory of Propositions containing one Apparent Variable, p.143 -- 11. Theory of two Apparent Variables, p.157 -- 12. The Hierarchy of Types and the Axiom of Reducibility, p.168 -- 13. Identity, p.176 -- 14. Descriptions, p.181 -- SECTION C. CLASSES AND RELATIONS, p.196 -- 20. General Theory of Classes, p.196 -- 21. General Theory of Relations, p.211 -- 22. Calculus of Classes, p.217 -- 23. Calculus of Relations, p.226 -- 24. The Universal Class, the Null-Class, and the Existenee of Classes, p.229 -- 25. The Universal Relation, the Null Relation, and the Existence of Relations, p.241 -- SECTION D. LOGIC OF RELATIONS, p.244 -- 30. Descriptive Functions, p.245 -- 31. Converses of Relations, p.251 -- 32. Referents and Relata of a given Term with respect to a given Relation, p.255 -- 33. Domains, Converse Domains, and Fields of Relations, p.260 -- 34. The Relative Product of two Relations, p.269 -- 35. Relations with Limited Domains and Converse Domains, p.278 -- 36. Relations with Limited Fields, p.291 -- 37. Plural Descriptive Functions, p.293 -- 38. Relations and Classes derived from ll. Doulıle Deseriptive Function, p.311 -- SECTION E. PRODUCTS AND SUMS OF CLASSES, p.317 -- 40. Products and Sums of Classes of Classes, p.319 -- 41. The Prodııet and Sum of a Class of Relations, p.331 -- 42. Miscellaneous Propositions, p.336 -- 43. The Relations of a Relative Product to ita Factors, p.336 -- PART II. PROLEGOMENA TO CARDINAL ARITHMETIC -- SECTION A. UNIT CLASSES AND COUPLES, p.347 -- 50. ldentity and Diversity as Relations, p.347 -- 51. Unit Classes, p.349 -- 52. The Cardinal Number 1, p.363 -- 53. Miscellaneous Propositions involving Unit Classes, p.368 -- 54. Cardinal Couples, p.376 -- Ordinal Couples, p.383 -- The Ordinal Number 2, p.395 -- SECTION B. SUB-CLASSES, SUB-RELATlONS, AND RETATIVE TYPER, p.404 -- 60. The Sub-Classes of a given Class, p.406 -- 61. The Sub-Relations of a given Relation, p.412 -- 62. The Relation of Membership of a CIass, p.414 -- 63. Relative Types of Classes, p.419 -- 64. Relative Types of Relations, p.429 -- 65. On the Typical Definition of Ambiguous Symbols, p.434 -- SECTION C. ONE-MANY, MANY-ONE, AND ONE-ONE RELATIONS, p.437 -- 70. Relations whose Classes of Referents and of Relata belong to given Classes, p.439 -- 71. One-Many, Many-One, and One-One Relations, p.446 -- 72. Miscellaneous Propositions concerning One-Many, Many-One, and One-One Relations, p.462 -- 73. Similarity of Classes, p.476 -- 74. On One-Many and Many-One Relations with Limited Fields, p.490 -- SECTION D. SELECTIONS, p.500 -- 80. Elementary Properties of Selections, p.505 -- 81. Selections from Many-One Relations, p.519 -- 82. Selections from Relative Products, p.524 -- 83. Selections from Classes of Classes, p.531 -- 84. Classes of Mutually Exclusive Classes, p.540 -- 85. Miscellaneous Propositions, p.549 -- 88. Conditions for the Existence of Selections, p.561 -- SECTION E. INDUCTIVE RELATIONS, p.569 -- 90. On the Ancestral Relation, p.576 -- 91. On Powers of a Relation, p.601 -- 92. Powers of One-Many and Many-One Relations, p.607 -- 93. Inductive Analysis of the Field of a Relation, p.617 -- 94. On Powers of Relative Products, p.626 -- 95. On the Equi-factor Relation, p.637 -- 96. On the Posterity of a Term -- 97. Analysis of the Field of a Relation into Families, p.654.
234. Continuity of functions, p.753. PART III. CARDINAL ARITHMETIC -- Summary of Part III, p.3 -- SECTION A. DEFINITION AND LOGICAL PROPERTIES OF CARDINAL NUMBERS, p.4 -- 100. Definition and elementary properties of cardinal numbers, p.13 -- 101. On 0 and 1 and 2, p.19 -- 102. On cardinal numbers of assigned types, p.24 -- 103. Homogeneous cardinals, p.36 -- 104. Ascending cardinals, p.42 -- 105. Descending cardinals, p.52 -- 106. Cardinals of relational types, p.60 -- SECTION B. ADDITION, MULTIPLICATION AND EXPONENTIATION, p.66 -- 110. The arithmetical sum of two classes and of two cardinals, p.75 -- 111. Double similarity, p.88 -- 112. The arithmetical sum of a class of classes, p.97 -- 113. On the arithmetical product of two classes or of two cardinals, p.105 -- 114. The aritmetical product of a class of classes, p.135 -- 115. Multiplicative classes and arithmetical classes, p.135 -- 116. Exponentiation, p.143 -- 117. Greater and less, p.171 -- General note on cardinal correlators, p.185 -- SECTION C. FINITE AND INFINITE, p.187 -- 118. Arithmetical substitution and uniform formal numbers, p.193 -- 119. Subtraction, p.201 -- 120. Inductive cardinals, p.207 -- 121. Intervals, p.223 -- 122. Progressions, p.253 -- 123. %0, p.268 -- 124. Reflexive classes and cardinals, p.278 -- 125. The axiom of infinity, p.289 -- 126. On typically indefinite inductive cardinals, p.293 -- PART IV. RELATION-ARITHMETIC -- Summary of Part IV., p.301 -- SECTION A. ORDINAL SIMILARITY AND RELATION-NUMBERS, p.303 -- 150. Internal transformation of a relation, p.306 -- 151. Ordinal similarity, p.319 -- 152. Definition and elementary properties of relation-numbers, p.330 -- 153. The relation-numbers 0r, 2r, and 1s, p.334 -- 154. Relation-numbers of assigned types, p.339 -- 155. Homogeneous relation-numbers, p.344 -- SECTION B. ADDITION OF RELATIONS, AND THE PRODUCT OF TWO RELATIONS, p.347 -- 160. The sum of two relations, p.351 -- 161. Addition of a term to a relation, p.357 -- 162. The sum of the relations of a field, p.362 -- 163. Relations of mutually exclusive relations, p.369 -- 164. Double likeness, p.376 -- 165. Relations of relations of couples, p.386 -- 166. The product of two relations, p.396 -- SECTION C. THE PRINCIPLE OF FIRST DIFFERENCES, AND THEMULTIPLICATION AND EXPONENTIATION OF RELATIONS, p.403 -- 170. On the relation of the first differences among the sub-classes of a given class, p.411 -- 171. The principle of the first differences (continued), p.423 -- 172. The product of the relations of a field, p.428 -- 173. The product of the relations of a field (continued), p.443 -- 174. The associative law of relational multiplication, p.447 -- 175. Exponentiation, p.458 -- 176. Propositions connecting Pdf with products and powers, p.471 -- SECTION D. ARITHMETIC OF RELATION-NUMBERS, p.473 -- 180. The sum of two relation-numbers, p.477 -- 181. On the addition of unity to a relation-number, p.482 -- 182. On separated relations, p.487 -- 183. The sum of the realiton-numbers of a field, p.496 -- 184. The product of two relation-numbers, p.501 -- 185. The product of the relation-numbers of a field, p.505 -- 186. Powers of relation-numbers, p.507 -- PART V. SERIES Summary of Part V., p.513 -- SECTION A. GENERAL THEORY OF SERIES, p.516 -- 200. Relations contained in diversity, p.518 -- 201. Transitive relations, p.525 -- 202. Connected relations, p.533 -- 204. Elementary properties of series, p.547 -- 205. Maximum and minimum points, p.559 -- 206. Sequent points, p.577 -- 207. Limits, p.594 -- 208. The correlation of series, p.605 -- SECTION B. ON SECTIONS, SEGMENTS, STRETCHES, AND DERIVATES, p.612 -- 210. On series of classes generated by the relattion of inclusion, p.615 -- 211. On sections and segments, p.624 -- 212. The series of segments, p.651 -- 213. Sectional relations, p.668 -- 214. Dedekindian relations, p.684 -- 215. Stretches, p.691 -- 216. Derivatives, p.700 -- 217. On segments of sums and converses, p.710 -- SECTION C. ON CONVERGENCE, AND THE LIMITS OF FUNCTIONS, p.715 -- 230. On convergents, p.720 -- 231. Limiting sections and ultimate oscillation of a function, p.727 -- 232. On the oscillation of a function as the argument approaches a given limit, p.737 -- 233. On the limits of functions, p.745 -- 234. Continuity of functions, p.753.
375. PART V. Principal ratios, p.487. SECTION D. WELL-ORDERED SERIES, p.1 -- 250. Elementary properties of well-ordered series, p.4 -- 251. Ordinal numbers, p.18 -- 252. Segments of well-ordered series, p.27 -- 253. Sectional relations of well-ordered series, p.32 -- 254. Greater and less among well-ordered series, p.44 -- 255. Greater and less among ordinal numbers, p.58 -- 256. The series of ordinals, p.73 -- 257. The transfinite ancestral relation, p.81 -- 258. Zermole's theorem, p.96 -- 259. Inducively defined correlations, p.102 -- SECTION E. FINITE AND INFINITE SERIES AND ORDINALS, p.108 -- 260. On finite intervals in a series, p.109 -- 261. Finite and infinite series, p.118 -- 262. Finite ordinals, p.131 -- 263. Progressions, p.143 -- 264. Derivatives of well-ordered series, p.156 -- 265. The series of alephs, p.169 -- SECTION F. COMPACT SERIES, RATIONAL SERIES, AND CONTINUOUS SERIES, p.179 -- 270. Compact series, p.180 -- 271. Median classes in series, p.186 -- 272. Similarity of position, p.191 -- 273. Rational series, p.199 -- 274. On series of finite sub-classes of a series, p.207 -- 275. Continuous series, p.218 -- 276. On series of infinite sub-classes of a series, p.221 -- PART VI. QUANTITY -- Summary of Part VI., p.233 -- SECTION A. GENERALIZATION OF NUMBER, p.234 -- 300. Positive and negative integers, and numerical relations, p.235 -- 301. Numerically defined powers of relations, p.244 -- 302. On relative primes, p.251 -- 303. Ratios, p.260 -- 304. The series of ratios, p.278 -- 305. Multipliation of simple ratios, p.283 -- 306. Addition of simple ratios, p.289 -- 307. Generalized ratios, p.296 -- 308. Addition of generalized ratios, p.299 -- 309. Multiplication of generalized ratios, p.309 -- 310. The series of real numbers, p.316 -- 311. Addition of concordant real numbers, p.320 -- 312. Algebraic addition of real numbers, p.327 -- 313. Multiplication of real numbers, p.333 -- 314. Real numbers as realtions, p.336 -- SECTION B. VECTOR-FAMILIES, p.339 -- 330. Elementary properties of vector-families, p.350 -- 331. Connected families, p.360 -- 332. On the representive of a relation in a family, p.367 -- 333. Open families, p.376 -- 334. Serial families, p.383 -- 335. Initial families, p.390 -- 336. The series of vectors, p.393 -- 337. Multiples and submultiples of vectors, p.403 SECTION C. MEASUREMENT, p.407 -- 350. Ratios of members of a family, p.412 -- 351. Submultipliable families, p.418 -- 352. Rational multiples of a given vector, p.423 -- 353. Rational families, p.431 -- 354. Rational nets, p.436 -- 356. Measurement by real numbers, p.442 -- 359. Existence-theorems for vector-families, p.452 -- SECTION D. CYCLIC FAMILIES, p.457 -- 370. Elementary properties of cyclic families, p.462 -- 371. The series of vectors, p.466 -- 372. Integral sections of the series of vectors, p.470 -- 373. Submultiples of identity, p.475 -- 374. Principal submultiples, p.485 -- 375. Principal ratios, p.487.

ISBN:

1603864393
9781603864398
1603864385
9781603864381
1603864377
9781603864374

OCLC:

(OCoLC)908699599

Locations:

PMAX975 -- Morningside University - Hickman-Johnson-Furrow Library (Sioux City)