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Kneebone G.T. — Mathematical Logic and the Foundation of Mathematics
Kneebone G.T. — Mathematical Logic and the Foundation of Mathematics

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Название: Mathematical Logic and the Foundation of Mathematics

Автор: Kneebone G.T.

Аннотация:

Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert's metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.


Язык: en

Рубрика: Математика/Алгебра/Математическая логика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 224

Добавлена в каталог: 22.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$X_0$      72 127 161 246
$\epsilon$-formula (Hilbert & Bernays)      101 119
$\epsilon$-number      242 386
$\epsilon$-symbol (Hilbert)      100 ff. 119 123 242 380 381 386 391
$\epsilon$-symbol, interpreted as a selection operator      101 130 303
$\epsilon$-term      100 123
$\epsilon$-theorems (Hilbert & Bernays)      103 107 381
$\lambda$-conversion      275 ff.
$\lambda$-definability      275 ff. 380
$\mu$-symbol      221 263 268
$\omega$-consistency      237 279
$\tau$-symbol (Bourbaki)      119 303
$\varkappa$-derivation      238
'Metaphysical'      245 248
A priori      249 339 361
Absolute presupposition      337
Abstractive element      348
Abstractive set      346
Abuse of language      119
Achilles and the tortoise      354
Ackermann, W. (1896— )      27 242 272 307 380 386 387 393 398
Activity of thinking      134 315 357
Adian, S.I. (1931— )      394
Affirmative proposition      11
Algebra of logic      184 ff.
Algebra of propositions      28 31 35
Algebraic number, algebraic integer      153
Algorithms (Markov)      394
Almagest of Ptolemy      136
Ambrose & Lazerowitz      25 56
Analytical absorption      365
Animal inference      374
Anschauung      248 312
Antinomies      112 ff. 127
Apartness      251
Apollonius of Perga (260?—200? B.C.)      136
Apparent variable      60
Application of mathematics      202 332
Applied mathematics      4 8 162 332
Arabic mathematics      137
Archimedean      197 199
Archimedes (287?—212 B.C.)      138
Argument by cases      122
Argument of a function      58
Argument-function (von Neumann)      293
Aristotle (384—322 B.C.)      7 15 18 21 129 134 151 354
Arithmetization of metamathematics      230 380
Assemblage      119
Asser, G. (1926— )      130 384
Assertion of a propositional function      165 266
Assertion sign      164 174 188
Assertion-stroke      174
Assumption      121
Atomic proposition      58
Ausdehnungslehre (Grassmann)      148
Aussagenform      382
Aussonderung      253 288 290 292 294 299 302
Autonomy of mathematical thinking      201 312 325
Avoidance of clashes of bound variables      67 93 101 120
Axiom (Aristotle)      134
Axiom (or postulate) of parallels      136 182 196
Axiom of Choice      101 116 130 245 289 294 301 303 389 396
Axiom of extensionality (or determination)      116 286 288 298
Axiom of foundation (Fundierung)      292 301
Axiom of infinity      289 301 302 319
Axiom of reducibility      167 233
Axiom of replacement (Fraenkel)      291 294 302
Axiom of separating out ((Aussonderung)      253 288 290 294 299 302
Axiom-schemata      44 116 119 234
Axiomatic method      40
Axiomatic methods, concrete and formal      201
Axiomatic systems of arithmetic: $(A_0)$      98 210 267
Axiomatic systems of arithmetic: (A)      219
Axiomatic systems of arithmetic: (B)      220
Axiomatic systems of arithmetic: (D)      222
Axiomatic systems of arithmetic: (Z)      223 241 242 265 267
Axiomatic theory of sets      117 284
Axioms $(J_1)$, $(J_2)$ for identity      90 177
Axioms for geometry (Euclid)      135
Axioms for geometry (Hilbert)      195
Axioms for the extended calculus of predicates      116 ff.
Axioms for the propositional calculus      43 125 176
Axioms for the restricted calculus of predicates      65 126
Axioms of Peano for the natural numbers      146 159 190 204 232 259
Bain, A. (1818—1903)      25
Baker, H. F. (1866-1956)      199
Barcan, Ruth (1921— )      398
Barycentric calculus      148 225
Basic logic (Fitch)      385 387
Basis of a formal system (Post)      281
Begriffsschrift (Frege)      173 ff.
Bell, Clive (1881— )      4
Bell, E.T. (1883—1960)      154
Bergson, H. (1859—1941)      343
Bernays, P. (1888— )      27 29 129 294 307 396
Beth, E. W. (1908— )      379
Beweistheorie (Hilbert)      229
Bi-implication      31
Birkhoff & MacLane      53 307
Black, M. (1909— )      189
Bolyai, J. (1802—1860)      182
Bolzano, B. (1781—1848)      383 397
Bonola, R. (1874—1911)      183
Boole, G. (1815—1864)      23 32 51
Boolean algebra      32 35 109 332 400
Boone, W. W. (1920— )      394
Borel, E. (1871—1956)      244 246
Bound variable      60 65 93 101 120 179 276
Bourbaki, N.      4 86 118 275 284 301 307 326
Boyle, R. (1627—1691)      337
Brackets      50 86
Britton, J.L.      394
Broad, C.D. (1887— )      399
Brouwer's criticism of traditional logic      246
Brouwer, L.E.J. (1881- )      244 246 256 319 342 353 362 364
Burali-Forti, C. (1861—1931)      127 128 385
Burnet, J. (1863—1928)      354
Bussey, W.H. (1879— )      227
Calculus of predicates      63
Canonical form (Post)      280
Canons of valid reasoning      17
Cantor, G. (1845—1918)      111 127 160 172 230 244 250 285 305 307
Cantor, M. (1829—1920)      154
Cardinal couple      171
cardinal number      71 111 154 160 172 180 181 289
Carnap, R. (1891— )      129 398 399
Categorical proposition      11
Categories (Kant)      248 340
Cauchy sequence      250
Cauchy, A.-L. .(1789—1857)      139 244
Chain (Dedekind)      159
Characteristic function      95 ff. 262
Choice, axiom of      101 116 130 245 289 294 301 303 389 396
Church's schema      298
Church's thesis      275 277
Church, A. (1903— )      6 25 56 57 66 98 129 273 274 275 279 283 387 393
class      108 ff. 169 179
Class (Bernays)      296
Codification (Schmidt)      382
Cogredience      350
Collective (von Mises)      371
Common notion (Euclid)      91 136
Communication      149 362
Complement      109 298
Complementary law $\Gamma$      253
Completeness      48 70 76 88 219 223 224
complex numbers      139
Comprehension, principle of      233 253 285 293 298 397
Concept-script (Frege)      173 313
concepts      360 364 374
Conceptual grid      365
Condition-stroke      175
Confirmation      398
Congruence      196 200 226 350
Conic sections      136
Conjunction      31 63
Connective      29 119
Consequence (Bolzano)      383 397
Consequential set      237
Consistency      104 197 207 239 241 322 325 385 388
Constructive proof      86 244 266
Content-stroke      174
Contextual definition      92 169 179
Continuum Hypothesis      306 322 389
Continuum problem      306
Contradictory propositions      13
Contrary propositions      13
Convergence and uniform convergence      62
Convergence to simplicity (Whitehead)      345 347
Converse domain of a relation      172
Converse of a proposition      47
Converse of a relation      110 185
Conversio per accidens      14
Conversion of propositions      13 19
Conversion of propositions by limitation      14
Conversion of propositions by negation      14
Convertibility (Ueberfiihrbarkeit)      72 78
Copula      10 185
Courant, R. (1888— )      193 228
Course of values      179
Course-of-values recursion      270
Couturat, L. (1868—1914)      151
Cramer, H. (1893— )      371
Critical s-number      386 387
Cross ratio      225
Crystalline structure      339 355
Cultural tradition      364
Curry, H. B. (1900— )      384
Das Kontinuum (Weyl)      246 256 395
Davis, M. (1928- )      283
de la Vallee Poussin, Ch.-J. (1866—1962)      301
De Morgan, A. (1806—1871)      22 162 184 309
Decision problem      279 322 392
Dedekind, R. (1831—1916)      131 140 146 154 156 157 158 190 226 243 250 259 313
Deduction Theorem      78 ff. 120 122
Deductive equivalence      72 78
Definite description (Russell)      91 179
Definiteness (Zermelo)      288 290 300
Definition (Aristotle)      135
Definition in use      92
Denumerably infinite      161
Derivability symbol      188
Derivation      43 68 124
Desargues, G. (1593—1662)      199 225
Descartes, R. (1596—1650)      7 137 247
description      91 ff. 170 179
Descriptive function      170
Determinative and conceptual induction      366
Dialectical thinking      360 364 367 374
Dictum de omni et nullo      15 61
Dilemmas      20
Diophantine equations      307 322
Discerned and discernible      344 358 361
Discharge of an assumption      125
Disjunction      30 63
Distributed term      12 17
Distributive operations      35
Diversity      90
Division algorithm      264
Divisors of zero      251
Domain of a relation      172
Domain of individuals      63 71 296 298 304 318
Dots as brackets      86 164
Double Negation      46 124 255
Duality in the propositional calculus      35
Dummy variable      60
Duration (Whitehead)      345
Duration of validity (Schroeder)      188
Durie (Bergson)      343
Eddington, A.S. (1882—1944)      338 341
Effectiveness      274 278 282 380 394
Einstein, A. (1879—1955)      334 342 363
Elective symbol (Boole)      52
Element of a set      288
Elementary calculus with free variables      105 107 267
Elementary transformations in the propositional calculus      34 ff. 49
Elements of Euclid      7 26 134ff. 182 260
Elevation of type      233
Eliminability of the $\epsilon$-symbol      103
Eliminability of the i-symbol      95 269
Elimination of bound variables      105 ff.
Elliptic geometry      183
Empty class      109 169 299
Empty subconjunction      38
Entscheidungsproblem      279 392
Epicycles      136
Epimenides      127
Epistemological considerations (Eddington)      341
Equinumeric (Frege)      181
Equipotent      111 160 172
Equivalence relation      33 90
Equiveridic      32
Euclid (c. 300 B.C.)      7 26 91 134 162 201
Euclid's Algorithm      271
Euler diagrams      12 17 24
Euler, L. (1707—1783)      12
Event      346
Event-particle      349
Excess of one natural number over another      263
Excluded Middle      46 55 113 206 247 250 255 386 387
Existence of a class      169
Existential quantifier      60
Experience      5 202 324 332 333 335 361 373
Explicit definition      41 42 99 260 268
Extended calculus of predicates      65 110 165 174 295
Extension of a predicate or relation      110 179 296 297
Extensionality      117 286
Extensive abstraction (Whitehead)      346 ff.
Extraordinary set      291
Factorial      264
Fallacy of the undistributed middle      16
Fano, G. (1871— )      226
Father      62 170
Field of a relation      172
Figures of the syllogism      15
Finitary inference      205 240 247 266 387
Finite geometries      204 227
Fishing-net      341
Fitch, F.B. (1908— )      385 387
Flying arrow      345 354
Focus of organization      360 365
Formalism, philosophy of      156 200 243
Formalized mathematical theories      86 95 98 208
Formula      31 42 65 93
Formulaire de Mathematique (Peano)      145 ff.
Fraenkel & Bar-Hillel      127 130 189 308
Fraenkel, A.A. (1891— )      290 ff. 300 307 308
Free variable      60 65
Frege, G. (1848-1925)      49 137 154 157 173 183 190 313
Function (Fraenkel)      290
Function, the mathematical notion      58 276 292
Fundamental theorem of algebra      139
Fundamental Theorem of Arithmetic      205
Fundierung (von Neumann)      292 301
Galileo (1564—1642)      7 342
Galois field      227
Gandy, R.O.      392
Gauss, C.F. (1777—1855)      139 182 183
General recursive function      273 274 277 380 395
General term      10
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