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| Kneebone G.T. — Mathematical Logic and the Foundation of Mathematics |
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| Предметный указатель |
 72 127 161 246
 -formula (Hilbert & Bernays) 101 119
-number 242 386
-symbol (Hilbert) 100 ff. 119 123 242 380 381 386 391
-symbol, interpreted as a selection operator 101 130 303
-term 100 123
-theorems (Hilbert & Bernays) 103 107 381
 -conversion 275 ff.
-definability 275 ff. 380
 -symbol 221 263 268
 -consistency 237 279
 -symbol (Bourbaki) 119 303
 -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:  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  ,  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  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 -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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