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| Kneebone G.T. — Mathematical Logic and the Foundation of Mathematics |
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| Предметный указатель |
Genocchi, A. (1817-1889) 142
Gentzen, G. (1909—1945) 121 130 168 241 255 315 380 383 385 386
Geometrie der Lage (von Staudt) 225
German alphabet 28 41 65 87 175 424
Gibbs, J. Willard (1839—1903) 148
Goedel numbering 234 380
Goedel's completeness theorem 77
Goedel, K. (1906— ) 72 76 116 190 224 229 273 305 307 358 381 389 390 396
Goldbach, C. (1690—1764) 223
Goodman, N. (1906— ) 399
Goodstein, R. L. (1912— ) 189 261 283 388 395
Grassmann, H. (1809—1877) 148
Greek science and mathematics 7 134
Grelling — Nelson antinomy 128
Group 121 203 322 327
Grundlagen der Mathematik (Hilbert & Bernays) 27 56 72 100 201 228 240 261 283
Grundlagen der Oeometrie (Hilbert) 193 ff. 228 389
Grundziige der theoretischen Logik (Hilbert & Ackermann) 27 44 56 66 68 72 88 116 123 380 381
Haar, A. (1885—1933) 328
Hall, Marshall, Jr. (1910— ) 394
Hamilton, W., philosopher, (1788—1856) 22 185
Hamilton, W.R., mathematician, (1805—1865) 148
Hanson, N.R. (1924— ) 242
Harley, Rev. R. 51 186
Harmonic relation 226
Hasenjaeger, G. (1919— ) 382 390
Hausdorff, F. (1868- ) 307
Heath, T.L. (1861—1940) 134 136 154
Heaviside, O. (1850—1925) 148
Hecke, E. (1887—1947) 154
Hegel, G.F.W. (1770—1831) 309 358
Helmer, O. (1910— ) 399
Hempel, C.G. (1905— ) 398
Henkin, L. (1921— ) 76 390 397
Hensel, K. (1861—1941) 328
Herbrand, J. (1908—1931) 273
Hermes & Scholz 130 286 382
Hermes, H. (1912— ) 283
Heterological 128
Heyting, A. (1898— ) 250 254 256 396
Hilbert, D. (1862—1943) 27 49 100 104 192 228 279 322
Historical evolution of ideas 7 9 134 319 359 362 375
Hobbes, T. (1588—1679) 9
Hume, D. (1711—1776) 339
Huntington, E.V. (1874—1952) 188
Hyperbolic geometry 183 227
i-schema 93
i-symbol 92 102 221 263 268 297
Ideal calculus (Hermes & Scholz) 286
Ideal number (Kummer) 141 153
Ideal, in arithmetic and algebra 141 154 193
Idempotent 35
Identical calculus (Schroeder) 187
Identical formula 33 48 71
Identical truth-function 33
Identity 23 60 89 111 168 169 291 297
Identity of indiscernibles (Leibniz) 90 169 180
Illegitimate totalities 113
Implication 31 54 146 187
Incidence geometry 226
inclusion 109
Incompatibility 51
Indefinite description (Russell) 91 101
Indeterminate 28
Indirect reduction of syllogisms 19
Individual function 94
Individual variable 59
Induction 6 25 366 399
Inference 14
Infinite class (Dedekind) 159
Infinite induction 386
Infinitely proceeding sequence 251
Infinitesimal calculus 137 140 142 354
Information theory 400
Initial formulae in derivations 68 121
Inner and outer sense (Kant) 248
Inner model 391
Interlingua 149
Intersection 54 108 298
Intuition 144 150 194 247 312 328 340
Intuitionism 244 ff. 319 388 395
Intuitionist logic 247 254 396
Intuitive geometry 202
Inverted commas 87 ff.
Irrevocable character of logistic systems 316
Jevons, W.S. (1835—1882) 17 24 25 186 187
Joint denial 51
Jordan, C. (1838—1922) 301
Jourdain, P.E.B. (1879—1919) 285
Judgement 5 369
Kalmar, L. (1905— ) 275 393
Kant, I. (1724—1804) 192 194 207 248 317 320 339 361 376
Kemeny, J.G. (1926— ) 129 390 398 399
Keynes, J.M. (1883—1946) 371
Klaua, D. 393 395
Kleene hierarchy 395
Kleene, S.C. (1909— ) 228 242 261 273 275 283 387 388 395
Klein, F. (1849—1925) 139 154 183 199 226 227 228
Kneale, W. & Kneale, M. 25
Kneale, W. (1906— ) 53 190 399
Kneebone, G.T. (1918— ) 360 372
Koerner, S. (1913— ) 189
Kolmogorov, A.N. (1903— ) 255 371
Kreisel, G. 388 394 395
Kronecker, L. (1823—1891) 244 249 266
Kummer, E.E. (1810—1893) 141 153
Kuratowski, K. (1896— ) 171 294
Lagrange, J.-L. (1736—1813) 139
Laguerre, E. (1834—1866) 228
Landau, E. (1877—1938) 41 140
Language 6 98 128 149 292 321 353 362
Laplace, P.-S. (1749—1827) 371
Latino sine flexione 149
Laws of algebra 35
Least number, principle of 220 268
Least upper bound 117
Legendre, A.-M. (1752—1833) 139
Lehman, R.S. (1930— ) 399
Leibniz, G.W. (1646—1716) 53 90 137 151
Level 349
Lewis & Langford 53 54 55 56 130
Lewis's calculi S1-S5 55 398
Lewis, C.I. (1883— ) 54
Liar 127 168 230
Limit number 300
Littlewood, J.E. (1885— ) 308
Lobachevsky, N.I. (1793—1856) 182
Locke, J. (1632—1704) 337
Loewenheim — Skolem theorem 78 304 389
Loewenheim, L. (1878— ) 78 188 304 393
Logical constant 29 157
Logical positivists 245 376
Logical sum and product 53
Logistic philosophy of mathematics 156 200 243 312 315
Lorenzen, P. (1915— ) 384 386 388 395
Lukasiewicz, J. (1878—1956) 22 49 55 56 86
Mach, E. (1838—1916) 342 356
Machines 277 292 400
Major term and major premiss 15
Manipulative thinking 360 364
Many-valued logic 55 397
Markov, A.A. (1903— ) 393
Martin, R.M. (1916— ) 399
Materialism (Whitehead) 343
Mathematical beings (Bourbaki) 328
Mathematical induction 147 159 205 220 258 267
Matrix, in the sense of Prindpia Mathematica 166
McColl, H. (1837—1909) 186 ff.
McKinsey, J.C.C. (1908— ) 393 398
McNaughton, R. (1924— ) 308
| Measurement 163
Membership relation 284 286 288 296
Metalogic 33 164
Metamathematics 104 164 194 197 207 295
Metamathematics in the large 381
Michelson — Morley experiment 335
Middle term of a syllogism 15
Mill, J.S. (1806—1873) 25
Minor term and minor premiss 15
Mirimanoff, D. (1861—1925) 291
Mnemonics: affirmo-nego 11
Mnemonics: Barbara, Celarent,... 18
Modal logic 55 398
Model 197 203 380 389 397 398
modus ponens 43 177 179 255 281
Moebius net 225
Moebius, A.F. (1790—1868) 148 225 355
Molecular proposition 58 77
Moment (Whitehead) 345 348
Moods of the syllogism 16
Mostowski, A. 242 379 390 391 392 397
Mother-structures 326
Nagel, E. (1901— ) 242 356
Naive logic 114
Naive realism 336
Naive theory of sets 285 ff.
NAME 9 10 87 91 92 128 183
Natural deduction 121 ff. 130
Natural numbers 147 159 259 289 301
Negative proposition 11
Neighbourhood 327 344
Newton, I. (1642—1727) 137 201 342
Nominalism (Quine) 396 399
Non-Euclidean geometry 162 182 198 227 306 380
Non-existence theorems 380
Non-standard model 391
Normal form (Post) 281
Normal forms for logical formulae: conjunctive 36
Normal forms for logical formulae: disjunctive 36
Normal forms for logical formulae: prenex 73
Normal forms for logical formulae: Skolem 74
Normal forms for logical formulae: special conjunctive 38
Normative discipline 8
Noumena (Kant) 339
Novak, Use (1924— ) 391
Novikov, P.S. (1901— ) 394
Null class 109
Numeral induction 301
Numerals 204 ff.
Objects (Whitehead) 350 ff.
Omnipotence 114
Onymatic 185
Operative variable 80
Oppenheim, P. 399
Or, senses of 29
Order of a propositional function 166
Order of precedence among connectives 86
Order-type 161
Ordered pair 170 171 232 294 299
Ordinal couple 171
Ordinal number 127 161 300 387
Ordinally similar 172
Orey, S. (1928— ) 392
Organon of Aristotle 7 21
Over-large totalities 293 294
Pager, D. (1935— ) 66
Pappus (c. 300a.d.) 199
Paradoxes 112 127 192
Parallel moments 348
PARAMETER 82 94 170
Particular proposition 11
Pascal, B. (1623—1662) 199
Pasch, M. (1843—1931) 226
Passage of nature (Whitehead) 343
Peano axioms for the natural numbers 146 190 204 232 259
Peano, G. (1858—1932) 49 141 154 156 173 227 259
Pedoe, D. 228
Peirce, C.S. (1839—1914) 187
Perfect syllogism 18
Peter, Rozsa (1905- ) 261 262 283 395
Phenomena (Kant) 339
Philosophy, nature of 3 373
Pieri, M. (1860—1913) 227
Platonic view of concepts 321 399
Poincare, H. (1854—1912) 199 227 244 249
Point-track 350
Pointer readings 338
Poncelet, J.-V. (1788—1867) 225
Popper, K.R. (1902— ) 356
Positive and negative terms 10
Possibility (Lewis) 54
Post, E.L. (1897— ) 55 280 283 393
Postulate (Aristotle) 135
Power (cardinal number) 160
Predecessor function 262
Predicate 60
Predicate variable 59
Predicative function 166
Premiss 14
Prenex normal form 73
Primary and secondary qualities 337
Prime numbers 224 234 264 265 270 322
Primitive ideas and propositions 144 157 288 291 296 297
Primitive recursive function 236 270
Prindpia Mathematica (Whitehead & Russell) 27 49 57 113 127 130 161 191 315 381
Prior, A.N. (1914— ) 49
probability 370 ff. 399
Problems 255 322
Production (Post) 280
Progression 259 289
Projective geometry 121 224
Proper axioms 107
Proper nouns and common nouns 10
Proper subclass 109
Proposition 10 27
Propositional calculus 32 279
Propositional function 59 67 165
Propositional variable 27 41 163 177
Psychology 8 309
Ptolemy (85?—160? a.d.) 136
Punct 349
Pure and applied functional calculi (Church) 98
Pure mathematics, as defined by Russell 156 162
Putnam, H. (1926— ) 392
Pythagoras, Theorem of 26 162
Quality 11
Quantification of the predicate 22
Quantifier 60 102
quantity 11 181
Quaternions 148
Question-begging 363
Quine, W.V. (1908— ) 57 128 130 190 191 296 381 385 389 393 396 399 400
Rabin, M.O. 394
Ramified analysis 386
Ramified theory of types 168
Ramsey, F.P. (1903—1930) 189
Rational activity 3 373
Rational dynamics 162
Real number-generator 250
Real numbers 117 141 250 274 386
Realization 203
Recognition 350 361 369
Rect 349
Recursive definition 147 205 221 236 258 260
Recursively enumerable 279
Reducibility, axiom of 167 233
Reductio ad absurdum 19 182
Reductio ad impossibile 19
Reduction of arithmetical formulae 211 ff. 241
Reduction of syllogisms 18 ff.
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