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| Brown J.R. — Philosophy of Mathematics: An Introduction to a World of Proofs and Pictures |
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| Ïðåäìåòíûé óêàçàòåëü |
A priori/a posteriori 13 18 65 114 154 173 192
Abraham, R.H., and Shaw, C.D. 48
Abstract objects xii 8—9 12 16 40 50 54—55 58 62 100 149—151 153 193;
Abstract objects, problem of access for 15—18
Ackermann 70
Adams and Leverier 170
Adleman, L. 156
Aesthetics 40 80 152
Albert, D. 193
Aleksandrov, A.D. 194
Alexander 86
Algebra 108 115;
Algebra, abstract algebra 62
Algorithms 72 80 83 92 138 196;
Algorithms, theory of 70
Analysis 115 128—129 172—173
Analytic/synthetic distinction 115 127 140 174
Anosov 183
Anti-realism 57 118—120 151
Apostol, T. 25—26
Apostoli, P. 196
Appel, K., and Haken, W. 154
Applied mathematics 46—61 125 141 182 185
Aristotle 110 123 190 194
Arithmetic 73—74 90 155 181;
Arithmetic addition 99 133 141—142 152;
Arithmetic counting 133;
Arithmetic multiplication 141—142
Arithmetic, Kantian view of 64 114—115 126
Arnheim, R. 40 152
Arnold 183
Artefacts 49—51
Artin 197
Atiyah, M. 188—189
Augustine 160
Automorphisms 105—106
Axiomatics 70 172
Axioms 22 31—32 63 73 96—97 101 170—171 187—188;
Axioms, testable by their consequences 18—19 29 31—32 170 180
Ayer, A.J. 140 173—174
Barwise, J. and Etchemendy, J. 37—38 194
Bayesian theory 32
Beetle in the box 139^*0
Behaviourism 139
Belief 98 123 133 155 159 188
Bell results 17 193
Bell, J. and Machover, M. 122
Benacerraf, P. 57 58 193
Bernays, P. 70 see
Bernoulli family 124
Berry paradox 71 74
biology 13 156
Bird, A. 193 194
Birkoff 183
Bishop, E. 117—118 123 124 127
Bivalence 118—119
Bloor, D. 181
Bohm 50
Bollobas, B. 107 196
Bolzano, B. 25—30 194;
Bolzano, Bolzano — Weierstrass Theorem 128
Boolean algebra 62
Boolos and Jeffrey, R. 195
Boolos, G. 71 73—77 193;
Borel, A. 188—189
Borwein, J.Borwein, P. et al 197
Bourbaki, Bourbaki group 172 173 183 198
Bourbaki, N. 197;
Bowen, W. 186
Bowman 186
Boyer, C.B. 25
Bridges. D. 117
Brouwer. L.E.J. xii 115—117 120 122 124 126—127 139—140 174—176 197
Brown, J.R. 193 194 198
Burali — Forti paradox 173
Campbell, N. 49
Cantor's paradox 65
Cantor, G. 22 65 111;
Cartan 197
Cartier. P. 173 197
Catastrophe theory 182 186 189
Category theory 122
Causal theory of knowledge 18—18
Causation 114 144—146 150 194
Certainty 2 7 32 65—66 154—156 189 191 192;
Certainty, challenges to 14 16—23 170
Chaos theory 125 182—185
Chemistry 13 56 58 195
Chihara, C. 193
Choice, axiom of 111 197
Chudnovsky and Chudnovsky 197
Classical mathematics 66 69 77 115 125 128
Coffa, A. 28
Collins. A. 196
Columbus, C. 110
Combinatorial mathematics 106
Complex analysis 69 129
Complexity theory 125
Comprehension. Axiom of 19
Computation/calculation 55 70 117—118 122 123—124 127 139 159 162 164—165 166 183;
Computation/calculation, computational role 92—93;
Computation/calculation, theory of 70
Computer science 122
Computers in mathematics xii 14 84 107 124 155 158—160 162—164 184 192 197;
Computers in mathematics, computer proofs 6 7 151 154—158 192 197
concepts 22 101—102 109—110 112 142 158 191;
Concepts and definition 98 108—109 110;
Concepts, proof generated. 99 110 131
Congruence Axioms of 96
Conjectures 18—23 32 108 110 158—161 165 167—168 170—171 187—188
Connotation/denotation 147; see also intension/extension; sense and reference
Consequence 140;
Consequence, logical 54 72;
Consequence, semantical 54;
Consequence, syntactical 54
Consistency 66—70 75—77 100
Constructive proof 77 113 127—128
Constructivism 12 23 100 113—129 192 197;
Constructivism and logic 120—122;
Constructivism and the infinite 65 122—124 196;
Continental philosophy xii
Continued fractions 85—86 90—91
Continuity 25—30 52 194;
Continuity, axioms of continuity 96
Continuum Hypothesis 7 192
Contradictions 66 126
Conventionalism 13 62 170;
Conventionalism and Wittgenstein 63 140—142;
Conventionalism, language conventions 18 40—41 140—141
Conventionalism, linguistic conventionalism 63 173;
Coordinates (Cartesian and spherical) 91
Counter-examples 21 108 121 163 166
Courant, R. and Robbins, H. 26 195
Coxeter, H.S.M. 195
David 40 152
Davis, P.J. and Hersh. R. 197
Dedekind. R. 57 99
Deduction 67 182
definitions 67 94—112 185;
Definitions, abstract 67;
Definitions, contextual 95—96 101;
Definitions, eliminability and non-creativity of 94—95 101
Definitions, nominal 111;
Definitions, official/standard view of 94—95 101 110 112
Definitions, theoretical status of 1 10
Demopoulos. W. 196
Derivation 130 171 178 181
Descartes — Euler theorem see Euler theorem
Descartes, R. xi 130 160 176
description 18 56—58 67;
| Description versus representation 55—56
Determinism 54
Detlefsen, M. 78
Devlin, B. ci at. 194
Diagrams 88—89 131—132 172—173 178 189 197;
Diagrams as a psychological aide 3 7 107 174 191;
Diagrams as instruments to aid the mind's eye 39
Diagrams, misleading 3 25 42—43 191;
Dieudonne, J. 172 197
Dirichlet, J. 165
Discovery 19 31 136 140;
Discovery, 'context of discovery' 22 31;
Discovery, versus, invention/creation 89—90 137
Duhem, P. 66
Dummett, M. 92 118—120 124 127 141 142
Dunham, W. 127 197
Education 52 181
Edwards, H.M. 167
Eigenvalues 55
Einstein, A. 16 see
Elliptic curve 166
Empiricism 49 154
EPR thought experiment 16—17 193
Epstein, D. 186 187
Equations 88—89 91 100 167
Errors/mistakes 146 155—156
Errors/mistakes in computation/calculation 70 155 156;
Errors/mistakes in diagrams/pictures 88 132 152—153
Etchemendy, J. see Barwise J. J.
Euclid 2
Euclidean geometry 98 101 170 see
Euler, Euler's theorem 19—22 104—105
Euler, L. 31 165 166 168—170;
evidence 18 30 157—159 162—163 171 174 191;
Evidence, empirical 154 168—169 178;
Evidence, pictures as 25 42 172 176 178 180—181 187 192;
Evidence, statistical 165 197
Excluded middle, law of 5
Existence 95 100 124 146
Experience 18 55 66 123;
Experimentation in mathematics xii 181 183 186—189 191—192
Explanation 96—97 182
Facts and verification 51
Facts of natural history 143;
Facts, brute 145
Facts, categorical 138 196
Facts, correspondence to 144
Facts, dispositional 138
Facts, verbal/symbolic 174
Fallacies 28 51
Fallibilism 14 18—23 28 110 146 154—156 158 170 178 187 191 192;
Falling, G. 166
Fallis, D. 197
Feigenbaum 183
Fermat — Wiles Theorem see Fermat's Last Theorem
Fermat, Fermat's Last Theorem (FLT) 156 165—166 187
Fermat, P. 127 156 165;
Feyerabend, P. 98
Fictionalism 194
Fictions 66 114
Field, H. 46 53—55 62 125 193
Fields medal 186—188 198
Finitism 64—65 139
Finitistic mathematics 66—68 70 75—77 181
Formalism 13 23 62—71 1 1 192;
Formalism and Goedel's theorem 11—12 77—78;
Formalism and linguistic conventions 18 173;
Formalism and mathematical existence 100;
Formalism and notation 79 81 89 173; D.;
Formalization 69—70 110
Forms of life 141 143 145
Foundations 99 111 173
Four Colour Theorem (4CT) 6 149 151 154—155 157—158
Fractals 183—186 198
Franks, J. 182—183
Frege, G. xi 9—10 29 64 95—102 109—110 115 136 144 147 150 196
Friedman, M. 40 50 194
Functions 102 125 136—137 145 149—150 163 194;
Functions, recursive function theory 70;
Functions, zeta function 167
Galileo 48 190
Gary, M. and Johnson, D. 194
Gauss, C.F. 186
Gaussian curvature 41
Geometry 40 48 56 62 88—89 95—96 108 126—127
Geometry, algebraic 91 166
Geometry, analytic 89 91 196
Geometry, Archimedian 98
Geometry, fractal 184;
Geometry, Kantian view of 64 114—115 126
Geometry, seven point geometry 69 155;
Giaquinto, M. 194
Gleason's theorem 125
Gleick, J. 182—183
God 6 91 100 117 120 160 183 191
Goedel, Goedel numbering 74;
Goedel, Goedel's Incompleteness Theorems 7 12 70 71—78 81 195
Goedel, K. 11 18 29 31—32 59 62—78 170 180
Goldbach's conjecture 2 6 30—31 113 122 124 162 168 170 188
Goldfarb, W. 196
Goodman, N. 32 163
Gorenstein, D. 158
Graph theory 101 103—107 112 126 156 196;
Graph theory, crossings in 103 104;
Graph theory, edges in 103 107;
Graph theory, faces in 104 107
graphs 103;
Graphs, complete graph 103;
Graphs, connected graph 104;
Graphs, equivalence of 105;
Graphs, random graphs 107;
Graphs, unlabelled graph 105—106;
Graphs, utility graph 104
Greek mathematicians 48 65 160 173
groups 12 61—62 197;
Groups, classification of simple groups 158
Grue 163—164
hadamard 166
Hahn, H. 174 176—177
Haken, W. see Appel K. W.
Hale, B. 54 193
Hamlet 113—114
Hammer, E. 38 194
Hardy, G.H. 10 137
Heine 63
Hellman, G. 125 196
Hermite, C. 124 183
Herrstein, R. and Murray, C. 51
Hersh, R. see Davis R.J. R.
Heyting, A. 120 126
Hilbert and definition 95—101 109;
Hilbert and formalism 63 64—68 70 76;
Hilbert and solvability 181 192;
Hilbert spaces 46 50 55 125
Hilbert — Bernays — Loeb derivability conditions 76
Hilbert's Programme 68—71 75 77—78
Hilbert, D. xii 115 176;
Hirsch, M. 182—183 185
History of mathematics 6—7 56 62 107—112 173 191—192
Homomorphism 38 47 48
Horgan, J. 186
Hume, D. 144—146
Huntington, S. 51—52
Husserl xii
Ideal agent, ideal mathematician 55 159
Ideal elements 66 115
Ideal end of inquiry/theorizing 99 150
Idealism 122
Ideas, Fregean 9 136;
Ideas, intuitive/preanalytic 104 109—110;
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