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Brown J.R. Ч Philosophy of Mathematics: An Introduction to a World of Proofs and Pictures
Brown J.R. Ч Philosophy of Mathematics: An Introduction to a World of Proofs and Pictures



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Ќазвание: Philosophy of Mathematics: An Introduction to a World of Proofs and Pictures

јвтор: Brown J.R.

јннотаци€:

Philosophy of Mathematics is clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: Older Edition

√од издани€: 1999

 оличество страниц: 215

ƒобавлена в каталог: 23.05.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
A priori/a posteriori      13 18 65 114 154 173 192
Abraham, R.H., and Shaw, C.D.      48
Abstract objects      xii 8Ч9 12 16 40 50 54Ч55 58 62 100 149Ч151 153 193;
Abstract objects, problem of access for      15Ч18
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 128Ч129 172Ч173
Analytic/synthetic distinction      115 127 140 174
Anosov      183
Anti-realism      57 118Ч120 151
Apostol, T.      25Ч26
Apostoli, P.      196
Appel, K., and Haken, W.      154
Applied mathematics      46Ч61 125 141 182 185
Aristotle      110 123 190 194
Arithmetic      73Ч74 90 155 181;
Arithmetic addition      99 133 141Ч142 152;
Arithmetic counting      133;
Arithmetic multiplication      141Ч142
Arithmetic, Kantian view of      64 114Ч115 126
Arnheim, R.      40 152
Arnold      183
Artefacts      49Ч51
Artin      197
Atiyah, M.      188Ч189
Augustine      160
Automorphisms      105Ч106
Axiomatics      70 172
Axioms      22 31Ч32 63 73 96Ч97 101 170Ч171 187Ч188;
Axioms, testable by their consequences      18Ч19 29 31Ч32 170 180
Ayer, A.J.      140 173Ч174
Barwise, J. and Etchemendy, J.      37Ч38 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.      117Ч118 123 124 127
Bivalence      118Ч119
Bloor, D.      181
Bohm      50
Bollobas, B.      107 196
Bolzano, B.      25Ч30 194;
Bolzano, Bolzano Ч Weierstrass Theorem      128
Boolean algebra      62
Boolos and Jeffrey, R.      195
Boolos, G.      71 73Ч77 193;
Borel, A.      188Ч189
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 115Ч117 120 122 124 126Ч127 139Ч140 174Ч176 197
Brown, J.R.      193 194 198
Burali Ч 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      18Ч18
Causation      114 144Ч146 150 194
Certainty      2 7 32 65Ч66 154Ч156 189 191 192;
Certainty, challenges to      14 16Ч23 170
Chaos theory      125 182Ч185
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 117Ч118 122 123Ч124 127 139 159 162 164Ч165 166 183;
Computation/calculation, computational role      92Ч93;
Computation/calculation, theory of      70
Computer science      122
Computers in mathematics      xii 14 84 107 124 155 158Ч160 162Ч164 184 192 197;
Computers in mathematics, computer proofs      6 7 151 154Ч158 192 197
concepts      22 101Ч102 109Ч110 112 142 158 191;
Concepts and definition      98 108Ч109 110;
Concepts, proof generated.      99 110 131
Congruence Axioms of      96
Conjectures      18Ч23 32 108 110 158Ч161 165 167Ч168 170Ч171 187Ч188
Connotation/denotation      147; see also intension/extension; sense and reference
Consequence      140;
Consequence, logical      54 72;
Consequence, semantical      54;
Consequence, syntactical      54
Consistency      66Ч70 75Ч77 100
Constructive proof      77 113 127Ч128
Constructivism      12 23 100 113Ч129 192 197;
Constructivism and logic      120Ч122;
Constructivism and the infinite      65 122Ч124 196;
Continental philosophy      xii
Continued fractions      85Ч86 90Ч91
Continuity      25Ч30 52 194;
Continuity, axioms of continuity      96
Continuum Hypothesis      7 192
Contradictions      66 126
Conventionalism      13 62 170;
Conventionalism and Wittgenstein      63 140Ч142;
Conventionalism, language conventions      18 40Ч41 140Ч141
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 94Ч112 185;
Definitions, abstract      67;
Definitions, contextual      95Ч96 101;
Definitions, eliminability and non-creativity of      94Ч95 101
Definitions, nominal      111;
Definitions, official/standard view of      94Ч95 101 110 112
Definitions, theoretical status of      1 10
Demopoulos. W.      196
Derivation      130 171 178 181
Descartes Ч Euler theorem      see Euler theorem
Descartes, R.      xi 130 160 176
description      18 56Ч58 67;
Description versus representation      55Ч56
Determinism      54
Detlefsen, M.      78
Devlin, B. ci at.      194
Diagrams      88Ч89 131Ч132 172Ч173 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 42Ч43 191;
Dieudonne, J.      172 197
Dirichlet, J.      165
Discovery      19 31 136 140;
Discovery, 'context of discovery'      22 31;
Discovery, versus, invention/creation      89Ч90 137
Duhem, P.      66
Dummett, M.      92 118Ч120 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      16Ч17 193
Epstein, D.      186 187
Equations      88Ч89 91 100 167
Errors/mistakes      146 155Ч156
Errors/mistakes in computation/calculation      70 155 156;
Errors/mistakes in diagrams/pictures      88 132 152Ч153
Etchemendy, J.      see Barwise J. J.
Euclid      2
Euclidean geometry      98 101 170 see
Euler, Euler's theorem      19Ч22 104Ч105
Euler, L.      31 165 166 168Ч170;
evidence      18 30 157Ч159 162Ч163 171 174 191;
Evidence, empirical      154 168Ч169 178;
Evidence, pictures as      25 42 172 176 178 180Ч181 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 186Ч189 191Ч192
Explanation      96Ч97 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 18Ч23 28 110 146 154Ч156 158 170 178 187 191 192;
Falling, G.      166
Fallis, D.      197
Feigenbaum      183
Fermat Ч Wiles Theorem      see Fermat's Last Theorem
Fermat, Fermat's Last Theorem (FLT)      156 165Ч166 187
Fermat, P.      127 156 165;
Feyerabend, P.      98
Fictionalism      194
Fictions      66 114
Field, H.      46 53Ч55 62 125 193
Fields medal      186Ч188 198
Finitism      64Ч65 139
Finitistic mathematics      66Ч68 70 75Ч77 181
Formalism      13 23 62Ч71 1 1 192;
Formalism and Goedel's theorem      11Ч12 77Ч78;
Formalism and linguistic conventions      18 173;
Formalism and mathematical existence      100;
Formalism and notation      79 81 89 173; D.;
Formalization      69Ч70 110
Forms of life      141 143 145
Foundations      99 111 173
Four Colour Theorem (4CT)      6 149 151 154Ч155 157Ч158
Fractals      183Ч186 198
Franks, J.      182Ч183
Frege, G.      xi 9Ч10 29 64 95Ч102 109Ч110 115 136 144 147 150 196
Friedman, M.      40 50 194
Functions      102 125 136Ч137 145 149Ч150 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 88Ч89 95Ч96 108 126Ч127
Geometry, algebraic      91 166
Geometry, analytic      89 91 196
Geometry, Archimedian      98
Geometry, fractal      184;
Geometry, Kantian view of      64 114Ч115 126
Geometry, seven point geometry      69 155;
Giaquinto, M.      194
Gleason's theorem      125
Gleick, J.      182Ч183
God      6 91 100 117 120 160 183 191
Goedel, Goedel numbering      74;
Goedel, Goedel's Incompleteness Theorems      7 12 70 71Ч78 81 195
Goedel, K.      11 18 29 31Ч32 59 62Ч78 170 180
Goldbach's conjecture      2 6 30Ч31 113 122 124 162 168 170 188
Goldfarb, W.      196
Goodman, N.      32 163
Gorenstein, D.      158
Graph theory      101 103Ч107 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      105Ч106;
Graphs, utility graph      104
Greek mathematicians      48 65 160 173
groups      12 61Ч62 197;
Groups, classification of simple groups      158
Grue      163Ч164
hadamard      166
Hahn, H.      174 176Ч177
Haken, W.      see Appel K. W.
Hale, B.      54 193
Hamlet      113Ч114
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      95Ч101 109;
Hilbert and formalism      63 64Ч68 70 76;
Hilbert and solvability      181 192;
Hilbert spaces      46 50 55 125
Hilbert Ч Bernays Ч Loeb derivability conditions      76
Hilbert's Programme      68Ч71 75 77Ч78
Hilbert, D.      xii 115 176;
Hirsch, M.      182Ч183 185
History of mathematics      6Ч7 56 62 107Ч112 173 191Ч192
Homomorphism      38 47 48
Horgan, J.      186
Hume, D.      144Ч146
Huntington, S.      51Ч52
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 109Ч110;
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