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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 |
Incidence, Axioms of 96
incommensurability 29 98 173
Incompleteness 91;
Incompleteness theorems see Goedel's Incompleteness Theorems
Indispensability (of mathematical objects for science) 46 53—54 125
Induction 2 14 29—32 41—42 155 158—159 163—164 180 187;
Induction, mathematical induction 34 42
Inference, logical 69;
Inference, mathematical 171;
Inference, rational 170
Infinite, infinity 65—68 146 195;
Infinite, infinity, analogy with unobservable entities 123;
Infinite, infinity, countable 90;
Infinite, infinity, infinite sequence 151;
Infinite, infinity, infinite series 34—37 42 45 169;
Infinite, infinity, infinite sets 102 122—123 128;
Infinite, infinity, infinite structures 39;
Infinite, infinity, paradoxes of 65;
Infinite, infinity, potential versus actual 39 65 123 195
Infinitesimals 65 173
Informal mathematics 70 111
Inkeri 166
Instrumentalism 66—67
Intension/extension 147; see also connotation/denotation; sense and reference
Intentions 134 137 139
Intermediate Value Theorem 25—30 172
Intrinsic and extrinsic features 40—41
Intuition 11 32 115 172 174 177 180 187;
Intuition of mathematical objects 13 67 116;
Intuition of space and time 64 120
Intuitionism 13 100 139;
Intuitionism, Brouwer's intuitionism 115—117 120 122 126;
Intuitionism, Dummett's intuitionism 118—120; see also constructivism; finitism; logic intuitionistic
Irvine, A. 54 194
Isomorphism 37—38 104—105
Jaffe, A., and Quinn, F. 187—190
Jeffrey, R. see Boolos G. R.
Johnson, D. see Gary M. D.
Jones, V. 86
Jordan curve theorem 104
Julia 185
justification 25 42 138 144 180 187;
Justification, 'context of justification' 22 31
Kant, I. xi 39 64—68 114—115 126 150
Kari, L. 197
Kelvin 81
Kempe, A. 156
Kitcher, P. 13 18 28 55 193
Klein, F. 28
Kline, M. 25
Knot theory 81—93 126 194;
Knot theory, Conway notation 84—85 90;
Knot theory, crossings in 83 85 87 90;
Knot theory, Dowker notation 83—84 90;
Knot theory, projection in 82 84 87 90 91;
Knot theory, Reidermeister moves 82 84 86—88 90;
Knot theory, tangles 84—86;
Knot theory, unknot 82 86
Knots 79;
Knots, Borromean rings 87;
Knots, composite knots 84;
Knots, equivalence of 82 86;
Knots, figure eight knot 82;
Knots, prime knots 84;
Knots, trefoil 82
Koblitz, N. 51—52 194
Koch snowflake 185
Kolmogorov 183
Krantz, D.H. et.al 49
Krantz, S. 183—186 198
Kripke, S. 135—136 144—145
Kuhn, T.S. 98
Kummer 166
Lagrange, J.L. 172
Lakatos, I. 19—22 32 42 99 107—112 158 183
Lam, C.W.H. et al 155—156
Lang, S. 52
Langford 183
Language 37 49 61 92 93 117 118 120 125 133 144 174;
Language and structures 59—60
Language and truth 18 140 173;
Language, language L, of formal arithmetic 71—72 74—75
Language, languageless activity 116—117 126
Language, separation of mathematics from its language 116 174 see
Language-game 140 144
Laws of nature 24 49 55 143—144 146 193 194
Legendre, A. 165
Leibniz, G.W. xi 169
Leverier see Adams and Leverier
Levinson 183
Liar paradox 71
Lickorish, W.B.R. and Millett, K. 91
Linear spaces 125;
Linear spaces, linear operators 55 125
links 87;
Links, Hopf link 87;
Links, unlink 87;
Links, Whitehead Link 87
Littlewood, J.E. 10 162 179—180
Loeb see Hilbert — Bernays — Loeb derivability conditions
Logic 28 49 54 56 120 181;
Logic and set theory 54 102
Logic of discovery 31;
Logic, classical logic 5 7 120—121 191—192;
Logic, intuitionistic logic 77 120—122;
Logic, relation to mathematics 67 115 120;
Logicism xii 29 102 115 196
Lonergin xii
Lorenz 183
Lucas, J. 78
Machover, M. see Bell J. M.
Maddy, P. 13 171 193
Malament, D. 54
Mandelbrot, B. 183—186 189 198
Manders, K. 88
Math Wars 181—191
Mathematical image 1—7 14 191—192
Mathematical practice/activity 30 88 99 116—139 158
Mathematical realm 141 159
Maxwell 50
McDowell, J. 196
Meaning 97—98 114 139;
Meaning and truth 119 144
Meaning and use 118—120;
Meaning, meaningfulness 6 62 64 66—69 92 117 122 144 147 151;
Meaning, picture theory of 130
Measurement theory 46—50
Membership relation 60 102
Mendelson, E. 195
Mersenne primes 161—162 167 197
Mill, J.S. 55
Millett, K. see Lickorish W.B.R. K.
Milnor, J. 186
Milton 79—80
Mind's eye, the 13—15 18 39 41 43 178
Misner, C. er al 98
Mittag — Leffler 124
Models 68 101 182 186;
Models and applied mathematics 53 56;
Models, model theory 70;
Models, truth in 43
Mohs scale 48
Moore, A.W. 195 196 197
Mordell conjecture 166
Morning star/evening star 92 147
Moschovakis, Y. 92
Moser 183
Mundy, B. 49
Murray, C. see Hermstein R. C.
n-body problem 124—125 127
| Nagel, E. 49
Napoleon 40 152—153
Natural kinds 41—42
naturalism 13 16 23 142—144 181
Naturalistic entities 139
Nelson, R. 43
Newton, I. 48 50 55 155;
Newton, Newton's Laws 124 170
Newton, Newtonian celestial mechanics, Newtonian theory of gravitation 55 124
Newton, Newtonian physics 2;
Newton-Smith, W.H. 194
Nobel prize 51 198
Nominalism 46 48 53—55 62—63 81
Non-contradiction, law of 3
Non-Euclidean geometry 13 56 62 68 101 115
Non-linear dynamics 182—183 185
Non-standard/alternative techniques 14 18—19 153—154 180 192; hypothetico-deductive
Notation 79—93 173
Noumena 150
Number theory 34 39 41 42 81 90 150 167;
Number theory, primitive concepts of 102
Numbers 55 64 90—91 99 115—117 123 149—150 152 193;
Numbers, cardinal numbers 102 109 173;
numbers, complex numbers 66;
Numbers, composite numbers 102 127;
Numbers, irrational numbers 164;
Numbers, natural numbers 58 60 80—81 103;
numbers, ordinal numbers 109 115—116 173;
Numbers, perfect numbers 102 119—120 160—162 167;
Numbers, real numbers 99 116;
Numbers, representational character of 48—49;
Numbers, transcendental numbers 164
Numerals 48 62 80—81;
Numerals, Arabic 80—81 91—92 195;
Numerals, Roman 80
Objectivity 2 7 10 64 138 143—144 151 191—192;
Objectivity, objective reality 114
Objects/entities of mathematics 13 14 43 46 53—54 57 91 114 147—149 193
Objects/entities of mathematics as abstract 12—13 141
Objects/entities of mathematics as real 11 136 143
Observable/unobservable (theoretical) entities 123 150—151 157
Observation 30 32 178;
Observation, observation statements 66—67
Occam's razor 101
Omniscient being 114 157
Order, axioms of 96
Papineau, D. 194
Paradoxes 19 22 32 65 71 111 173 197
Parallel postulate/axiom 32 62 96 101
Parsons, C. 61 193
Peano axioms 72 170
Penrose, R. 78
Perception 29 64—66 114—115;
Perception, sense perception/experience 11 5—7 13—15 18 59 192
Physics 13 32 58 61 98 141—142;
Physics, analogy with mathematics 11 32 116 133 156 189;
Physics, astrophysics 133;
Physics, classical physics 56;
Physics, electrodynamics 50;
Physics, high energy physics 41;
Physics, normality of 164—165
Physics, particle physics 54;
Physics, quantum mechanics 12 121 151;
Physics, relationship between mathematics and xii 13 53 61 81 86 125;
Physics, space-time 40 46 50—51 55
Physics, string theory 189 see
Picture proofs 34—37 88 130—153 157 179—180 191;
Picture proofs and Platonism xii 25—45
pictures 106—107 130—153 172—174 184—185;
Pictures and symbols 40 152—153;
Pictures as evidence 42 172 176 180—181;
Pictures as windows to Plato's heaven 38 40;
Pictures, explanatory/psychological value of 28 42 152—153 176;
Pictures, misleading 4 177—178;
Pierce, C.S. 150
Plato xi 8 193;
Plato, Plato's heaven/Platonic realm 14 38 78 101 163
Plato, Platonic forms 8—9;
Platonic entities 143;
Platonic entities, Frege's sense as 147 151 163
Platonism xii 8—24 48 56 65 78 89 100 115 116 122 140 149 174 178 191—192 193;
Platonism about the physical world 49;
Platonism and fallibilism 14 18—23 192;
Platonism and picture proofs xii 25—45;
Platonism and realism 149—151;
Platonism and rules 136—138 145 147 149;
Platonism and structuralism 57—58
Podolsky 16. see also EPR thought experiment
Poetry 79—81 93
Poincare, H. xii 64 100 124 183
POINTS 101 123;
Points at infinity 66;
Points, contextual definition of 95—96 98;
Points, isolated 127 175;
Points, limit or cluster point 127—128
Polyhedra 19—22 99 104 108—109 111—112
Polynomials 12 162—163 169;
Polynomials in knot theory 86—88 91;
Polynomials, HOMFLY polynomial 86;
Polynomials, Jones polynomial 85;
Polynomials, Laurent polynomial 97
Pope 79
Popper, K. 32 38 159
Positivism 18
Possibility 100 141 163
Pour-El. M and Richards, L 125
Power set axiom 65 111
Prime numbers 1 102 127 166—168;
Prime numbers, prime number theorem 166 168 188;
Prime numbers, twin primes 151 168;
Primitive terms 94—99 101—102 111—112
Private/public 140 145
probability 155—157 165
Proofs 11 19—23 22 68 110 130 172 174 180 186—188;
Proofs and explanation/persuasion 28 42 131—132 152 157;
Proofs, errors in 156 189 192;
Proofs, method of proofs and refutations 19—23 110;
Proofs, necessity of 2 7 182 187 189 191;
Proofs, rigorous 25—28 187—188;
Proofs, surveyabilily of 151—152 154—155 157—158;
Properties 49 55 89 91—92
Properties, essential and accidental 60;
Properties, intrinsic and extrinsic 194
Pseudo-science 5 1—2 194
Ptolemy 155
Pure mathematics 48 55 124 125
Putnam, H. xi 53 56 78 125 150 168—171 193
Pythagoreans 55;
Pythagoreans, Pythagorean relation 165
Pythagoreans, Pythagorean theorem 2—3 33 98 136 151 188;
quantum mechanics 2 32 50 125 196
Quantum mechanics, quantum field theory 194; 198;
Quantum mechanics, quantum state 46 50 55 125;
Quantum mechanics, quantum systems 55—56
Quasi-empirical nature of mathematics 111 168
Quine, W.V. xi 13 46 53—56 125 140
Quinn, F. see Jaffe A. F.
Ramsey number; Ramsey theory 107
Randomness 148 164
Rationality 146 157 158 171
Rawls. J. 32
Realism xii 38 46 57 58 118 123 144 170—171 193;
Realism and Platonism 149—151
Realism, scientific/internal realism 67 123^1 150;
Reasoning, abstract 174;
Reasoning, demonstrative 187;
Reasoning, hypothetico-dcductive (H-D) 32 168 180;
Reasoning, probabilistic 155 165;
Recursiveness (of the natural numbers) 80—81 91—92
Reductionism 102—103
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