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| Leng M. (ed.), Paseau A. (ed.), Potter M. (ed.) — Mathematical Knowledge |
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| Предметный указатель |
A posteriori 25
A priori 4 25 155
Aboutness, two notions of 25
Abstract objects, knowledge of see “Benacerraf Paul Benacerraf’s
Abstractionism 152 163 171
Antirealist programmes, epistemological problems with 89
Armchair knowledge 21 22 30
Axioms 3 4 14 84 90 91 103 104
Background theory 18—20
Baillargeon, R. 76 note
Baker, Alan 8 14 35 105 128 128 132 142 143
Baker, Alan (Fields medallist) 62
Balaguer, Mark 10 89
Bayesian analysis 36
Beebee, Helen 21
Bell, David 23
Benacerraf, Paul 1 3 111 145 149
Benacerraf, Paul, Benacerraf’s problem 25 29 30 32 84 86 93—95 103 105 107 110 112
Blackburn, Simon 151
Boolos, George 155 173
Boroditsky, L. 80
Brandstein, M. 72
Brent, R.P. 72
Brown, Jessica 21
Bueno, O. 122 note
Burge, Tyler 25 note
Burgess, John 115 125 127 128 128 129 129 138 139 174
Butterworth, Brian 13 81
Butterworth, Brian, the number module 75
Cantor, Georg 69
Cappelletti, Marinella 12 13 78 79
Carey, Susan 13
Causal theory of knowledge 27 110
Causation, epistemological role of 93
Cipolotti, L. 77 78
Cognitive science 10
Cognitive science, limits of 82
Cognitive science, two levels of evolution, biological 74
Cognitive science, two levels of evolution, cultural 75
Cognitive science, understanding numbers 74
Cognitive science, understanding numbers, ontogenetic perspective 74 75
Cognitive science, understanding numbers, phylogenetic perspective 74
Cohen, L. 78
Colyvan, Mark 6 87 109 111 117 117 121 122 128 128 132 137 140 142
Comprehension axioms 164 165
Concrete objects, mathematical truths as truths about 4
Confirmation 109 117 118 143
Confirmation, confirming instances 35
Confirmation, Nicod’s criterion of 72
Conservation of energy 27
Conservative extension 88
Consistency 20 84 85 89—95 101—105 107
Corfield, David 38
Counterexample 36
Crutch, S.J. 78 79
Davies, Martin 21
Davis, Philip J. 9
definitions 3
Deflationism 90—92 94
Dehaene, Stanislas 13 78 79 81
Dehaene, Stanislas, number sense 75
Delazer, M. 82
Desboves, A. 69
Dissociation between numerical and non-numerical domains 78
Distance and size effects 80
Dummett, Michael 169 169
Dummett, Michael, indefinite extensibility 31
Echeverria, J. 62 69
Elkies, Noam 35 36
Empirical knowledge, mathematical knowledge as 87
Empiricism 4 109 110 117 118 122
Empiricism, constructive see “van Fraassen Bas constructive
Empiricism, contrastive 118
Euclid 2 3
Euler, Leonhard 35 61 62
Evans, Gareth 162 note
Even Perfect Number Conjecture 61 63—64 68 69 71 72
Expectancy 76 77
Explication 37—39
Explication, precise and relative 38
Externalism, semantic 22 23 30 31
Feferman, Solomon 115 note
Feigenson, L. 76
Fermat, Pierre de 60
Fermat, Pierre de, Fermat numbers 60 61
Fermat, Pierre de, Fermat’s Last Theorem 35 36
Fictionalism 3 20 84 98 102 104 105 107
Fictionalism and counterexamples 86
Fictionalism and deflationism 93
Fictionalism and nominalism 90
Field, Hartry 10 85 87 90 94 95 98 110—112 138
Fine, Kit 174 note
Flew, Anthony 151
Formalism, axiomatic 20
Formalism, myth of 18
Forster, M. 141 note
Foundationalism 33
Frege, Gottlob 22 109 151 152 170
Frege, Gottlob, Basic Law V 31 152
Frege, Gottlob, Begriffsschrift 150—152 162
Frege, Gottlob, Grundgesetze der Arithmetik 128 note 152
Frege, Gottlob, Grundlagen der Arithmetik 66
Fuson, K.C. 81
Garavaso, P. 128 note
Gardner, Martin 9
Generalization 154 159
Genesis of mathematical beliefs 12
Gettier, Edmund 1 2
Giardino, Valeria 12 14
Ginzburg, L.R. 121
Godel, Kurt, Completeness theorem 99
Godel, Kurt, Incompleteness theorem 20 31 64 65 167 168
Godel, Kurt, independence of mathematical realm 31
Goldbach, Christian, Goldbach’s conjecture 21
Goldbach’s conjecture 8 61—64 68 71
Goldbach’s Conjecture, decidability of 64 65
Goldbach’s Conjecture, partition function 69
Goodman, Nelson 125
Goodman, Nelson, Fact, Fiction and Forecast 35
Goodman, Nelson, new riddle of induction 35
Goodman, Nelson, new riddle of induction, projectible properties 64
Gordon, Peter 80
Gowers, Timothy 14 32
Guy, R. 63
Habituation 76
Hacking, Ian 28
Hale, Bob 153 note 169 172 174
Hardy, G.H. 14 62
Hart, W.D. 26 27 110
Hebb, D.O. 5
Heider, E.R. 80
Hellman, Geoffrey, modal structuralism 5 133—134
Hempel’s paradox 72
Henschen, Salomon 79
Heraclitus 127
Herkommer, Mark 69 note
Hersh, Reuben 3 7 9 83
Hespos, Susan 79
Hilbert, David 19 151
Hirotugu, Akaike 141
Hodges, J.R. 77
Holism 6 131
Holism, epistemic 110—112
Hume, David 64
Hume, David, Hume’s principle 31 171
Hume, David, problem of induction 64
Hume, David, problem of induction, Principle of Uniformity 64 67
Ideas, mathematical objects as 2
Implicationism 17 19
Impredicativity 169 170
| Indispensability 6 103 104 109 112 113 115 127 137
Indispensability, a fictionalist perspective 88
Indispensability, transitivity of 113 114
Induction 34 35 59
Induction of the scientific kind 34
Induction, as deductive mathematical proof 59
Induction, biased samples 67 70
Induction, distinctive features of the mathematical case 65
Induction, distinctive features of the mathematical case, order 66
Induction, enumerative 14 59 61—65 67 70 72 73 105
Induction, enumerative and discovery 60 64
Induction, enumerative, legitimacy over the domain of natural numbers 60
Induction, enumerative, minuteness 67 68
Induction, functional 71
Induction, functional, Goodman’s second riddle see “Goodman Nelson new
Induction, mathematical as distinct from broad philosophical sense 59
Induction, mathematical as opposed to empirical 68
Induction, non-uniformity principle 66
Inference to the best explanation 105
Inferentialism 155 166 167
Innate capacity 12 76 77
Instrumentalist 89
Interdisciplinary 40 74
Internalism, semantic 22 23
Internalist conception of mathematics 31 32
Intuitive conception of mathematical structures 106
Isaacson, Daniel 122 note
Iterative conception of the sets 106
Jubien, Michael 145 note
Kitcher, Philip 5 12
Kreisel, Georg 95 98
Kreisel, Georg, ‘squeezing’ argument 100
Kripke, Saul 22
Kripke, Saul, Naming and Necessity 36 note
Lakatos, Imre 124 note
Lakatos, Imre, Proofs and Refutations 38
Lakoff, George 10
Language, relation between numbers and 79 81
Laudan, Larry 126 note
Law of excluded middle 32
Leibniz 66
Lemer, C. 78
Leng, Mary 89 note 109 117 119 121 149
Levinson, S.C. 79
Lewis, David 95 96
Lewis, David, concrete possibilia 136
Lewis, David, structuralism 133 134
Liggins, David 149 note
Littlewood, J.E. 62
Logic, triviality of 17
Logical knowledge 3 26 29 84 85 87—89 103 107 108
Logical knowledge, problems for fictionalism 89
Logical possibility 91 92 94 95
Logical possibility, pre-formal notions of 98—102
Logical possibility, reduction of 97
Logicism 16
Logicism, abstractionism see “Abstractionism”
Lyon, A. 121
MacBride, Fraser 153 note 174
Maddy, Penelope 4 13 114 115 121 122 130 132 137
Mathematical recreation 113 116 117 122 132
Mathematicians 7 33
Mathematicians, actual practice of 60 123
Matsuzawa, T. 76
McCulloch, Warren 1
Melia, J. 121 note
Memory 38 39 41
Memory, generated 41 43 47 55
Memory, linear 43
Memory, telephone numbers 42
Memory, visual 53
Mental arithmetic 49
Metaphysical possibility 95
Metaphysical possibility, reduction to possible worlds 95 96
Metaphysics, relation of mathematical practice to 123
Metaphysics, should be avoided 33
Mill, J.S. 5 12 60 64 66 109
Millar, Alan 32 note
Mistakes, about number 31
Mistakes, tennis match 24
Mistakes, undetectable 31
Mistakes, Wittgenstein and Russell’s treatment of 23
Modal structuralism 5 6 20 133 135 135 140 143
Modal structuralism, Hellman, Geoffrey 134
Model theory 93 94 97 98 100—104 107 162
Modelling view of applied mathematics 118 119
Modelling view of applied mathematics, versus explanatory view 120 121
Mother theories 19 20
Munduruku 80
Natural science 28 87 123 124
Naturalism, epistemological 27
Neo-Fregean logicism 21 155
Neo-Fregean logicism, abstractionism see “Abstractionism”
Neuropsychology 77 78
Neutralism 153 154 156 157 164—166 168 169 171
Neutralism, extreme 159 160 164
Nieder, A. 81
Nolan, Daniel 17 note
Nominalism 90 128 138 139
Numerical competence in animals 76
Numerical competence, loss of 77
Nunez, Rafael E. 10
Oliver, Alex 149 note
Oliver, D. 80
Ontology 115 133 135 146
Ontology, expertise in 28
Ontology, ontological commitment 150 160
Ontology, ontological economy 125
Ontology, ontological rights 113 117
Ontology, trading ontology for modality 86 89
O’Bryant, K. 71
Parietal lobes 78
Parsons, Charles 112
Paseau, Alexander 6 33
Peano arithmetic 20 65
Perceptual knowledge of mathematical objects 5
Physical laws 9 10 35
Physicalism 27
Piaget, Jean 5
Pica, P. 80
Pincock, Christopher 117 note
Piraha 80
Plato, Cratylus 127 note
Plato, Meno 29
Platonism 93 95 99—102 104 105 123 126—128 130 131 134 137—139 143 144 147
Platonism, indifference objection 131 132 135—138 146 147 149
Platonism, mathematical-cum-scientific 129 129n
Platonism, pragmatic objection 131 132 137 137 149
Platonism, Quinean 105
Platonism, scientific 123 126 127 129—132 135 140 144—146 149
Platonism, scientific, strong 135 136
Platonism, scientific, weak 135 136
Platonism, versus fictionalism 89
Polk, T.A. 78
Postponement 20 29
Potter, Michael 1 note 3 21 149
Priest, Stephen 151
Probabilistic language 36
proof 3 40
Proof of the existence of a prime factorisation 44 45
Proof theory 19 93 94 98 100—102 107
Proof, as a form of communication 56
Proof, as conceived by fictionalists 84
Proof, beautiful 39
Proof, containing ideas 48
Proof, interesting 15
Proof, memorable 15 37 43
Proof, quality of 37
Proof, that the square root of 2 is irrational 46 47
Propositions 93
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