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Leng M. (ed.), Paseau A. (ed.), Potter M. (ed.) — Mathematical Knowledge
Leng M. (ed.), Paseau A. (ed.), Potter M. (ed.) — Mathematical Knowledge

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Название: Mathematical Knowledge

Авторы: Leng M. (ed.), Paseau A. (ed.), Potter M. (ed.)

Аннотация:

What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense of the current state of debate in this fascinating field.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 230

Добавлена в каталог: 10.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
1 2
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