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Index of Names

Addison, J. W. 43 d'Alembert, J. Ie Rond 93 Alston, W. P. 92 Aristotle 9, 13, 74 Arnauld, A. 10

Benacerraf, P. 105, 124, 128 Bernays, P. 6, 22, 50, 81-85, 94,

99, 101, 109, 114 Beth, E. W. 39, 78, 87, 92, 93, 107

108 '

Birkhoff, G. 14, 105, 108 Boolos, G. 99 Bourbaki, N. 129 Bunge, M. 33, 45-48 Buridan, J. 64

Cantor, G. 50, 74, 76, 77, 90 Carnap, R. 3, 20, 35, 53, 60, 64,

78-82 Cheng, C. Y. 136 Church, A. 60, 131 Cohen, P. 43, 66, 79, 93 Curry, H. B. 16

Davidson, D. 44, 68 Dedekind, R. 138, 139 Descartes, R. 11, 127

Feferman, S. 94, 101

Fermat, P. 127 Feyerabend, P. 111 Feys, R. 16 Fraassen, B. van 59 Fraenkel, A. 94, 101 Frege, G. 19, 121, 138, 139, 142 Freud, S. 88 Freyd, P. 104 Freytag-L6ringhoff, B. van 74,

75,77 Frisch, J. c. 9, 11

Glymour, C. 111, 129 Goble, L. F. 45 G6del, K. 22-25 43 45 50 64 , , , , ,

67, 77, 90, 93, 94, 101, 109, 112, 113, 114, 127, 131, 133, 136

Goguen, J. A. 36, 37, 73, 110 Gonseth, F. 80-82, 89, 110 Goodman, N. 66 Goodstein, R. L. 65, 66, 79 Granger, G.-G. 7, 95-97, 105 Grassman, H. G. 105

Hanf, W. 124, 129 Hart, W. D. 43 Hatcher, W. S. 19, 44, 101, 105,

112, 121 Heijenoort, J. van 67

154

Hempel, C. 45, 46, 58, 59, 60, 62 Henkin, 1. 19, 20, 24, 29, 43,

56, 77 Herbrand, J. 115, 125, 128 Hilbert, D. 50, 115, 124 Hintikka, J. 43, 44

Inhelder, B. 89

Jones, T. 73 Jubien, M. 136, 141

Kalmar,1. 65, 66 Kant, I. 108 Kauppi, R. 11 Keynes, J. N. 12, 15, 33, 34 Kleene, S. C. 55, 63, 112 Klein, F. 105 Kneale, M. 10 Kneale, W. 10 Korner, S. 37, 38 Kreisel, G. 6, 7, 50, 66, 83-86,

88, 93, 94, 96, 98, 108, 109, 113-117, 124, 125, 129, 130, 131, 136, 142, 143

Kripke, S. 24 Kumar, D. 37

Ladriere, J. 50 Lakatos, I. 52, 65, 66, 68, 86,

90,93 Lawvere, F. W. 100, 103, 105,

108-110 Leibniz, G. W. 11 Lewis, C. I. 6, 41, 46, 58-63,

68-71, 73, 97 Lowenheim,1. 43, 55, 114, 129,

137, 140 Lyndon, R. 44, 50

MacLane, S. 95, 100, 103, 105 Marcus, R. Barcan 80, 133

Martin, R. M. 39 Mates, B. 64 Mehlberg, H. 50 Mill, J. S. 33, 34 Mobius, A. F. 105 Monk, D. 29

Index of Names

Montague, R. 39, 68, 71-73 Moody, E. W. 10, 64 Morris, C. 3, 20 Moss, J. M. B. 84, 94 Mostowski, A. 94, 114 Myhill, J. 50, 67, 86

Nagel, E. 74, 75, 79, 111, 112, 116, 129

Neumann, J. von 22, 120, 138, 142 Nicole, P. 10

Parsons, C. 133, 134 Peano, G. 42, 105 Peirce, C. S. 41, 42, 46 Piaget, J. 7, 78, 86-90, 92, 94,

95, 97, 99, 109, 110, 134 Poincare, H. 74, 75 Polya, G. 65 Porphyry 9 Poszgay, 1. 93 Prior, A. N. 135 Putnam, H. 85, 86, 128

Quine, W. V. 8, 45, 57, 70, 80, 92, 130-143

Rescher, N. 68-71, 136 Robinson, A. 79, 92, 109, 126 Robinson, R. M. 114 Russell, B. 19, 20, 67

Scheffler, I. 90 Scott, D. 66 Sheffer, H. M. 61

Index of Names

Skolem, Th. 43, 50, 55, 114, 129, 137, 140

Solovay, R. M. 43 Stone, M. H. 126 Suszko, R. 28, 39 Svenonius, L. 123

Takeuti, G. 67, 93 Tarski, A. 17, 29, 31, 32, 42, 43,

44, 57, 109, 114 Tharp, L. 139, 142

Thorn, R. 86, 87, 89, 108, 109, 121, 130

Thomason, J. F. 142

Ullian, J. S. 67

Wang, H. 112, 113, 114, 118, 119, 141

Weierstrass, K. 92 Whitehead, A. N. 20

Zermelo, E. 94, 101, 120

155

Subject Index

adequate translation 115 analyticity 58, 88

Aristotelian view of existence 74

background theory 33, 49, 51, 52, 56, 112, 113, 117, 134, 142

category theory 88, 95, 100-110

coherence view of meaning 41, 45, 66,88

coherence view of truth 64-68, 93, 128

co-intension 47

comprehension 12, 22, 27, 55, 59

connotation 12, 34, 58

consequence, theory of 10, 39

consistency 53, 74-77, 78, 90, 107, 117, 121

construct 12

constructivism, in mathematics 78, 87-91, 94-98, 102, 105, 109, 133

core intension 33, 47, 48, 62, 63

correct translation 123

correspondence view of meaning 41-45, 66, 88

correspondence view of truth 44, 64-68, 93, 128

cross-fertilization of mathematical theories 102, 110, 127, 131, 141, 142

cylindric algebra 29

denotation 58 dual homomorphism 14, 28, 29,

32, 107 dualistic view of meaning 46, 47,

55 -57, 66, 68, 70, 122

entailment, relation of 12, 16, 21, 49-54, 56, 58, 61, 66, 71, 83, 92,97, 107, 108, 113, 118-124, 126, 128

entailment relation induced by reference 16, 22, 61, 73

evidence, mathematical 81,84-86, 88, 93, 106

existence, mathematical 74-84, 88-94, 99,

44, 66, 101, 102,

130, 136, 140, 141 explanation 50, 86, 111, 122,

124-129, 139 extension 9-40, 47, 54, 58,

107, 122 extension of a set of constructs 30 extensional component of meaning

54, 143 extensional vagueness 34-38, 63

Subject Index

factual theories 40, 45, 79, 136, 142

faithful translation 53, 116, 119, 123

formalism 55, 64, 85, 86 formalization, as process 49-54,

66, 86, 88, 90, 121, 122, 125, 126

formalization of a theory 49, 54, 121

formalized theory 16, 36 fruitfulness 78, 79, 93, 94, 100,

106, 110, 127, 140, 142 functor 104

heuristic component of a theory 38, 57, 63, 66, 85, 92, 95, 97, 100, 103, 118, 125, 128, 129, 133, 141

heuristics, mathematical 52, 55, 64, 67, 78, 87, 91-95, 97, 98, 101, 106, 110, 126-129, 138, 142, 143

informal rigour 83 - 86, 90, 93, 94, 96, 125, 127

intended model 56, 123 intension 9-40, 47, 53, 54, 58,

59, 107, 119-121 intension of a set of constructs 30 intensional component of meaning

50, 52, 55, 57, 92, 116, 120, 121, 124, 143

intensional vagueness 35 intensionally related formulas 119 intuitionist mathematics 51, 55,

78, 79, 88, 102 inverse ratio, law of 9, 13, 107

L-comprehension 59 Lindenbaum algebra 26 linguistic component of meaning

40, 47, 50, 66, 68, 120, 128

157

meaning 41-48, 55, 58, 61-63, 97, 101, 143

meaning, mathematical 43,49-57, 95 -97, 101, 109, 115, 117, 118, 121-124, 143

meaning-preserving correspondences 51-54,102, 104,118-124,129, 139

model 17 model theory 17-23, 40, 42,

55-57, 117, 123, 137 morphism 103

natural mathematical theory 49,51, 55, 66, 116, 121, 122, 126

naturalness 99, 100, 101, 104 bis 106, 127, 139.

non-existent possibles 59, 60, 68-73

non-standard model 25, 57, 92, 109

objectivity, mathematical 50, 54, 63, 82-93, 99, 100, 106, 118, 120, 124, 126, 134

objects, mathematical 38, 43, 50, 55, 66, 74-84, 87-91, 95 bis 99, 102-105, 109, 118, 124, 126, 130, 132-137, 141

ontological commitment 130, 131-137

ontological reduction 131-143 ontology, for mathematics 37, 43,

57,80, 102, 103, 118, 133-137, 140, 142

Platonism, in mathematics 42-44, 50, 66, 74-77, 84, 87, 88, 90-94, 98, 107

Platonist view of existence 74 possible world 61, 68, 70-73 proof theory 21, 40, 55, 115 proof-theoretic content of a theory

115-117, 124, 142, 143

158

proper explication of intension 15, 21

quasi-translation 51, 57, 67, 80, 118, 125

rank of a formula 21 reduction 42, 100, 103, 111-118,

124, 129, 135, 139, 140, 142 reference, relation of 12, 16, 18,

55 -58, 60, 62, 69, 70, 83, 107, 108, 132, 135-137, 143

referential component of meaning 40, 47, 48, 50, 54, 55 -57, 68, 83, 91, 97, 100, 103

referential explication of intension 15, 22, 24, 40, 60, 61

referential view of meaning 42-45, 56, 68, 99

reflective abstraction 87-90 92 , , 94, 97, 99, 100, 110, 126

regular formula 26 relative existence 81-83, 89 rigour, mathematical 86, 90

semantical interpretation 53, 57, 114, 118, 140

semantically adequate theory 23, 59,69

Subject Index

semantics of a formalized theory 23-25, 54-57, 143

set-theoretic semantics 25, 42-44, 56, 57, 70, 73, 77, 94, 99, 123, 130, 133, 135, 137, 143

signification 55, 58, 61-63, 84, 96, 97, 100, 129, 130

standard model 56, 123 structure, mathematical 82-84,

87-89, 94-96, 99, 102, 109, 118, 120, 124-128, 130, 131, 138

style 95-101, 127 substitutional interpretation of 3

80, 133, 136 suggestiveness 100, 105, 127 supposition, theory of 10, 39 syntactical interpretation 53, 96,

112, 113, 115, 118 syntax of a formalized theory

17,77

Tarskian explication of extension 20

translation 112, 119, 132 truth, mathematical 44, 64-68,

85,93 truth set 19, 20

Partial List of Symbols

d 14 ExtM 19 0 13 d k 27 ExtM (F) 18 0 12,22 c 13 Ext.lt (F) 22 OM 18 C 12 Ext.lt (T) 31 OAt 22 Cn(G) 32 F 17 cp 18 Com (c) 15 F 30 'Jtk 29 Com (F) 28 Fk 26 g; 26 Con(c) 34 §" 28 f-T (F~G) 21

~ 27,28 §"k 26 e 12 v 27,28 Int 27 eM 18 D 33 Int(c) 13 e.lt 22 Dic(c) 34 Int(F) 21 Rp 18 r! 14 IntM (F) 22 T 17 tffk 27 Int.lt (F) 22 T 53 3 17 Int(T) 31 e 26

'YJ 12 L 17 15 'YJM 22 M 17 ,:., 27,28

'YJ.It 22 vIt 22 U 17 Ext (c) 13