Index

a
absolute continuity 157
absoluteness 1 , 55-6 , 78 , 101-2 , 104 , 127-8 , 188 , 219 , 230
actual infinite, the:
as an amalgam of the mathematically infinite and the metaphysically infinite 44 , 77 , 103 , 113 ;
defined 39-40 ;
in relation to the potential infinite 39-40 , 47 , 51-2 , 77 , 93 , 117 , 132 , 142 , 149 , 171 , 204 , 208
‘all at once’ 29 , 39-40 , 43-4 , 47 , 81 , 88 , 110
analogy of the field of vision, the 189-94passim, 226
analysis 58 , 64 , 66 , 68 , 114 , 173 ;
non-standard see non-standard analysis;
see also analytic geometry
analytic geometry 58 , 62 , 66 , 68 , 114
Anaxagoras 34 , 36
Anaximander 15 , 17-27passim, 34-8 , 99 , 106 , 202
antinomies, Kant’s see Kant’s antinomies
apeiron, to15 , 17-28passim, 35 , 99 , 187 , 202 , 237 ;
the imposition of the peras on it 19-20 , 27 , 105 , 246 n.16
appearance/reality distinction, the 18 , 23-28passim, 35 , 45 , 77-9 , 85 , 92-104 , passim;
in relation to the mathematical/metaphysical distinction 24 , 45-6 , 78-9 , 87-8 , 97-9 , 222
Aquinas, St T. 48-9 , 78 , 184
Archimedes 30 , 32-3 , 51 , 55 , 57 , 61-2 , 66
Archytas 28-9 , 38 , 56 , 80 , 134
Aristotle 5 , 15 , 29 , 34-44 , 70 , 78 , 82 , 84 , 88 , 92 , 96-7 , 99 , 104 , 110 , 112 , 138 , 143 , 198 , 207 , 211 , 213 , 216 , 222 , 237 n.2, 237 n.5, 240 n.23;
and the actual/ potential distinction 3-44 , 47 , 52 , 73 , 143 , 204 , 207-8 , 216 ;
on the infinitude of time 38-40 , 44 , 47 , 88 , 91 , 207-8 , 216 , 221 ;
his influence on his successors 34 , 39-40 , 44-56 , 76-81passim, 87 , 90-3 , 99-100 , 110 , 113 , 117 , 132-3 , 208 ;
on his predecessors 17-18 , 34-9 , 43-4 , 75 , 80 , 97 , 99 , 237 n.5;
on Zeno’s paradoxes 3 , 5 , 25 , 37-8 , 42 , 70-3passim, 104 , 158 , 216
arithmetic 29 , 114 , 133 , 153 , 174-85passim
‘as if’ 89 , 95 , 108 , 135 , 186 , 223-4 , 228 , 232
atomism 25-7 , 35-7 , 79 , 82 , 92 , 104 ;
logical see logical atomism
Augustine, St 46-51passim, 78
Aureol, P. 52
Avicenna 48
axiomatization 29-30 , 75 , 77 , 116 , 129-30 , 134 , 154-5 , 160 , 169 , 172-83 , 243 n.44;
see also the Euclidean paradigm
axioms of infinity (axioms concerning the infinite) 116 , 129 , 155 , 157 , 166 , 179 , 182

b
Beethoven, L. 145
Benardete, J. 5 , 9 , 70 , 143
Beresford, G. 239 n.16
Bergson, H. 103-4 , 107 , 110 , 117 , 158 , 203
Berkeley, G. 57 , 65-6 , 80-2
Boethius, A. 47
Bolzano, B. 66 , 112-17 , 198 , 242 n.4
Bradley, F. 101-3 , 187

-261-

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The Infinite
Table of contents

Table of contents

  • Title Page iii
  • Contents vii
  • Preface to the Second Edition xi
  • Preface xx
  • Introduction: Paradoxes of the Infinite 1
  • Part One - The History 15
  • Chapter 1 - Early Greek Thought 17
  • Chapter 2 - Aristotle 34
  • Chapter 3 - Medieval and Renaissance Thought 45
  • Chapter 4 - The Calculus 57
  • Chapter 5 - The Rationalists and the Empiricists 75
  • Chapter 6 - Kant 84
  • Chapter 7 - Post-Kantian Metaphysics of the Infinite 96
  • Chapter 8 - The Mathematics of the Infinite, and the Impact of Cantor 110
  • Chapter 9 - Reactions 131
  • Part Two - Infinity Assessed 145
  • Chapter 10 - Transfinite Mathematics 147
  • Chapter 11 - The Löwenheim-Skolem Theorem 159
  • Chapter 12 - Gödel's Theorem 172
  • Chapter 13 - Saying and Showing 186
  • Chapter 14 - Infinity Assessed. the History Reassessed 201
  • Chapter 15 - Human Finitude 218
  • Glossary 234
  • Bibliography 250
  • Index 261
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