Preface ........................................................ ix
Introduction .................................................... 1
I The Problem ................................................. 2
1 An historical reversal ................................... 3
2 How applied mathematics became pure ...................... 6
3 Where we are now ........................................ 27
II Proper Method .............................................. 38
1 The meta-philosophy ..................................... 38
2 Some examples from set-theoretic practice ............... 41
3 Proper set-theoretic method ............................. 52
4 The challenge ........................................... 55
III Thin Realism ............................................... 60
1 Introducing Thin Realism ................................ 61
2 What Thin Realism is not ................................ 64
3 Thin epistemology ....................................... 71
4 The objective ground of Thin Realism .................... 77
5 Retracing our steps ..................................... 83
IV Arealism ................................................... 88
1 Introducing Arealism .................................... 88
2 Mathematics in application .............................. 89
3 What Arealism is not .................................... 96
4 Comparison with Thin Realism ............................ 99
5 Thin Realism/Arealism .................................. 103
V Morals .................................................... 113
1 Objectivity in mathematics ............................. 114
2 Robust Realism revisited ............................... 117
3 More examples from set-theoretic practice .............. 123
4 Intrinsic versus extrinsic ............................. 131
Bibliography .................................................. 138
Index ......................................................... 147
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