What is included with this book?
Acknowledgements | p. vii |
Preface | p. ix |
Infinity | p. 1 |
Introduction | p. 1 |
Zeno's paradoxes | p. 2 |
Potential versus actual infinity | p. 7 |
The ordinal notion of infinity | p. 12 |
The cardinal notion of infinity | p. 13 |
Summary | p. 22 |
Mathematical Platonism and realism | p. 23 |
Introduction | p. 23 |
Historical origins | p. 23 |
Realism in general | p. 26 |
Kurt Godel | p. 35 |
Penelope Maddy | p. 37 |
General problems with set-theoretic realism | p. 41 |
Conclusion | p. 46 |
Summary | p. 47 |
Logicism | p. 49 |
Introduction | p. 49 |
Frege's logicism: technical accomplishments | p. 52 |
Frege's logicism: philosophical accomplishments | p. 58 |
Problems with Frege's logicism | p. 63 |
Whitehead and Russell's logicism | p. 66 |
Philosophically, what is wrong with Whitehead and Russell's type theory? | p. 71 |
Other attempts at logicism | p. 78 |
Conclusion | p. 78 |
Summary | p. 79 |
Structuralism | p. 81 |
Introduction | p. 81 |
The motivation for structuralism: Benacerraf's puzzle | p. 83 |
The philosophy of structuralism: Hellman | p. 85 |
The philosophy of structuralism: Resnik and Shapiro | p. 90 |
Critique | p. 96 |
Summary | p. 100 |
Constructivism | p. 101 |
Introduction | p. 101 |
Intuitionist logic | p. 106 |
Prima facie motivations for constructivism | p. 113 |
Deeper motivations for constructivism | p. 114 |
The semantics of intuitionist logic: Dummett | p. 121 |
Problems with constructivism | p. 123 |
Summary | p. 124 |
A pot-pourri of philosophies of mathematics | p. 127 |
Introduction | p. 127 |
Empiricism and naturalism | p. 130 |
Fictionalism | p. 134 |
Psychologism | p. 137 |
Husserl | p. 141 |
Formalism | p. 147 |
Hilbert | p. 153 |
Meinongian Philosophy of Mathematics | p. 157 |
Lakatos | p. 163 |
Proof: ex falso quod libet | p. 167 |
Glossary | p. 169 |
Notes | p. 177 |
Guide to further reading | p. 191 |
Bibliography | p. 195 |
Index | p. 201 |
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