Sam Cowling is Assistant Professor, Denison University, USA.

Acknowledgements

Introduction

1 The case for platonism

1.1 Platonism

1.2 Semantic arguments

1.3 Alethic arguments

1.4 Indispensability arguments

1.5 Metaphysical explanation

2 The abstract-concrete distinction

2.1 The standard view

2.2 Analyzing abstractness

2.3 Primitivism

2.4 Eliminativism

3 Paradox, parsimony, and infinite regresses

3.1 Paradox

3.2 Parsimony

3.3 Infinite regresses

4 Causal concerns

4.1 Epistemic access

4.2 Ensuring epistemic access

4.3 Semantic access

4.4 Cognitive access

4.5 Eleaticism

5 Non-uniqueness

5.1 The non-uniqueness problem

5.2 Living with non-uniqueness

5.3 Metaphysical underdetermination

5.4 Overcoming underdetermination

6 Modal objections

6.1 Necessary existents

6.2 Necessary connections

6.3 Contingent platonism

6.4 Abstracta and actuality

7 Nominalist options

7.1 Nominalisms

7.2 Meaning

7.3 Truth

7.4 Commitment

7.5 Harvard nominalism revisited

Conclusion

Glossary

References

Index