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Think of a number, any number, or properties like fragility and humanity. These and other abstract entities are radically different from concrete entities like electrons and elbows. While concrete entities are located in space and time, have causes and effects, and are known through empirical means, abstract entities seem to be altogether different. They seem to be immutable and imperceptible and to exist necessarily and "outside" of space and time. The peculiar nature of these entities raises hard questions about whether they exist and what they might really be like.
This book provides a thorough introduction to the problems raised by abstract entities and the debates about existence, truth, ontology, and knowledge that surround them. It sets out the key issues that inform the metaphysical disagreement between Platonists who accept abstract entities and nominalists who deny their existence. Beginning with the essentials of the Platonist-nominalist debate, it explores the following arguments and issues that drive the debate over abstract entities:
- the abstract-concrete distinction and various proposals for making sense of the divide between abstract and concrete reality
- the case for Platonism and its connections to semantics, science, and the nature of metaphysical explanation
- the epistemological puzzles surrounding abstract entities and Platonist proposals for explaining our knowledge of mathematical entities and the rest of abstract reality
- arguments for nominalism that are premised upon concerns about paradox, parsimony, infinite regresses, underdetermination, and the causal isolation of abstract reality
- the connections between the metaphysics of abstract entities and the metaphysics of possibility and the prospects for reconciling nominalism with the existence of merely possible entities
- the variety and vices of nominalist options that seek to replace Platonism and make sense of our best scientific and metaphysical theories.
Throughout the book, key questions about abstract entities are examined in light of foundational work by Frege, Quine, Lewis, and Benacerraf and with an eye toward recent developments in the debate between nominalists and Platonists.
Including chapter summaries, annotated further reading and a glossary, this book is essential reading for anyone seeking a clear and informative introduction to the problems raised by abstract entities.