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 like meanings and possibilities are remarkably different. They seem to be immutable and imperceptible and to exist "outside" of space and time.
This book provides a comprehensive critical assessment of the problems raised by abstract entities and the debates about existence, truth, 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 abstract entities exist. Beginning with the essentials of the platonist–nominalist debate, it explores the key arguments and issues informing the contemporary debate over abstract reality:
- arguments for platonism and their connections to semantics, science, and metaphysical explanation
- the abstract–concrete distinction and views about the nature of abstract reality
- epistemological puzzles surrounding our knowledge of mathematical entities and other abstract entities.
- arguments for nominalism premised upon concerns about paradox, parsimony, infinite regresses, underdetermination, and causal isolation
- nominalist options that seek to dispense with abstract entities.
Including chapter summaries, annotated further reading, and a glossary, Abstract Entities is essential reading for anyone seeking a clear and authoritative introduction to the problems raised by abstract entities.
Table of Contents
1. The Case for Platonism
2. The Abstract-Concrete Distinction
3. Paradox, Parsimony, and Infinite Regresses
4. Causal Concerns
6. Modal Objections
7. Nominalist Options
Sam Cowling is Assistant Professor, Denison University, USA.
'This is a terrific book, and the first full-length introduction to this fascinating topic. Writing in an accessible and student-friendly style, Sam Cowling presents a thorough and systematic presentation of the metaphysical, semantic and epistemological issues raised by abstract entities. Highly recommended!' - Christopher Daly, University of Manchester, UK
'In this impressive book Sam Cowling provides both a clear introduction to the debate over abstract entities, and a careful examination of the platonist position. He is scrupulously fair to both sides, conceding much to the combination of nominalism with realism about possibilities.' - Peter Forrest, University of New England, Australia
'One of the most important problems in philosophy is whether there are abstract objects - such as numbers, properties and propositions. Sam Cowling does a superb job in introducing the debates and problems around this issue. The book is written very clearly and shows an excellent command of the literature. Highly recommended.' - Gonzalo Rodriguez-Pereyra, University of Oxford, UK"Readers should come away from Cowling’s excellent book appreciating the merits and the plausibility of contemporary platonism, even if they disagree with some of the details. It is largely written for those at home with analytic metaphysics and epistemology. Philosophers of mathematics have overlapping interests, so will learn lots from this fine book." - James Robert Brown, University of Toronto, Toronto, ON, Canada