The Metaphysics and Mathematics of Arbitrary Objects

Leon Horsten (University of Bristol)

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English

Cambridge University Press
28 October 2021

Philosophy: metaphysics & ontology; Philosophy of mathematics

Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the relation between specific and arbitrary objects and between specific and arbitrary systems of objects. His book shows how this innovative theory is highly applicable to problems in the philosophy of arithmetic, and explores in particular how arbitrary objects can engage with the nineteenth-century concept of variable mathematical quantities, how they are relevant for debates around mathematical structuralism, and how they can help our understanding of the concept of random variables in statistics. This fully worked through theory will open up new avenues within philosophy of mathematics, bringing in the work of other philosophers such as Saul Kripke, and providing new insights into the development of the foundations of mathematics from the eighteenth century to the present day.

By: Leon Horsten (University of Bristol)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 244mm, Width: 169mm, Spine: 14mm
Weight: 441g
ISBN: 9781108706599
ISBN 10: 1108706592
Pages: 249
Publication Date: 28 October 2021
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

1. Introduction; 2. Metaphysics of mathematics; 3. Arbitrary objects; 4. Mathematical objects as arbitrary objects; 5. Structure in mathematics; 6. Mathematical structures; 7. Kit fine; 8. Generic systems and mathematical structuralism; 9. Reasoning about generic w-sequences; 10. Probability and random variables; 11. Directions for future research.

Leon Horsten is Professor of Philosophy at the University of Bristol. His publications include The Tarskian Turn: Deflationism and Axiomatic Truth (2011) and Goedel's Disjunction: The Scope and Limits of Mathematical Knowledge (co-edited with Philip Welch, 2016).