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.

Develops and defends a new metaphysical and logical theory of arbitrary objects that will reinvigorate the philosophy of mathematics.

About the Author
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).

Reviews
'For the initiated reader, the book promises to add new life to research on arbitrary objects.' R. L. Pour, Choice
'... the work constitutes an important contribution to the analytical philosophy of mathematics.' Athanase Papadopoulos, zbMATH



Book Information
ISBN 9781108706599
Author Leon Horsten
Format Paperback
Page Count 249
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 441g
Dimensions(mm) 244mm * 169mm * 14mm