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  3. The Metaphysics and Mathematics of Arbitrary Objects
  • Cited by 16
Publisher:
Cambridge University Press
Online publication date:
May 2019
Print publication year:
2019
Online ISBN:
9781139600293
DOI:
https://doi.org/10.1017/9781139600293
Subjects:
Mathematics (general), Mathematics, Philosophy of Science, Philosophy
Information

Book description

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.

Reviews

‘For the initiated reader, the book promises to add new life to research on arbitrary objects.’

R. L. Pour Source: Choice

‘… the work constitutes an important contribution to the analytical philosophy of mathematics.’

Athanase Papadopoulos Source: zbMATH

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