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The Metaphysics and Mathematics of Arbitrary Objects

The Metaphysics and Mathematics of Arbitrary Objects

$99.99 (C)

  • Date Published: August 2019
  • availability: In stock
  • format: Hardback
  • isbn: 9781107039414

$ 99.99 (C)
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About the Authors
  • 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.

    • Provides valuable new explorations of an understudied area of mathematical theory
    • Investigates particular and arbitrary systems of objects in relation to contemporary problems in philosophy of mathematics
    • Engages with logic, metaphysics, structuralism, and statistics, making the book relevant for researchers in multiple fields
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    Product details

    • Date Published: August 2019
    • format: Hardback
    • isbn: 9781107039414
    • length: 246 pages
    • dimensions: 254 x 178 x 18 mm
    • weight: 0.6kg
    • contains: 15 b/w illus.
    • availability: In stock
  • Table of Contents

    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.

  • Author

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

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