The Metaphysics and Mathematics of Arbitrary Objects

Leon Horsten

250 pages, parution le 12/06/2019

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Résumé

This book develops a new theory of arbitrary entities and connects it to issues and debates in metaphysics and contemporary philosophy of mathematics. It investigates the relation between particular and arbitrary objects, and between particular and arbitrary systems of objects. These concepts are then applied to problems in 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.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).

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Leon Horsten
Parution	12/06/2019
Nb. de pages	250
EAN13	9781107039414

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The Metaphysics and Mathematics of Arbitrary Objects

Résumé

Caractéristiques techniques

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