Thin Objects: An Abstractionist Account

ISBN : 9780199641314

Oystein Linnebo
288 Pages
156 x 234 mm
Pub date
May 2018
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Mathematics appears to be concerned with abstract objects such as numbers and sets. What are these objects? Oystein Linnebo develops an account of thin or lightweight objects, applicable in mathematics but also more generally, according to which certain objects do not require very much for their existence. This account builds on ideas due to the great logician and philosopher Gottlob Frege (1848-1925). The result is a distinctive approach to ontology, that is, the metaphysical study of what there is. Abstract objects such as numbers and sets are demystified and allowed to exist alongside more familiar physical objects. The account involves a novel approach to set theory (generally regarded as the foundation of all of mathematics) which takes seriously the idea that sets are formed successively.


Part I: Essentials
1 In search of thin objects
2 Thin objects via criteria of identity
3 Dynamic abstraction
Part II: Comparisons
4 Abstraction and the question of symmetry
5 Unbearable lightness of being
6 Predicative vs. impredicative abstraction
7 The context principle
III: Details
8 Reference by abstraction
9 The Julius Caesar problem
10 The natural numbers
11 The question of platonism
12 Dynamic set theory

About the author: 

Oystein Linnebo took up a Professorship at the University of Oslo in 2012, having previously been a Professor at Birkbeck, University of London, and held positions at Bristol and Oxford. He obtained his PhD in Philosophy from Harvard in 2002 and an MA in Mathematics from Oslo in 1995. His main research interests lie in philosophical logic, philosophy of mathematics, metaphysics, early analytic philosophy (especially Frege), as well as parts of philosophy of language and philosophy of science. He has published more than fifty articles and is the author of Philosophy of Mathematics (Princeton University Press 2017).

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