Book ID: CBB819236580

Thin Objects: An Abstractionist Account (2018)


Are there objects that are "thin" in the sense that not very much is required for their existence? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for theseobjects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. Oystein Linnebo aims to do so by drawing on some Fregean ideas. First, to be an object is to be a possible referent of a singular term. Second, singular reference can be achieved byproviding a criterion of identity for the would-be referent. The second idea enables a form of easy reference and thus, via the first idea, also a form of easy being. Paradox is avoided by imposing a predicativity restriction on the criteria of identity. But the abstraction based on a criterion ofidentity may result in an expanded domain. By iterating such expansions, a powerful account of dynamic abstraction is developed. The result is a distinctive approach to ontology. Abstract objects such as numbers and sets are demystified and allowed to exist alongside more familiar physical objects. And Linnebo also offers a novel approach to set theory which takes seriously the idea that sets are "formed" successively.

Reviewed By

Review Nathaniel Gan (2019) Review of "Thin Objects: An Abstractionist Account". Metascience: An International Review Journal for the History, Philosophy and Social Studies of Science (pp. 167-169). unapi

Citation URI

Similar Citations

Book Philip A. Ebert; Marcus Rossberg; (2017)
Abstractionism: Essays in Philosophy of Mathematics (/isis/citation/CBB220910667/)

Chapter Haaparanta, Leila; (2009)
The Relations between Logic and Philosophy, 1874--1931 (/isis/citation/CBB001210347/)

Article Anna Longo; Ben Woodward; (2017)
Infinitely Generative Structure: Fichte, Schelling, and Modern Geometry (/isis/citation/CBB205102574/)

Book Ricketts, Tom; Potter, Michael D.; (2010)
The Cambridge Companion to Frege (/isis/citation/CBB001211647/)

Article Waldegg, Guillermina; (2001)
Ontological Convictions and Epistemological Obstacles in Bolzano's Elementary Geometry (/isis/citation/CBB000101855/)

Book Emanuele Gambetta; (2023)
Il Teorema di Dio (/isis/citation/CBB058518438/)

Thesis Theodora Vardouli; (2017)
Graphing Theory: New Mathematics, Design, and the Participatory Turn (/isis/citation/CBB982144600/)

Book Woods, John; (2003)
Paradox and Paraconsistency: Conflict Resolution in the Abstract Sciences (/isis/citation/CBB000301990/)

Book Fine, Kit; (2002)
The Limits of Abstraction (/isis/citation/CBB000302227/)

Book Sam Cowling; (2017)
Abstract Entities (/isis/citation/CBB032581953/)

Article Gray, Jeremy J.; (2004)
Anxiety and Abstraction in Nineteenth-Century Mathematics (/isis/citation/CBB000500122/)

Article Susanna Lindberg; (2017)
Technics of Space, Place, and Displace (/isis/citation/CBB313146803/)

Article Simon, Gérard; (2007)
Le problème inverse de Lévi-Strauss (/isis/citation/CBB000954363/)

Book Wisnovsky, Rob; (2001)
Aspects of Avicenna (/isis/citation/CBB000101599/)

Article Yang, Baoshan; (2004)
The Historical Transmission of Diophantine Mathematics (/isis/citation/CBB000401209/)

Authors & Contributors
Gutas, Dimitri
Stone, Abraham D.
Wisnovsky, Robert
Hasse, Dag Nikolaus
Reisman, David C.
Waldegg, Guillermina
Science and Education
Journal of Dialectics of Nature
Science in Context
Revue d'Histoire des Sciences
Studies in History and Philosophy of Science
Cambridge University Press
Oxford University Press
Markus Wiener
Vittorio Klostermann
University of California, Irvine
Philosophy of mathematics
Philosophy of science
Frege, Gottlob
Bolzano, Bernard
Descartes, René
Time Periods
19th century
20th century, early
20th century
Early modern
Ming dynasty (China, 1368-1644)
Czech Republic
United States
Great Britain

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment