Two types of abstraction for structuralism

Bibliographic Data

ID4352128
AuthorsØystein Linnebo (0000-0002-3530-0295, University of Oslo), Richard Pettigrew (0000-0003-0822-4300, University of Bristol)
Year2014
Volume64
Issue255
Pages267-283
Publication date2014-04-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueThe Philosophical Quarterly (JOURNAL)
Journal identifiersISSN: 0031-8094 • E-ISSN: 1467-9213
PublisherOxford University Press (PUBLISHER • GB)
DOI10.1093/pq/pqt044
OpenAlexW2122194815
LanguageEN
Citations received10

If numbers were identified with any of their standard set-theoretic realizations, then they would have various non-arithmetical properties that mathematicians are reluctant to ascribe to them. Dedekind and later structuralists conclude that we should refrain from ascribing to numbers such ‘foreign’ properties. We first rehearse why it is hard to provide an acceptable formulation of this conclusion. Then we investigate some forms of abstraction meant to purge mathematical objects of all ‘foreign’ properties. One form is inspired by Frege; the other by Dedekind. We argue that both face problems.

Abstraction · Epistemology · Library science · Media studies · Sociology · Structuralism (philosophy of science) · Computer Science · Epistemology, Ethics, and Metaphysics · Philosophy · Philosophy and History of Science · Philosophy and Theoretical Science

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