Structuralism and the Notion of Dependence

Oystein Linnebo

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

The notion of dependence figures prominently in recent discussions of non-eliminative mathematical structuralism. Structuralists often argue that mathematical objects from one and the same structure depend on one another and on the structure to which they belong. Their opponents often argue that there cannot be any such dependence. I first show that the structuralists' claims about dependence are more important to their view than is generally recognized. Then I defend a compromise view concerning the dependence relations between mathematical objects, according to which the structuralists are right about some mathematical objects but wrong about others. I end with some remarks about the crucial notion of dependence.
Original languageEnglish
Pages (from-to)59-79
Number of pages21
JournalThe Philosophical Quarterly
Volume58
Issue number230
Early online date10 Sep 2007
DOIs
Publication statusPublished - Jan 2008

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Structuralism and the Notion of Dependence. / Linnebo, Oystein.

In: The Philosophical Quarterly, Vol. 58, No. 230, 01.2008, p. 59-79.

Research output: Contribution to journalArticle

Linnebo, Oystein. / Structuralism and the Notion of Dependence. In: The Philosophical Quarterly. 2008 ; Vol. 58, No. 230. pp. 59-79.
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