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Structuralism and the notion of dependence

Linnebo, Øystein (2008) Structuralism and the notion of dependence. The Philosophical Quarterly 58 (230), pp. 59-79. ISSN 0031-8094.

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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.

Item Type: Article
School or Research Centre: Birkbeck Schools and Research Centres > School of Social Sciences, History and Philosophy > Philosophy
Depositing User: Administrator
Date Deposited: 08 Mar 2011 08:04
Last Modified: 17 Apr 2013 12:20

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