Structuralism and the notion of dependence

Philosophical Quarterly 58 (230):59-79 (2008)
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Abstract

This paper has two goals. The first goal is to show that the structuralists’ claims about dependence are more significant to their view than is generally recognized. I argue that these dependence claims play an essential role in the most interesting and plausible characterization of this brand of structuralism. The second goal is to defend a compromise view concerning the dependence relations that obtain between mathematical objects. Two extreme views have tended to dominate the debate, namely the view that all mathematical objects depend on the structures to which they belong and the view that none do. I present counterexamples to each of these extreme views. I defend instead a compromise view according to which the structuralists are right about many kinds of mathematical objects (roughly, the algebraic ones), whereas the anti-structuralists are right about others (in particular, the sets). I end with some remarks about how to understand the crucial notion of dependence, which despite being at the heart of the debate is rarely examined in any detail.

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2009-01-28

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Øystein Linnebo
University of Oslo

References found in this work

What is Structural Realism?James Ladyman - 1998 - Studies in History and Philosophy of Science Part A 29 (3):409-424.
XIV—Ontological Dependence.Kit Fine - 1995 - Proceedings of the Aristotelian Society 95 (1):269-290.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
Mathematics Without Foundations.Hilary Putnam - 1967 - Journal of Philosophy 64 (1):5-22.

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