Structuralism and the notion of dependence

Philosophical Quarterly 58 (230):59-79 (2008)
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.
Keywords structuralism   dependence   WAYS
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    References found in this work BETA
    George Boolos (1971). The Iterative Conception of Set. Journal of Philosophy 68 (8):215-231.
    Kit Fine (1995). Ontological Dependence. Proceedings of the Aristotelian Society 95:269 - 290.

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