Structuralism and the notion of dependence

Philosophical Quarterly 58 (230):59-79 (2008)
Øystein Linnebo
University of Oslo
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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DOI 10.1111/j.1467-9213.2007.529.x
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References found in this work BETA

What is Structural Realism?James Ladyman - 1998 - Studies in History and Philosophy of Science Part A 29 (3):409-424.
Ontological Dependence.Kit Fine - 1994 - Proceedings of the Aristotelian Society 95:269 - 290.
The Identity Problem for Realist Structuralism.J. Keranen - 2001 - Philosophia Mathematica 9 (3):308--330.

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Citations of this work BETA

Ontological Dependence.Fabrice Correia - 2008 - Philosophy Compass 3 (5):1013-1032.
Essence in Abundance.Alexander Skiles - 2015 - Canadian Journal of Philosophy 45 (1):100-112.
Priority and Particle Physics: Ontic Structural Realism as a Fundamentality Thesis.Kerry McKenzie - 2014 - British Journal for the Philosophy of Science 65 (2):353-380.

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