David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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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.
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References found in this work BETA
J. Ladyman (1998). What is Structural Realism? Studies in History and Philosophy of Science Part A 29 (3):409-424.
Kit Fine (1995). Ontological Dependence. Proceedings of the Aristotelian Society 95:269 - 290.
George Boolos (1971). The Iterative Conception of Set. Journal of Philosophy 68 (8):215-231.
J. Keranen (2001). The Identity Problem for Realist Structuralism. Philosophia Mathematica 9 (3):308--330.
Charles Parsons (1990). The Structuralist View of Mathematical Objects. Synthese 84 (3):303 - 346.
Citations of this work BETA
Alexander Skiles (2015). Essence in Abundance. Canadian Journal of Philosophy 45 (1):100-112.
Kerry McKenzie (2014). Priority and Particle Physics: Ontic Structural Realism as a Fundamentality Thesis. British Journal for the Philosophy of Science 65 (2):353-380.
Fabrice Correia (2008). Ontological Dependence. Philosophy Compass 3 (5):1013-1032.
Steven French (2010). The Interdependence of Structure, Objects and Dependence. Synthese 175 (S1):89 - 109.
Stewart Shapiro & Geoffrey Hellman (forthcoming). Frege Meets Aristotle: Points as Abstracts. Philosophia Mathematica:nkv021.
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