David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophia Mathematica 16 (3):285-309 (2008)
Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of the other. I suggest that i functions like a parameter in natural deduction systems. I gave an early version of this paper at a workshop on structuralism in mathematics and science, held in the Autumn of 2006, at Bristol University. Thanks to the organizers, particularly Hannes Leitgeb, James Ladyman, and Øystein Linnebo, to my commentator Richard Pettigrew, and to the audience there. The paper also benefited considerably from a preliminary session at the Arché Research Centre at the University of St Andrews. I am indebted to my colleagues Craige Roberts, for help with the linguistics literature, and Ben Caplan and Gabriel Uzquiano, for help with the metaphysics. Thanks also to Hannes Leitgeb and Jeffrey Ketland for reading an earlier version of the manuscript and making helpful suggestions. I also benefited from conversations with Richard Heck, John Mayberry, Kevin Scharp, and Jason Stanley. CiteULike Connotea Del.icio.us What's this?
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References found in this work BETA
D. M. Armstrong (1986). In Defence of Structural Universals. Australasian Journal of Philosophy 64 (1):85 – 88.
John Bigelow (1986). Towards Structural Universals. Australasian Journal of Philosophy 64 (1):94 – 96.
John P. Burgess (1999). Book Review: Stewart Shapiro. Philosophy of Mathematics: Structure and Ontology. [REVIEW] Notre Dame Journal of Formal Logic 40 (2):283-291.
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Citations of this work BETA
Peter Ainsworth (2011). Ontic Structural Realism and the Principle of the Identity of Indiscernibles. Erkenntnis 75 (1):67-84.
Julian C. Cole (2010). Mathematical Structuralism Today. Philosophy Compass 5 (8):689-699.
Luca Incurvati (2012). How to Be a Minimalist About Sets. Philosophical Studies 159 (1):69-87.
Rafael de Clercq (2012). On Some Putative Graph-Theoretic Counterexamples to the Principle of the Identity of Indiscernibles. Synthese 187 (2):661-672.
Simon Friederich (2010). Structuralism and Meta-Mathematics. Erkenntnis 73 (1):67 - 81.
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