David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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?
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Décio Krause & Antonio M. N. Coelho (2005). Identity, Indiscernibility, and Philosophical Claims. Axiomathes 15 (2):191-210.
John Forge (2002). Reflections on Structuralism and Scientific Explanation. Synthese 130 (1):109 - 121.
Jacob Busch (2003). What Structures Could Not Be. International Studies in the Philosophy of Science 17 (3):211 – 225.
Stewart Shapiro (2011). Epistemology of Mathematics: What Are the Questions? What Count as Answers? Philosophical Quarterly 61 (242):130-150.
Fraser MacBride (2008). Can Ante Rem Structuralism Solve the Access Problem? Philosophical Quarterly 58 (230):155-164.
Geoffrey Hellman (2001). Three Varieties of Mathematical Structuralism. Philosophia Mathematica 9 (2):184-211.
Jukka Keränen (2001). The Identity Problem for Realist Structuralism. Philosophia Mathematica 9 (3):308--30.
Hannes Leitgeb & James Ladyman (2008). Criteria of Identity and Structuralist Ontology. Philosophia Mathematica 16 (3):388-396.
Added to index2009-01-28
Total downloads63 ( #19,110 of 1,004,686 )
Recent downloads (6 months)4 ( #22,154 of 1,004,686 )
How can I increase my downloads?