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Category-theoretic structure and radical ontic structural realism

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Abstract

Radical ontic structural realism (ROSR) claims that structure exists independently of objects that may instantiate it. Critics of ROSR contend that this claim is conceptually incoherent, insofar as, (i) it entails there can be relations without relata, and (ii) there is a conceptual dependence between relations and relata. In this essay I suggest that (ii) is motivated by a set-theoretic formulation of structure, and that adopting a category-theoretic formulation may provide ROSR with more support. In particular, I consider how a category-theoretic formulation of structure can be developed that denies (ii), and can be made to do work in the context of formulating theories in physics.

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References

  • Ainsworth P. (2010) What is ontic structural realism? Studies in History and Philosophy of Modern Physics 41: 50–57

    Article  Google Scholar 

  • Awodey S. (2010) Category theory (2nd ed.). Oxford University Press, Oxford

    Google Scholar 

  • Baez J. (2006) Quantum quandries: A category-theoretic perspective. In: Rickles D., French S., Saatsi J. (eds) Structural foundations of quantum gravity. Clarendon Press, Oxford, pp 240–265

    Chapter  Google Scholar 

  • Bell, J. (1988). Toposes and local set theories, Dover Edition (2007).

  • Belot, G. (preprint). Background independence. http://sitemaker.umich.edu/belot/background-independence.

  • Chakravartty A. (2003) The structuralist conception of objects. Philosophy of Science 70: 867–878

    Article  Google Scholar 

  • Dorato M. (2008) Is structural spacetime realism relationism in disguise? The supererogatory nature of the substantivalism/relationism debate. In: Dieks D. (ed.) The ontology of spacetime. Elsevier Press, Amsterdam, pp 17–37

    Chapter  Google Scholar 

  • Döring A., Isham C. (2011) “What is a thing?”: Topos theory in the foundations of physics. In: Coecke R. (ed.) New structures for physics. Springer, New York, pp 753–937

    Google Scholar 

  • Earman J. (1995) Bangs, crunches, whimpers, and shrieks: Singularities and acausalities in relativistic spacetimes. Oxford University Press, New York

    Google Scholar 

  • Esfeld M., Lam V. (2008) Moderate structural realism about spacetime. Synthese 160: 27–46

    Article  Google Scholar 

  • French S. (2010) The interdependence of structure, objects and dependence. Synthese 175: 89–109

    Article  Google Scholar 

  • French S., Ladyman J. (2003) Remodeling structural realism: Quantum physics and the metaphysics of structure. Synthese 136: 31–56

    Article  Google Scholar 

  • Geroch R. (1972) Einstein algebras. Communications in Mathematical Physics 26: 271–275

    Article  Google Scholar 

  • Greaves, H. (2009). In search of spacetime structuralism. Preprint. http://users.ox.ac.uk/~mert2255.

  • Heller M., Sasin W. (1995) Structured spaces and their application to relativistic physics. Journal of Mathematical Physics 36: 3644–3662

    Article  Google Scholar 

  • Heunen C., Landsman N., Spitters B. (2009) A topos for algebraic quantum theory. Communications in Mathematical Physics 291: 63–110

    Article  Google Scholar 

  • Isham C., Butterfield J. (2000) Some possible roles for topos theory in quantum theory and quantum gravity. Foundations of Physics 30: 1707–1735

    Article  Google Scholar 

  • Jones R. (1991) Realism about what?  Philosophy of Science 58: 185–202

    Article  Google Scholar 

  • Jozsa R. (1984) Sheaf models and massless fields. International Journal of Theoretical Physics 23: 67–97

    Article  Google Scholar 

  • Kraus D. (2005) Structures and structural realism. Logic Journal of the IGPL 13: 113–126

    Article  Google Scholar 

  • Lawvere W., Shanuel S. (1997) Conceptual mathematics. Cambridge University Press, Cambridge

    Google Scholar 

  • Mac Lane S., Moerdijk I. (1992) Sheaves in geometry and logic. Springer, Berlin

    Book  Google Scholar 

  • Pedroso M. (2009) On three arguments against categorical structuralism. Synthese 170: 21–31

    Article  Google Scholar 

  • Pooley O. (2006) Points, particles, and structural realism. In: Rickles D., French S., Saatsi J. (eds) The structural foundations of quantum gravity. Clarendon Press, Oxford, pp 83–120

    Chapter  Google Scholar 

  • Stachel J. (2006) Structure, individuality, and quantum gravity. In: Rickles D., French S., Saatsi J. (eds) The structural foundations of quantum gravity. Oxford University Press, Oxford, pp 53–82

    Chapter  Google Scholar 

  • Wüthrich C. (2009) Challenging the spacetime structuralist. Philosophy of Science 76: 1039–1051

    Google Scholar 

Download references

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  1. Department of Humanities and Social Sciences, Polytechnic Institute of New York University, 6 Metrotech Center, Brooklyn, NY, 11201, USA

    Jonathan Bain

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  1. Jonathan Bain
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Correspondence to Jonathan Bain.

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Bain, J. Category-theoretic structure and radical ontic structural realism. Synthese 190, 1621–1635 (2013). https://doi.org/10.1007/s11229-011-9896-6

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  • DOI: https://doi.org/10.1007/s11229-011-9896-6

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