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On some putative graph-theoretic counterexamples to the Principle of the Identity of Indiscernibles

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Abstract

Recently, several authors have claimed to have found graph-theoretic counterexamples to the Principle of the Identity of Indiscernibles (PII). In this paper, I argue that their counterexamples presuppose a certain view of what unlabeled graphs are, and that this view is optional at best.

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References

  • Black M. (1952) The identity of indiscernibles. Mind 61: 153–164

    Article  Google Scholar 

  • Buhrman H., Li M., Tromp J., Vitànyi P. (1999) Kolmogorov random graphs and the incompressability method. SIAM Journal on Computing 29: 590–599

    Article  Google Scholar 

  • Burgess J. (1999) Review of Shapiro (1997) Philosophy of mathematics: Structure and ontology. Notre Dame Journal of Formal Logic 40: 283–291

    Article  Google Scholar 

  • Button T. (2006) Realistic structuralism’s identity crisis: A hybrid solution. Analysis 66: 216–222

    Article  Google Scholar 

  • Chartrand G., Lesniak L. (2004) Graphs and digraphs (4th ed.). CRC Press, London

    Google Scholar 

  • French S., Redhead M. (1988) Quantum physics and the identity of indiscernibles. British Journal for the Philosophy of Science 39: 233–246

    Article  Google Scholar 

  • Fulling S. A., Borosh I., da Conturbia A. (1998) Cataloguing general graphs by point and line spectra. Computer Physics Communications 115: 93–112

    Article  Google Scholar 

  • Hawley K. (2006) Weak discernibility. Analysis 66: 303–315

    Google Scholar 

  • Hawley K. (2009) Identity and indiscernibility. Mind 118: 101–119

    Article  Google Scholar 

  • Janson, S. (1994). Orthogonal decompositions and functional limit theorems for random graph statistics. Memoirs of the American Mathematical Society, Vol. 111. Providence, RI: American Mathematical Society.

  • Keränen J. (2001) The identity problem for realist structuralism. Philosophia Mathematica 9: 308–390

    Article  Google Scholar 

  • Ladyman J. (2005) Mathematical structuralism and the identity of indiscernibles. Analysis 64: 218–221

    Article  Google Scholar 

  • Ladyman J. (2007) On the identity and diversity of objects in a structure. Proceedings of the Aristotelian Society, Supplementary Volume LXXXI: 23–43

    Article  Google Scholar 

  • Leitgeb H., Ladyman J. (2008) Criteria of identity and structuralist ontology. Philosophia Mathematica 16: 388–396

    Article  Google Scholar 

  • Lowe E. J. (1999) Objects and criteria of identity. In: Hale B., Wright C. (eds) A companion to the philosophy of language. Blackwell, Oxford

    Google Scholar 

  • McDiarmid C. (2008) Random graphs on surfaces. Journal of Combinatorial Theory Series B 98: 778–797

    Article  Google Scholar 

  • Muller F. A., Saunders S. W. (2008) Discerning fermions. British Journal for the Philosophy of Science 59: 499–548

    Article  Google Scholar 

  • Parsons C. (2004) Structuralism and metaphysics. Philosophical Quarterly 54: 56–77

    Article  Google Scholar 

  • Quine W. V. O. (1976) Grades of discriminability. Journal of Philosophy 73: 113–116

    Article  Google Scholar 

  • Resnik M. (1997) Mathematics as a science of patterns. Clarendon Press, Oxford

    Google Scholar 

  • Robinson R. W., Walsh T. R. (1993) Inversion of cycle index sum relations for 2- and 3- connected graphs. Journal of Combinatorial Theory, Series B 57: 289–308

    Article  Google Scholar 

  • Saunders S. (2003a) Indiscernibles, general covariance, and other symmetries. In: Ashtekar A., Howard D., Renn J., Sarkar S., Shimony A. (eds) Revisiting the foundations of relativistic physics: Festschrift in honour of John Stachel. Kluwer, Dordrecht

    Google Scholar 

  • Saunders S. (2003b) Physics and Leibniz’s principles. In: Brading K., Castellani E. (eds) Symmetries in physics: Philosophical reflections. Cambridge University Press, Cambridge

    Google Scholar 

  • Saunders S. (2006) Are quantum particles objects?. Analysis 66: 52–63

    Article  Google Scholar 

  • Shapiro S. (1997) Philosophy of mathematics: Structure and ontology. Oxford University Press, Oxford

    Google Scholar 

  • Shapiro S. (2008) Identity, indiscernibility, and ante rem structuralism: The tale of i and −i. Philosophia Mathematica 16: 285–309

    Article  Google Scholar 

  • Strawson P. F. (1959) Individuals. Methuen, London

    Book  Google Scholar 

  • Tutte W. T. (1984) Graph Theory. Addison-Wesley, Menlo Park, CA Current edition published by Cambridge University Press

    Google Scholar 

  • van Fraassen B. (2007) Structuralism(s) about Science: Some common problems. Proceedings of the Aristotelian Society, Supplementary Volume LXXXI: 45–61

    Article  Google Scholar 

  • West D. B. (2001) Introduction to graph theory (2nd ed.). Prentice Hall, Upper Saddle River, NJ

    Google Scholar 

  • Wiggins D. (2001) Sameness and substance renewed. Cambridge University Press, Cambridge

    Book  Google Scholar 

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Correspondence to Rafael De Clercq.

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De Clercq, R. On some putative graph-theoretic counterexamples to the Principle of the Identity of Indiscernibles. Synthese 187, 661–672 (2012). https://doi.org/10.1007/s11229-010-9867-3

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  • DOI: https://doi.org/10.1007/s11229-010-9867-3

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