Relationalism about mechanics based on a minimalist ontology of matter
This paper elaborates on relationalism about space and time as motivated by a minimalist ontology of the physical world: there are only matter points that are individuated by the distance relations among them, with these relations changing. We assess two strategies to combine this ontology with physics, using classical mechanics as an example. The Humean strategy adopts the standard, non-relationalist physical theories as they stand and interprets their formal apparatus as the means of bookkeeping of the change of the distance relations instead of committing us to additional elements of the ontology. The alternative theoretical strategy seeks to combine the relationalist ontology with a relationalist physical theory that reproduces the predictions of the standard theory in the domain where these are empirically tested. We show that, as things stand, this strategy cannot be accomplished without compromising a minimalist relationalist ontology.
KeywordsRelationalism Parsimony Atomism Matter points Ontic structural realism Humeanism Classical mechanics
We are grateful to Vincent Lam, Dustin Lazarovici, Andrea Oldofredi and Christian Wüthrich for helpful discussions. A. Vassallo’s work on this paper was supported by the Swiss National Science Foundation, grant no. 105212_149650, while D.-A. Deckert’s work was funded by the junior research group grant Interaction between Light and Matter of the Elite Network of Bavaria.
- Anderson, E. (2013). The problem of time and quantum cosmology in the relational particle mechanics arena. arXiv:1111.1472v3 [gr-qc].
- Anderson, E. (2015). Configuration spaces in fundamental physics. arXiv:1503.01507v2 [gr-qc].
- Ariew, R. (Ed.) (2000). G. W. Leibniz and S Clarke: correspondence. Hackett: Indianapolis.Google Scholar
- Bach, A. (1997). Indistinguishable classical particles. Berlin: Springer.Google Scholar
- Barbour, J. (2012). Shape dynamics. an introduction. In Finster, F., Müller, O., Nardmann, M., Tolksdorf, J., & Zeidler, E. (Eds.) Quantum field theory and gravity (pp. 257–297). Birkhäuser: Basel.Google Scholar
- Barbour, J., Foster, B., & Ó Murchadha, N. (2002). Relativity without relativity. Classical and Quantum Gravity, 19, 3217–3248.Google Scholar
- Barrett, J.A. (2014). Entanglement and disentanglement in relativistic quantum mechanics. Studies in History and Philosophy of Modern Physics, 48, 168–174.Google Scholar
- Belot, G. (2011). Geometric possibility. Oxford: Oxford University Press.Google Scholar
- Bhogal, H., & Perry, Z.R. (2016). What the Humean should say about entanglement. Noûs. doi: 10.1111/nous.12095.
- Blackburn, S. (1990). Filling in space. Analysis, 50, 62–65.Google Scholar
- Callender, C. (2015). One world, one beable. Synthese, 192(10), 3153–3177.Google Scholar
- Deckert, D. -A. (2010). Electrodynamic absorber theory – a mathematical study. Tönning: Der Andere Verlag.Google Scholar
- Earman, J. (1989). World enough and space-time. Absolute versus relational theories of spacetime. Cambridge, Massachusetts: MIT Press.Google Scholar
- Earman, J. (2002). Thoroughly modern mcTaggart or what mcTaggart would have said if he had read the general theory of relativity. Philosopher’s Imprint, 2(3). http://www.philosophersimprint.org/002003/.
- Esfeld, M. (2014). Quantum Humeanism, or: physicalism without properties. The Philosophical Quarterly, 64(256), 453–470.Google Scholar
- Esfeld, M., & Lam, V. (2011). Ontic structural realism as a metaphysics of objects. In A., & Bokulich, P. (Eds.) Scientific structuralism (pp. 143–159). Dordrecht: Springer.Google Scholar
- Frankel, T. (1997). The geometry of physics. Cambridge: Cambridge University Press.Google Scholar
- French, S. (2014). The structure of the world metaphysics and representation. Oxford: Oxford University Press.Google Scholar
- Gerhardt, C.I. (1890). Die philosophischen Schriften von G. W. Leibniz Band 7. Berlin: Weidmannsche Verlagsbuchhandlung.Google Scholar
- Gryb, S., & Thébault, K. P. Y. (2016). Time remains. British Journal for the Philosophy of Science. doi: 10.1093/bjps/axv009.
- Hall, N. (2009). Humean reductionism about laws of nature. Unpublished manuscript. http://philpapers.org/rec/halhra.
- Holland, P. (2001a). Hamiltonian theory of wave and particle in quantum mechanics I: Liouville’s theorem and the interpretation of the de broglie-Bohm theory. Il Nuovo Cimento B, 116, 1043–1070.Google Scholar
- Holland, P. (2001b). Hamiltonian theory of wave and particle in quantum mechanics II: Hamilton-jacobi theory and particle back-reaction. Il Nuovo Cimento B, 116, 1143–1172.Google Scholar
- Ladyman, J. (2007). On the identity and diversity of objects in a structure. Proceedings of the Aristotelian Society, Supplementary Volume, 81(1), 23–43.Google Scholar
- Ladyman, J., & Ross, D. (2007). Every thing must go: metaphysics naturalized. New York: Oxford University Press.Google Scholar
- Lanczos, C. (1970). The variational principles of mechanics. University of Toronto Press, fourth edition.Google Scholar
- Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell.Google Scholar
- Locke, J. (1690). An essay concerning human understanding.Google Scholar
- Mach, E. (1919). The science of mechanics: a critical and historical account of its development, 4th edn., Translation by Thomas J. McCormack. Chicago: Open Court.Google Scholar
- Maudlin, T. (2002). Thoroughly muddled mcTaggart or how to abuse gauge freedom to create metaphysical monstrosities. Philosopher’s Imprint, 2(4).Google Scholar
- Maudlin, T. (2007). The metaphysics within physics. New York: Oxford University Press.Google Scholar
- Miller, E. (2014). Quantum entanglement, Bohmian mechanics, and Humean supervenience. Australasian Journal of Philosophy, 92, 567–583.Google Scholar
- Misner, C.W., Thorne, K.S., & Wheeler, J.A. (1973). Gravitation. Freeman: San Francisco.Google Scholar
- Pooley, O. (2013). Substantivalist and relationalist approaches to spacetime. In Batterman, R. (Ed.) The oxford handbook of philosophy of physics (pp. 522–586). Oxford: Oxford University Press.Google Scholar
- Rovelli, C. (2004). Quantum gravity. Cambridge: Cambridge University Press.Google Scholar
- Vassallo, A. (2015). Can Bohmian mechanics be made background independent? Studies in History and Philosophy of Modern Physics, 52, 242–250.Google Scholar
- Vassallo, A., & Esfeld, M. (2016). Leibnizian relationalism for general relativistic physics. Studies in History and Philosophy of Modern Physics. doi: 10.1016/j.shpsb.2016.08.006
- Wheeler, J.A. (1962). Geometrodynamics. New York: Academic Press.Google Scholar
- Wüthrich, C. (2009). Challenging the spacetime structuralist. Philosophy of Science, 76, 1039–1051.Google Scholar