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Hamilton’s Principle and Dispositional Essentialism: Friends or Foes?

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Abstract

Most recently Smart and Thébault revived an almost forgotten debate between Katzav and Ellis on the compatibility of Hamilton’s Principle (HP) with Dispositional Essentialism (DE). Katzav’s arguments inter alia aim to show that HP (a) presupposes a kind of metaphysical contingency which is at odds with the basic tenets of DE, and (b) offers explanations of a different type and direction from those given by DE. In this paper I argue that though dispositional essentialists might adequately respond to these arguments, the question about the compatibility of HP with DE has not been answered yet; therefore, dispositional essentialists have not yet provided an illuminating DE-friendly metaphysical account of HP.

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Notes

  1. Vetter (2012) challenges the claim that laws can be derived from dispositional essences and Mumford (2004) argues for a lawless ontology in the context of which dispositional properties can play all the nomic roles.

  2. See, however, Hendry and Rowbottom (2009) for a version of DE which allows metaphysically contingent laws.

  3. In contrast to HP, PLA allows possible paths which end at different times than the actual path. By imposing certain constraints on the Hamiltonian function of the physical system (see, for example, Goldstein et al. 2000, 358), we get PLA in the form \(\Delta \int_{t1}^{t2} {p_{i } \dot{q}_{i} dt}\), where Δ stands for the corresponding variation and qi, pi are the canonical variables in phase space (generalised coordinates and conjugate momenta, respectively).

  4. Monogenic are those physical systems for which all forces (except perhaps for the forces of constraints) are derivable from scalar potentials that may be functions of the coordinates, velocities and time.

  5. There is also a modified HP which yields Hamilton’s equations of motion. This principle has the form \(\delta \int_{{t_{1} }}^{{t_{2} }} {\left( {p_{i } \dot{q}_{i} - H} \right)dt}\), where qi, pi are the canonical variables in phase space, H is the Hamiltonian function and the integral is evaluated over paths in phase space.

  6. In the quantum case, we are interested in finding the total probability amplitude for a certain process to occur. According to the path-integral formulation of quantum mechanics, this amplitude can be derived from the application of an action principle reducible (in the classical limit and under certain assumptions) to HP. In the so-called Feynman principle the classical action S is identified, up to a constant, with a phase associated with each of the alternative paths of the quantum system (Peskin and Schroeder 1995, 275–277). For technical details concerning the above-mentioned reducibility, see, for example, Basdevant (2007, 161), Duncan (2012, 88–89) and Greiner and Reinhardt (1996, 344).

  7. For instance, it is not quite clear whether HP has been the main heuristic tool for the development of the majority of physical theories. It is also controversial whether it had (and still has) a significant explanatory role in the theoretical context.

  8. A possible exception is the issue (discussed in Sect. 3) of the alternative paths required for the application of HP. In the classical realm they are clearly paths a physical system might follow but actually does not. This is not obviously the case for the paths appeared in Feynman’s action principle. According to one interpretation (Sharlow 2007), a quantum mechanically described physical system can actually follow all these paths simultaneously.

  9. I would like to thank an anonymous reviewer for pressing me on this point.

  10. This is not the only metaphysical problem associated with the modality of HP. Butterfield (2004) examines how the possible paths, when taken together with the actual one, can be truthmakers of the actual laws. I would like to thank an anonymous reviewer for bringing to my attention Butterfield’s work on the modality of variational principles in classical mechanics.

  11. The notion of metaphysical possibility is highly controversial. It is not clear whether there exists a sphere of metaphysical possibility between what is logically possible (in the sense that it does not imply a contradiction) and what is nomologically/physically possible (in the sense that is compatible with the actual nomic web). In fact, some philosophers who think that what is metaphysically possible is fixed by the natures or essences of the fundamental properties of our world also think that those natures fix the laws and, as a result, tend to identify metaphysical possibility with nomological/physical possibility. Nevertheless, an autonomous metaphysical possibility can make room for the strong intuition that laws of nature are contingent to make sense. Though I am sympathetic to the view that physical and metaphysical possibilities are distinct, I do not have to take sides on that issue here. What matters for my present purposes is just the contrast between possibilities such as the physical or metaphysical ones and epistemic possibilities which are fixed by what is known.

  12. The discussion in the sequel clearly shows that the previous points regarding the scientific explanation are not irrelevant to the metaphysical issue in question. On the contrary, I think we should be clear that metaphysicians could justifiably appeal to scientific explanations and practice to shed light on metaphysical issues (more on that in the next section).

  13. In fact, according to DE, HP is necessarily true.

  14. It might be objected that we have reasons to hold that DE can also account for laws that do not have associated specific stimuli or manifestations, such as conservation laws. Due to the a priori connection of the latter with the symmetries of dynamical laws (via Noether’s first theorem), a DE-ist might claim that she can provide an indirect ground for conservation laws by offering a direct ground for dynamical laws. The case, however, is not so clear, since the aforementioned connection is established only provided that the dynamical laws themselves are derivable from HP (see Earman 2004).

  15. I would like to thank an anonymous reviewer for insinuating such a kind of objection to the whole debate.

  16. Here the expression “physical theory” refers to both classical and quantum mechanics.

  17. The science-informed character of the present metaphysical discussion rules out the option of ignoring the issue of the compatibility of DE with at least one of the alternative formulations.

References

  • Audi, P. (2012). Grounding: Toward a theory of the in-virtue-of relation. Journal of Philosophy, 109, 685–711.

    Article  Google Scholar 

  • Basdevant, J. L. (2007). Variational principles in physics. New York: Springer.

    Google Scholar 

  • Bird, A. (2007). Nature’s metaphysics: Laws and properties. Oxford: Oxford Clarendon Press.

    Book  Google Scholar 

  • Butterfield, J. (2004). Some aspects of modality in analytical mechanics. In M. Stöltzner & P. Weingartner (Eds.), Formale Teleologie und Kausalität in der Physik. Paderborn: Mentis.

    Google Scholar 

  • Butterfield, J. (2006). Against pointillisme about mechanics. British Journal for Philosophy of Science, 57, 709–753.

    Article  Google Scholar 

  • Duncan, A. (2012). The conceptual framework of quantum field theory. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Earman, J. (2004). Laws, symmetry, and symmetry breaking: Invariance, conservation principles, and objectivity. Philosophy of Science, 71(5), 1227–1241.

    Article  Google Scholar 

  • Ellis, B. (2001). Scientific essentialism. Cambridge: Cambridge University Press.

    Google Scholar 

  • Ellis, B. (2005). Katzav on the limitations of dispositionalism. Analysis, 65, 90–92.

    Article  Google Scholar 

  • Fine, K. (2001). The question of realism. Philosophers’ Imprint, 1, 1–30.

    Google Scholar 

  • Goldstein, H., Poole, C., & Safko, J. (2000). Classical mechanics (3rd ed.). San Francisco: Addison-Wesley.

    Google Scholar 

  • Greiner, W., & Reinhardt, J. (1996). Field quantization. Berlin: Springer-Verlag.

    Book  Google Scholar 

  • Hendry, R. F., & Rowbottom, D. P. (2009). Dispositional essentialism and the necessity of laws. Analysis, 69(4), 668–677.

    Article  Google Scholar 

  • Katzav, J. (2004). Dispositions and the principle of least action. Analysis, 64, 206–214.

    Article  Google Scholar 

  • Katzav, J. (2005). Ellis on the limitations of dispositionalism. Analysis, 65, 92–94.

    Article  Google Scholar 

  • Livanios, V. (2017). Science in metaphysics: Exploring the metaphysics of properties and laws. Cham: Palgrave Macmillan-Springer Nature.

    Book  Google Scholar 

  • Mumford, S. (2004). Laws in nature. New York: Routledge.

    Book  Google Scholar 

  • Peskin, M. E., & Schroeder, D. V. (1995). An introduction to quantum field theory. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Sharlow, M. F. (2007). The quantum mechanical path integral: Toward a realistic interpretation. http://philsci-archive.pitt.edu/id/eprint/3780.

  • Smart, B., & Thébault, K. (2015). Dispositions and the principle of least action revisited. Analysis, 75(3), 386–395.

    Article  Google Scholar 

  • Vetter, B. (2012). Dispositional essentialism and the laws of nature. In A. Bird, B. Ellis, & H. Sankey (Eds.), Properties, powers and structures. New York: Routledge.

    Google Scholar 

  • Wilson, J. (2014). No work for a theory of grounding. Inquiry, 57(5–6), 1–45.

    Google Scholar 

  • Yourgrau, W., & Mandelstam, S. (1960). Variational principles in dynamics and quantum theory. New York: Pitman Publishing Corporation.

    Google Scholar 

  • Zwiebach, B. (2009). A first course in string theory (2nd ed.). Cambridge: Cambridge University Press.

    Book  Google Scholar 

Download references

Acknowledgements

Earlier versions of this paper were presented at the colloquium of the Department of Philosophy and History of Science, University of Athens (2015) and the Inaugural Conference of the East European Network for Philosophy of Science (New Bulgarian University, Sofia 2016). I would like to thank the participants for their helpful comments.

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Livanios, V. Hamilton’s Principle and Dispositional Essentialism: Friends or Foes?. J Gen Philos Sci 49, 59–71 (2018). https://doi.org/10.1007/s10838-017-9380-1

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