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A puzzle about rates of change

  • David Builes
  • Trevor TeitelEmail author
Article

Abstract

Most of our best scientific descriptions of the world employ rates of change of some continuous quantity with respect to some other continuous quantity. For instance, in classical physics we arrive at a particle’s velocity by taking the time-derivative of its position, and we arrive at a particle’s acceleration by taking the time-derivative of its velocity. Because rates of change are defined in terms of other continuous quantities, most think that facts about some rate of change obtain in virtue of facts about those other continuous quantities. For example, on this view facts about a particle’s velocity at a time obtain in virtue of facts about how that particle’s position is changing at that time. In this paper we raise a puzzle for this orthodox reductionist account of rate of change quantities and evaluate some possible replies. We don’t decisively come down in favour of one reply over the others, though we say some things to support taking our puzzle to cast doubt on the standard view that spacetime is continuous.

Keywords

Rates of change Motion Spacetime Gunk Instantaneous velocity Grounding At-at Truthmaking 

Notes

Acknowledgements

For helpful comments and discussion, we’d like to thank David Albert, Cian Dorr, Daniel Hoek, Boris Kment, Tim Maudlin, Miriam Schoenfield, Bradford Skow, Jack Spencer, Stephen Yablo, and two anonymous referees.

References

  1. Arntzenius, F. (2000). Are there really instantaneous velocities? The Monist, 83(2), 187–208.CrossRefGoogle Scholar
  2. Arntzenius, F. (2003). Is quantum mechanics pointless? Philosophy of Science, 70(5), 1447–1457.CrossRefGoogle Scholar
  3. Arntzenius, F. (2008). Gunk, topology and measure. In D. Zimmerman (Ed.), Oxford studies in metaphysics (Vol. 4). Oxford: Oxford University Press.Google Scholar
  4. Arntzenius, F. (2012). Space, time, & stuff. Oxford: Oxford University Press.CrossRefGoogle Scholar
  5. Arntzenius, F., & Hawthorne, J. (2005). Gunk and continuous variation. The Monist, 88, 441–465.CrossRefGoogle Scholar
  6. Barnes, E. (2010). Arguments against metaphysical indeterminacy and vagueness. Philosophy Compass, 5(11), 953–964.CrossRefGoogle Scholar
  7. Barnes, E., Robert, J., & Williams, G. (2011). A theory of metaphysical indeterminacy. In K. Bennett & D. W. Zimmerman (Eds.), Oxford studies in metaphysics (Vol. 6, pp. 103–148). Oxford: Oxford University Press.CrossRefGoogle Scholar
  8. Builes, D. (Manuscript). Derivatives and consciousness.Google Scholar
  9. Carroll, J. (2002). Instantaneous motion. Philosophical Studies, 110, 49–67.CrossRefGoogle Scholar
  10. Correia, F., & Schnieder, B. (2012). Metaphysical grounding: Understanding the structure of reality. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  11. Daly, C. (2012). Scepticism about grounding. In F. Correia & B. Schnieder (Eds.), Metaphysical grounding: Understanding the structure of reaLITY (Vol. 81). Cambridge: Cambridge University Press.Google Scholar
  12. Dasgupta, S. (2014). On the plurality of grounds. Philosophers’ Imprint, 14, 1–28.Google Scholar
  13. Easwaran, K. (2014). Why physics uses second derivatives. British Journal for the Philosophy of Science, 65(4), 845–862.CrossRefGoogle Scholar
  14. Field, H. (1980). Science without numbers. Princeton: Princeton University Press.Google Scholar
  15. Fine, K. (2012). Guide to ground. In F. Correia & B. Schnieder (Eds.), Metaphysical grounding (pp. 37–80). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  16. Forrest, P. (2004). Grit or gunk. The Monist, 87(3), 351–370.CrossRefGoogle Scholar
  17. Hofweber, T. (2009). Ambitious, yet modest, metaphysics. In D. J. Chalmers, D. Manley, & R. Wasserman (Eds.), Metametaphysics: New essays on the foundations of ontology (pp. 260–289). Oxford: Oxford University Press.Google Scholar
  18. Huggett, N., & Wüthrich, C. (2013). Emergent spacetime and empirical (in)coherence. Studies in History and Philosophy of Modern Physics, 44(3), 276–285.CrossRefGoogle Scholar
  19. Koslicki, K. (2015). The coarse-grainedness of grounding. Oxford Studies in Metaphysics, 9, 306–344.CrossRefGoogle Scholar
  20. Lange, M. (2005). How can instantaneous velocity fulfill its causal role? Philosophical Review, 114(4), 433–468.CrossRefGoogle Scholar
  21. Lewis, D. (1986). On the plurality of worlds. New York: Wiley-Blackwell.Google Scholar
  22. Miller, K., & Norton, J. (2017). Grounding: it’s (probably) all in the head. Philosophical Studies, 174, 3059–3081.CrossRefGoogle Scholar
  23. Raven, M. J. (2013). Is ground a strict partial order? American Philosophical Quarterly, 50(2), 191–199.Google Scholar
  24. Rosen, G. (2010). Metaphysical dependence: Grounding and reduction. In B. Hale & A. Hoffmann (Eds.), Modality: Metaphysics, logic, and epistemology (pp. 109–136). Oxford: Oxford University Press.CrossRefGoogle Scholar
  25. Rovelli, C. (2001). Quantum spacetime: What do we know? In C. Callender & N. Huggett (Eds.), Physics meets philosophy at the Planck scale (pp. 101–122). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  26. Russell, B. (1937). Principles of mathematics (2d ed.). London: G. Allen & Unwin.Google Scholar
  27. Russell, J. S. (2008). The structure of gunk: Adventures in the ontology of space. In D. Zimmerman (Ed.), Oxford studies in metaphysics (Vol. 4, pp. 248–274). Oxford: Oxford University Press.Google Scholar
  28. Schaffer, J. (2009). On what grounds what. In D. Manley, D. J. Chalmers, & R. Wasserman (Eds.), Metametaphysics new essays on the foundations of ontology (pp. 347–383). Oxford: Oxford University Press.Google Scholar
  29. Schaffer, J. (2012). Grounding, transitivity, and contrastivity. In F. Correia & B. Schnieder (Eds.), Metaphysical grounding: Understanding the structure of reality (pp. 122–138). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  30. Segal, A. (2017). A puzzle about points. Philosophical Perspectives, 30(1), 349–365.CrossRefGoogle Scholar
  31. Sider, T. (2011). Writing the book of the world. Oxford: Oxford University Press.CrossRefGoogle Scholar
  32. Tooley, M. (1988). In defense of the existence of states of motion. Philosophical Topics, 16, 225–254.CrossRefGoogle Scholar
  33. Wilson, J. (2013). A determinable-based account of metaphysical indeterminacy. Inquiry: An Interdisciplinary Journal of Philosophy, 56(4), 359–385.CrossRefGoogle Scholar
  34. Wilson, J. (2014). No work for a theory of grounding. Inquiry: An Interdisciplinary Journal of Philosophy, 57(5–6), 535–579.CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.New York UniversityNew YorkUSA

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