Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A Comment on Solari and Natiello’s Constructivist View of Newton’s Mechanics

  • 4 Accesses


The present comment on Solari and Natiello’s paper (Found. Sci. 2019) values their constructivist approach to Newtonian Mechanics. My critical point concerns only the link between the concept of force and phenomena. It will be shown that the idealised form of the law of inertia created by the authors avoids criticism of the law and that this law (idealised or not) leads to the concept of force as the cause of acceleration. This concept appears in the authors’ reconstruction as an assumption. They add that this assumption must be contrasted with experiments. Following this, I address an experiment, in which the force that is taken as the cause of acceleration, is not present in the phenomenon at stake. As it thus does not satisfy the property of locality, which any cause has to, force cannot be a cause.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4


  1. 1.

    Planck (1916), Lenard (1936), Sommerfeld (1947), Budó (1974), Hestenes (1987), Alonso and Finn (1992), Knudsen and Hjorth (1996), Young and Freedman (2004), Nolting (2005), Gerthsen (2006), Kuypers (2012), among others. Philosphers of science have also understood force as the cause of acceleration (Cartwright 1983; Wilson 2009a, b; Massin 2017).

  2. 2.

    Jammer’s historical book on force provides an overview about the criticism of concept. Among contemporary physicists, we find Hamel 1912, Ludwig 1985 and Wilczek 2004. Philosophers of science have also defended that force does not exist (Russell 1937; Nagel 1961; Ellis 1976; Bigelow et al. 1988; Hicks and Schaffer 2017).

  3. 3.

    The criticism of the law of inertia began with Neumann (1870). Some critical remarks can be found earlier (Jacobi 1996; Riemann 1876). Neumann’s proposal to solve the law of inertia problem was criticized by Mach (1872) and gave rise to the idea of an inertial reference frame (Lange 1885). Lange (1902) reported on the discussion on the law in his paper.

  4. 4.

    ‘It must be recognized that we cannot ‘‘prove’’ the principle of inertia by an experimental test, because we can never be sure that the object under test is truly free of all external interactions, such as those due to extremely massive objects at very large distances.’ (French 1971, p. 164) We find the same claim by Planck (1916), Nielsen (1935), Becker (1954), Hanson (1963), Bergmann and Schaefer (1998), Scobel et al. (2002) and Stachel (2005).

  5. 5.

    Wilson (2013) claims that the law of inertia is not ambiguous only if ‘body’ in Newton’s formulation (Newton 1999, p. 416) means ‘isolated point mass’.

  6. 6.

    Norton 2003, p. 17.

  7. 7.

    Cartwright (1983, p. 66), Wilson (2009a, pp. 535–536, b) and Massin (2017, p. 829).

  8. 8.

    Historians of science have disagreed on whether Newton’s second law is F=ma (Truesdell 1960; Pourciau 2006; Nauenberg 2012; Pisano and Capecchi 2013; Coelho 2018).

  9. 9.

    Halliday et al. 1993, p. 117.

  10. 10.

    Halliday et al. (1993), Bueche and Jerde (1995) and Serway and Jewett (2004).


  1. Alonso, M., & Finn, E. J. (1992). Physics. Wokingham: Addison-Wesley.

  2. Atwood, G. (1784). A treatise on rectilinear motion and rotation of bodies: With description of original experiments relative to the subject. Cambridge: Merril and Deighton.

  3. Becker, R. A. (1954). Introduction to theoretical mechanics. New York: McGraw-Hill.

  4. Bergmann, L., & Schaefer, C. (1998). Lehrbuch der Experimentalphysik (11th ed., Vol. I). Berlin: de Gruyter.

  5. Bigelow, J., Ellis, B., & Pargetter, R. (1988). Forces. Philosophy of Science,55, 614–630.

  6. Budó, A. (1974). Theoretische Mechanik (7th ed.). Berlin: VEB Deutscher Verlag der Wissenschaften.

  7. Bueche, F. J., & Jerde, D. (1995). Principles of physics. New York: McGraw-Hill.

  8. Cartwright, N. (1983). How the laws of physics lie?. Oxford: Oxford University Press.

  9. Coelho, R. L. (2018). On the deduction of Newton’s second law. Acta Mechanica,229, 2287–2290.

  10. Ellis, B. (1976). The existence of forces. Studies in History and Philosophy of Science,7, 171–185.

  11. French, A. P. (1971). Newtonian mechanics. New York: W. W. Norton.

  12. Gerthsen, C. (2006). Physik (22nd ed.). Berlin: Springer.

  13. Halliday, D., Resnick, R., & Walker, J. (1993). Fundamentals of physics. New York: Wiley.

  14. Hamel, G. (1912). Elementare mechanik. Leipzig: Teubner.

  15. Hanson, N. (1963). The law of inertia: A philosopher’s touchstone. Philosophy of Science,30, 107–121.

  16. Hestenes, D. (1987). New foundations for classical mechanics (republished). Dordrecht: D. Reidel.

  17. Hicks, M. T., & Schaffer, J. (2017). Derivative properties in fundamental laws. British Journal for the Philosophy of Science,68, 411–450.

  18. Jacobi, C. (1996). In H. Pulte (Ed.), Vorlesungen über analytische Mechanik Berlin 1847/48, Braunschweig, Vieweg.

  19. Knudsen, J. M., & Hjorth, P. G. (1996). Elements of Newtonian mechanics (2nd ed.). Berlin: Springer.

  20. Kuypers, F. (2012). Klassische mechanik (9th ed.). Weinheim: Wiley.

  21. Lange, L. (1885). Ueber die Wissenschaftliche Fassung des Galilei’schen Beharrungsgesetzes. Philosophische Studien,2, 266–297.

  22. Lange, L. (1902). Das inertialsystem vor dem Forum der Naturforschung. Philosophische Studien,20, 1–71.

  23. Lenard, P. (1936). Deutsche physik (Vol. 1). Muenchen: Lehmanns.

  24. Ludwig, G. (1985). Einführung in die Grundlagen der Theoretischen Physik (3rd ed., Vol. 1). Braunschweig: Vieweg.

  25. Mach, E. (1872). Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit (reprint, 1909). Lepizig: Barth.

  26. Massin, O. (2017). The composition of forces. British Journal for the Philosophy of Science,68, 805–846.

  27. Nagel, E. (1961). Structure of science: Problems in the logic of scientific explanation. New York: Harcourt, Brace & World.

  28. Nauenberg, M. (2012). Comment on Is Newton’s second law really Newton’s? By Bruce Pourciau. American Journal of Physics,80, 931–933.

  29. Neumann, C. (1870). Ueber die Principien der Galilei-Newtonschen Theorie. Leipzig: Teubner.

  30. Newton, I. (1999). The principia (I. Bernard Cohen & A. Whitman, Trans.). Berkeley, CA: University of California Press.

  31. Nielsen, J. (1935). Vorlesungen über elementare Mechanik (W. Fenchel, Trans.). Berlin: Springer.

  32. Nolting, W. (2005). Grundkurs: Theoretische Physik (7th ed., Vol. 1). Braunschweig: Vieweg.

  33. Norton, J. D. (2003). Causation as folk science. Philosophers’ Imprint,3(4), 1–22.

  34. Pisano, R., & Capecchi, D. (2013). Conceptual and mathematical structures of mechanical science between 18th and 19th centuries. Almagest,2(4), 86–121.

  35. Planck, M. (1916). Einführung in die Allgemeine Mechanik. Leipzig: S Hirzel.

  36. Pourciau, B. (2006). Newton‘s interpretation of Newton‘s second law. Archive for History of Exact Sciences,60, 157–207.

  37. Riemann, B. (1876). Bernhard Riemann’s gesammelte mathematische Werke und wissenschaftlicher Nachlass. Unter Mitwirkung von R. Dedekind hg. von H. Weber. Leipzig: Teubner.

  38. Russell, B. (1937). Principles of mathematics (2nd ed.). London: Allen & Unwin.

  39. Scobel, W., Lindström, G., & Langkau, R. (2002). Mechanik, Fluiddynamik und Wärmelehre (2nd ed.). Berlin: Springer.

  40. Serway, R., & Jewett, J. W. (2004). Physics for scientists and engineers (6th ed.). Belmont, CA: Thomson.

  41. Solari, H. G., & Natiello, M. A. (2019). A constructivista view of Newton’s mechanics. Foundations of Science,24, 307–341.

  42. Sommerfeld, A. (1947). Vorlesungen über Theoretische Physik (3rd ed., Vol. I). Leipzig: Geest & Portig.

  43. Stachel, J. (2005). Development of the concepts of space, time and space-time from Newton to Einstein. In A. Ashtekar (Ed.), 100 years of relativity/space-time structure: Einstein and beyond (pp. 3–36). Singapore: World Scientific.

  44. Truesdell, C. (1960). A program toward rediscovering the rational mechanics of the age of reason. Archive for History of Exact Sciences,1, 3–36.

  45. Wilczek, F. (2004). Whence the force of F = ma? I: Culture shock. Physics Today,57, 11–12.

  46. Wilson, A. (2009a). Dispositions-manifestations and reference-frames. Dialectica,63, 591–601.

  47. Wilson, J. (2009b). The causal argument against component forces. Dialectica,63, 525–554.

  48. Wilson, M. (2013). What is ‘classical mechanics’ anyway? In R. Batterman (Ed.), The Oxford handbook of philosophy of physics (pp. 43–106). Oxford: Oxford University Press.

  49. Young, H., & Freedman, R. (2004). Sears and Zemansky’s University physics (11th ed.). San Francisco: P. Addison-Wesley.

Download references

Author information

Correspondence to R. Lopes Coelho.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lopes Coelho, R. A Comment on Solari and Natiello’s Constructivist View of Newton’s Mechanics. Found Sci (2020).

Download citation


  • Law of inertia
  • Force
  • Cause
  • Foundations of mechanics