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Notes
Numbers in parentheses denote page numbers or sections in Friedman’s book. Numbers prefixed by “4:” denote pages in the Academy Edition of Foundations.
Newton’s kinematics is entirely implicit, and parasitic on the geometry of conics (the trajectories of the bodies he studies), and a heavily geometrized calculus, in which velocity is the local tangent to a given curve.
This sounds bizarre to modern ears: we know that addition—for elements of vector spaces, in linear algebra, and for vectors at different locations, in calculus on manifolds—is set down axiomatically, and any attempt to prove it is circular. The Enlightenment did not, and hoped to “prove” it from various premises. This raises deep issues that I cannot address here.
For instance, Friedman now makes clear that, in his initial description of the “Phaenomena”—the apparent motions of the five primary planets and Jupiter’s satellites—Newton leaves open the choice between Tycho (for whom the Earth rests) and Copernicus-Kepler (for whom it moves). This is analogous—much, though not fully—with Kant’s starting his constructive procedure (of locating the chief inertial frame) with a choice between taking the Earth to rest and taking it to move (relative to objects falling toward it).
See De Risi (2007) and fn. 4 above.
In his unpublished De Gravitatione, where Newton infers that space is not a substance, for substance is active, whereas space is dynamically inert. See Newton (2004: 21).
Friedman does not remark upon this, but here as elsewhere Kant rediscovers, unbeknownst to him, a Leibnizian theme. In the unpublished fragment “On Body and Force, against the Cartesians” (1702), Leibniz had argued that extension, far from being primitive, results in fact from the “repetition,” or “spreading out” of “resistance, diffused throughout the body” (Leibniz 1989, 250f). Kant is, of course, much more sophisticated in his account, and more modern too. A mark of his superiority over Leibniz is that he clearly distinguishes between “dynamical” resistance (to compression), the physical basis of impenetrability, and “mechanical” resistance to acceleration, the ground of inertial mass. Moreover, his account of force is closer to Newton than to Leibniz.
In Phenomenology, Kant articulates a concept of true motion. But that notion has a generalized analogue in continuum mechanics, where it is needed to constrain the range of admissible constitutive relationships between stress and strain. It is the concept of mechanical objectivity, often called “material frame indifference.” Its exact content is still being debated. For a sample, see Frewer (2009).
Modern philosophies of space–time physics focus heavily on the latter. However, in the Seventeenth century, the most heated debates concerned the former. Moreover, the early moderns—except Huygens—embedded their doctrines of space in a mixture of ontology (in modern parlance) and philosophical theology—that was “metaphysics” for them. As Friedman has shown elsewhere, Kant purges the doctrine of space of its earlier theological underpinnings.
I am not sure what Friedman’s evidence is for that thesis.
References
De Risi, V. 2007. Geometry and Monadology. Leibniz’s Analysis Situs and Philosophy of Space. Basel: Birkhäuser.
Frewer, M. 2009. More clarity on the concept of material frame-indifference in classical continuum mechanics. Acta Mechanica 202: 213–246.
Leibniz. G.W. 1989. Philosophical Essays. Trans. R. Ariew and D. Garber. Indianapolis: Hackett.
Newton, I. 2004. Philosophical Writings, ed. A. Janiak. Cambridge: Cambridge University Press.
Stan, M. 2013. Kant’s third law of mechanics: The long shadow of Leibniz. Studies in History and Philosophy of Science 44: 493–504.
Watkins, E. 1997. The laws of motion from Newton to Kant. Perspectives on Science 5: 311–348.
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Stan, M. Once more unto the breach: Kant and Newton. Metascience 23, 233–242 (2014). https://doi.org/10.1007/s11016-014-9874-y
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DOI: https://doi.org/10.1007/s11016-014-9874-y