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A Posteriori Deductions Dynamical Conception of Matter And, 126 Cambridge University Press 978-0-521-76618-0 - Interpreting Newton: Critical Essays Edited By Andrew Janiak and Eric Schliesser Index More information INDEX a posteriori deductions An Account of Sir Isaac Newton’s dynamical conception of matter and, Philosophical Discoveries 126–128 (MacLaurin), 300–301, 308–317 geometrical conception of matter Acta eruditorum (Leibniz), 39 and, 116–119, 134–136 action at a distance, 192–194, 347–348 aprioriassumption active force, Leibniz’s concept of, 40–41 causation and, 270–279 air resistance, laws of motion and, 171, Locke’s discussion of nature and, 366 265–266 alchemy, Newton’s interest in, 3nn7–8, spacetime theory and, 197 107–111 absolute motion d’Alembert,J.L.R.,109, 192, 195, 282, definitions of, 199 285n15, 378–379 DiSalle’s discussion of, 215–217 algebra dispositional account of mass and, as analysis, 223–224 329–331 curves expressed in, 225–226 Newton’s concept of, 196–218 Algebra (Kinckhuysen), 226 Scholium discussion of, 206–215 Analogies of Experience, Kant’s space-time theories and, development of, 355 200–206 analysis. See also theoretical analysis absolute rest influence of Principia on, 361–364, absolute motion and, 209–215 366–371 Euler’s theories on time and space Newton’s discussion of, 224–229, and, 173–175 250–253 absolute rotation, 204–206 terminology and definitions of, absolute space 221–224 Kant’s discussion of, 342–359 Analysis per Quantitatum, Series, Newton’s definition of, 200–206, Fluxiones, ac differentias cum 208–209, 211–215, 347–359 Enumeratio Linearum Tertii absolute velocities, Newtonian Ordinis (Newton), 8 space-time theory and, 202–206 Anstey, P. R., 57–58, 58n18 abstract quantity, fluxions theory and, apogee, mean motion of, 377–383 224 approximations acceleration Newton’s research and, 394n22 centripetal force and, 372–377 successive approximation, 100 force and, 163–167 area rule of Kepler, 156–158, 160–162 universal law of gravitation and, planetary bodies and, 162, 164, 162–167 179n20, 364–366 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-76618-0 - Interpreting Newton: Critical Essays Edited By Andrew Janiak and Eric Schliesser Index More information 420 index areas for curves, Cartesian Bacon, Francis, 57–59, 59n21, 62n27 co-ordinates, 220–221 Barber,K.F.,16n10, 17n11 argument for universal gravitation Barrow, Isaac, 8 (AUG). See universal gravitation composition of motion theory, Aristotle 236–239, 238n26–27, 239n29, analysis methods of, 221–226 245, 247 causation and, 85 on De Analysis, 224–229 Locke’s discussion of, 52–53 Geometrical lectures of, 236 metaphysics of, 320–321 geometrical objects defined by, model of science and mathematics, 71–77 70, 74–77, 77n17, 80, 82 justification of postulates by, 77–82 on motion, 213, 249 on mathematics as science, 70–71 teleology of, 345–346 on mechanics in geometry, 83–85 unities of form and matter of, 39 on nature and mathematics, 69–101 astronomy physical significance of mathematics influence of Principia on, 360–364, and, 96–97 393–395 on postulates as practice of natural philosophy and, 61–68, mechanics, 97–100 61n26, 65n31 Bayesian theory, models and Newton’s discussion of, 65n31, hypotheses in, 91n41 67–68 Bayle, Pierre, 310 simultaneity theory in, 368 Belkind, Ori, 6, 138–168, 210–211 atheism, 350 Bennett, Jonathan, 24–25 atomism, Newton’s discussion of, Bentley, Richard, 3, 87n32, 130n24, 29n30 285, 286n17, 291, 347–348 attraction Berkeley, George, 304–305, 308, 333 force proportional to mass, 175 Bernoulli, Johann, 40 hypotheses concerning, 139–146, Biener, Zvi, 6–7, 105–137 177–183 Blancanus, Josephus, 72n4, 75n11, Kant’s discussion of, 342, 355–356 77n17 lunar precession and, 193–194 Blay, Michel, 3n6 as matter property, 280–298 Bloch, Leon,´ 3n6 Maupertuis’s defense of, 286–298 bodies in motion motion and, 85–89, 88n34 bodies plural, Cartesian concept of, postulates of mathematical/physical 14n5 distinction, 89–91 “body in general,” Cartesian concept s’Gravesande’s defense of Newton’s of, 14–16, 14n4 theories concerning, 283–286 Boyle’s dispositional theory and, structural assumptions and, 320–326 146–156 closed systems of interacting bodies, third law of motion and, 121–124, 183–185 175–185 Descartes’s discussion of, 13–20, attraction-at-a-distance, Locke’s 16–17 concept of, 64–65 dispositional account of mass and, AUG (argument for universal 327–331 gravitation). See universal dynamical conception of matter and, gravitation 111–116 Axioms of Intuition, 353n17 Euler’s theories on time and space Ayers, Michael, 266n21, 284n14 and, 173–175 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-76618-0 - Interpreting Newton: Critical Essays Edited By Andrew Janiak and Eric Schliesser Index More information index 421 geometrical conception of matter Cambridge Companion to Newton, and, 116–119 3n9 gravity and, 128–130 Cambridge Platonism, 343, 357n25 Huygens’s rules for, 169–170, Carnap, Rudolf, 204–205 188–190 Cartesian co-ordinates Leibniz on force and, 33–41 areas for curves and, 220–221 Locke’s discussion of, 263–269 polynomial equations and, 234–236 mechanical aether principle, quadrature rules and, 226 107–111 Cassini, G. D., 191, 393n20 natural philosophy and role of, Cauchy, A.-L., 116n13 57–62, 85 causation Newtonian space-time principles deductive reasoning and, 140–146 and, 203n9 discrepancy as measurement and, Newton’s account of, 7, 13–32, 91–97 24n21 force and, 96n50 Newton’s divine phenomenalism Hume’s Newtonian ideal of, and, 335–338 269–279 Newton’s laws and force of, 42–47 Kant’s discussion of, 354–355 “problem of bodies” principle, mathematical/physical distinction 16–32 and, 85–89 proportionalities and, 130–136 mathematics and, 71–77 quantity of motion and, 151–156 Maupertuis’s discussion of, 287–288 solid bodies, Descartes’s discussion metaphysics of space and, 349–359 of, 18n12, 28–29 postulates of mathematical/physical space and, 111n9 distinction, 89–91 third law of motion and, 121–124 Cavendish, H., 194, 206n12, 363 Bonneau, Franc¸ois de (Sieur de Celestial Mechanics (Laplace), 361, Verdus), 239–241 394n23 bootstrap confirmation, laws of celestial mechanics, Newton’s influence motion and, 179n20 on, 382–383 Boscovichian point-particles, 116, 136 centrifugal force, Newtonian Boulliau, Ismael,¨ 364 space-time and, 206 Boyle, Robert centripetal force on bodies in motion, 7, 262 Area Law of Kepler and, 156–158 dispositional theory of, 320–326 Cotes’s commentaries on, 119–121 Locke and, 263 gravitation and, 142, 143n12 natural philosophy and work of, inverse-square measurements and, 49–51, 57–68, 58nn18–19, 59n21, 369–371 59n23, 60nn24–25, 62n27, 66n32 planetary bodies and, 179n20 Newtonian and Humean approaches chemistry, Newton’s legacy and history to problems of, 332–335 of, 2 Brading, Katherine, 7, 13–32 Child, J. M., 236, 238n26 Brahe, Tycho, 391 Christensen, David, 179n20 Brown, Harvey, 197 Clairaut, A. C., 192, 378–383, 391–392 bucket argument Clarke, Samuel, 109, 213, 285–286, 291 absolute vs. relative motion and, co-linearity, Newtonian space-time 207–208, 214–217 theory and, 202–206 Newtonian space-time and, 204–206 Cogitata physico mathematica Burtt, E. A., 2 (Mersenne), 240n34 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-76618-0 - Interpreting Newton: Critical Essays Edited By Andrew Janiak and Eric Schliesser Index More information 422 index Cohen, I. B. Corollary VI, 203n9, 216 on discrepancy as measurement, corpuscular hypothesis 92n42, 93n43 Boyle’s dispositional theory and, on dynamical conception of matter, 320–326 125 Newton’s concept of mass and, on force and motion theory, 326–331 44–47 Cotes, Roger, 6, 105–107 on Newton’s definitions, on attraction, 295n37, 297n41 198n2 on dynamical conception and status on Newton’s theories, 2–5 of laws, 124–128 Collins, John, 224–227, 239–240n34 on gravity as essential property, collisions 128–130, 276n29, 357n23 Huygens’s rules concerning, “invisible hand” commentaries of, 169–170, 188–190 119–130, 136–137 third law of motion concerning, Newton’s Challenge and, 307–308 146–147, 152–156, 171, on proportionalities, 130–136 178–183 third law critiqued by, 175–185 color, Boyle’s dispositional theory on third law of motion, 121–124 concerning, 320–326 critical philosophy, Kant and evolution common cause principle, of, 352–359 demonstrative induction and, Critique of Pure Reason (Kant), 144n14 300–301, 350n14 composition of motions. See rule of curves composition in De Methodis, 245, 247–251 of Barrow, 236–239 method of tangents and, 240–247 cycloids, 240–243 perihelion of Mercury and, 384–389 in De Methodis, 245, 250–253 squaring of, 225–226 ellipse and, 243, 245 Van Heuraet’s theorem and, 232, general law for, 243–248 235–236 quadratrix, composition of motion Cutting-off of a Ratio (Apollonius), for, 243, 245 222n5 speeds and, 253 cycloid, composition of motions for, spirals and, 243–245 240–243 theory of, 229 universal gravitation and, 155–156, data, evidence and, 361–364 161–162, 167–168 De Analysis per Aequationes Numero “Confesio naturae contra atheistas” Terminorum Infinitas (Newton), (Leibniz), 34 222, 224–229 conservation, of momentum, 150–151, “De Arcanis Motus et Mechanica ad 154–156, 158, 166–167 puramGeometriamreducenda” constant ratio, speeds of motions and, (Leibniz), 36n11 239n30 De Corpore (Hobbes), 34 continuum mechanics, Newtonian de Gandt, Franc¸ois, 3n6 theory and, 116 De Gravitatione et Aequipondio Copernicus, N., 361–362 Fluidorum (Newton), 4,
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