Kant on Newton, genius, and scientific discovery

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Acknowledgements

I would like to thank Bernd Buldt, Sorin Costreie, Robert Hanna, Dana Jalobeanu, Walter Ott, Bill Rumsey, and George E. Smith for their questions and comments on this paper. Thanks also to the anonymous readers at this journal whose comments were of great value in revising this paper for publication.

Notes

1. Kant, Critique of Judgment, 5:317. All citations to Kant's work use the Akademie-edition pagination from Kants Gesammelte Schriften except for those referring to the Critique of Pure Reason for which I use the standard A/B edition pagination.

2. See Kant, Critique of Judgment, 5:311. It is important to note that Kant did not always deny that Newton was a scientific genius. In the 1770s through much of the 1780s, the main criterion for genius seems to be a talent or ability to invent, which both artists as well as scientists share. In Reflection 778, written between 1772 and 1773, Kant suggests that Newton's discovery of the law of universal gravitation exhibited inventiveness and should count as an example of scientific genius notwithstanding the fact that he “imitated the fall of the apple” (15:340). In Reflection 812, written between 1769 and 1778, Kant claims that “in mathematics genius actually reveals itself in the invention of methods” (15:362). Likewise, in Reflection 1510, written between 1780 and 1784, Kant again suggests that Newton should count as a genius insofar as he invented a “new way” for science (15:826–827). As we shall see, these last two reflections are wholly consistent with my description of how Newton's mathematical natural philosophy exhibits genius. For more on Kant's early theory of genius and its relation to science, see Tonelli, “Kant's Early Theory” and Giordanetti, “Das Verhältnis von Genie.” The above naturally raises the question of why Kant changed his mind with respect to the possibility of scientific genius by the time he published Critique of Judgment in 1790. One view is that Kant's rejection of scientific genius stemmed from his growing dissatisfaction with the Sturm und Drang movement in Germany and, in particular, with one of its main figures, Johann Herder. Under this view, Kant saw Herder as trying to supplant the natural scientist with the artistic genius within the scientist's own domain. As one of the principal defenders of enlightenment thinking, it is not surprising that Kant would strongly disagree with Herder's view. This led Kant to hold that the domain of genius and science cannot overlap. If I am right, however, Kant's response to Herder was ultimately an overreaction. For more on this view, see Zammito, Kant's Critique of Judgment, 136–142. Another suggestion is that Kant was responding to Alexander Gerard's view that both scientists and artists can be geniuses insofar as they discover (scientist) or create (artist) things that will be universally accepted and appreciated. Kant's view on artistic appreciation, however, is far more complicated, and he discusses distinct ways in which a product of artistic genius might be received. I will argue below, however, that the reception of Newton's new approach toward argumentation in natural philosophy was equally complex. For more on this view, see Guyer, “Exemplary Originality.” Regardless of why Kant changed his mind on the possibility of scientific genius in Critique of Judgment, it should be noted that he again suggests in his 1798 Anthropology that both scientists and philosophers can be geniuses citing Newton and Leibniz as examples (7:226). This paper, however, will focus primarily on Kant's view in Critique of Judgment.

3. Kant, Critique of Judgment, 5:308.

4. Newton, Principia, 943.

5. Larry Laudan calls this the “generativist” approach toward scientific discovery and distinguishes it from the “consequentialist” approach which is hypothetico-deductive. While the former strategy is well-suited to discovering empirical laws that describe observable phenomena, Laudan argues that the latter strategy is well-suited for discovering the unobservable mechanisms that explain the observable phenomena that the empirical laws describe. See Laudan, “Logic of Discovery.”

6. Kant, Critique of Judgment, 5:307–8.

7. Ibid., 5:309.

8. Jeremy Proulx notes that these are the three “basic ways” that Kant defines genius. See Proulx, “Nature, Judgment and Art.”

9. Both philosophers of science and scientists themselves have, at times, appealed to creative insight when describing scientific discovery. As an example of the former, Karl Popper thinks that new ideas in science can only be described as the result of “creative intuition.” See Popper, Logic of Scientific Discovery, 32. As an example of the latter, August Kekulé claimed that a day-dream of Ouroboros inspired him in his discovery of the ring shape of the benzene molecule. See Kekulé, “Benzolfest: Rede.” Joke Meheus and Thomas Nickles suggest, however, that anecdotes like this are little more than hubris, scientists who fancy themselves romantic geniuses. In contrast to the above thinkers, they argue that scientific discovery is amenable to rational reconstruction. See Meheus and Nickles, “Creativity and Discovery,” 234. Although I agree with Meheus and Nickles that scientific discovery is amenable to rational reconstruction, in some cases, creativity will nonetheless play an indispensible role.

10. Kant, Critique of Judgment, 5:305

11. Ibid., 5:307.

12. Ibid., 5:310.

13. Ibid., 5:314–315.

14. Ibid., 5:316.

15. Allison, Kant's Theory of Taste, 286.

16. Kant, Critique of Judgment, 5:319.

17. Ibid.

18. Ibid., 5:320.

19. Ibid., 5:308.

20. Ibid., 5:318

21. Ibid.

22. Ibid.

23. Ibid.

24. Could a product of genius be exemplary without actually having any influence on others? One might think a product is exemplary as long as it adequately expresses an aesthetic idea regardless of its impact on others. As noted above, if a product adequately expresses an aesthetic idea, this seems sufficient for it to avoid being “nothing but nonsense.” Since Kant adds the second criterion in order to preclude to possibility of “original nonsense” counting as the product of genius, based on what he has already said, maybe he only means that the product adequately expresses an aesthetic idea. Although I believe something has to adequately express an aesthetic idea in order to be a product of genius, adequately expressing an aesthetic idea is not sufficient for the product to be exemplary. That exemplarity requires an influence on others is made clear both by Kant's elucidation of exemplary originality in terms of its influence on another genius (Kant, Critique of Judgment, 5:318) as well as his earlier claim that the products of genius must serve as models for others in order to be exemplary (Kant, Critique of Judgment, 5:308). As we will see below, an interesting consequence of this view is that a lack of influence can prevent an individual from counting as a genius by Kant's lights.

25. To give a (pseudo) scientific example, a sixteenth-century miller hypothesized that matter was ultimately constituted of a primordial cheese. Although the miller's speculations were extremely original, they were equally nonsensical. Even though the miller did not inspire a new school of cheese-based microphysical investigation (rather only persecution and ultimately execution at the hands of the Inquisition), as I will argue, Newton's logic of discovery served as an example for generations of natural philosophers after Newton including Kant himself. See Ginzburg, Cheese and the Worms.

26. Kant, Critique of Judgment, 5:317.

27. Ibid., 5:318.

28. Ibid., 5:304.

29. Ibid., 5:305.

30. See Kant, Lectures on Logic, 24:748. Immediately before his discussion of proof, Kant holds that one must “carefully distinguish between art and science” (ibid., 24:747). Immediately after his discussion of proof, he mentions the “bon mot (but is not always true)” of “aesthetic demonstration” (ibid., 24:749). Likewise, in Critique of Judgment, Kant says if one were to ask the practitioner of a science of the beautiful for “grounds or proofs,” one “would be sent packing with tasteful expressions (bons mots).” See Kant, Critique of Judgment, 5:305. Although Kant is clearly concerned with distinguishing art from science in this section of the Dohna-Wundlacken Logic, it is an ongoing concern by no means unique to these logic lectures (see, e.g., Kant, Lectures on Logic, 24:116, 747–749, and 811–812).

31. Kant, Critique of Judgment, 5:300.

32. Although Kant does talk about other kinds of proof in Critique of Judgment, proofs based on “rational inference” (or syllogism) are the only “logically correct” form of proof (Kant, Critique of Judgment 5:463).

33. William Harper notes that Newtonian “deduction” is not limited to logically valid inference, but describes “any appropriately warranted conclusion inferred from phenomena as available evidence” which can include induction. In my discussion below, I attempt to remain sensitive to how Newton incorporates induction into what is otherwise a logically deductive argumentative structure. See Harper, Isaac Newton's Scientific Method, 44.

34. For Proposition 7, see Newton, Principia, 810.

35. See Newton, Principia, 414–415. Michael Friedman makes this observation. See Friedman, Exact Sciences, 141

36. For Proposition 12, see Newton, Principia, 816. For Proposition 8 and its corollaries, see ibid., 811–815. Both Harper and Steffen Ducheyne take Newton's argument in Proposition 8 of Book III to be decisive in establishing his conclusion in Proposition 12. See Harper, “Newton's Argument,” 193 and Ducheyne, “Argument(s) for Universal Gravitation,” 440–441.

37. George E. Smith describes Newton's strategy this way using language first coined by Arthur Prior. See Smith, “Methodology of the Principia,” 143.

38. For the list of phenomena that Newton utilizes in his Book III arguments, see Newton, Principia, 797–801. I am taking this specific definition of “phenomena” from Harper, Isaac Newton's Scientific Method, 50.

39. In addition to these mathematical conditionals, Newton often invokes his laws of motion and his Rules of Reasoning in Philosophy within the context of his arguments in Book III. These should also be considered important components of his rule-governed argumentative procedure. For example, Newton's third law of motion (to any action there is always an equal and opposite reaction) plays an important role in his arguments for Propositions 5 and 7 of Book III. See Newton, Principia, 806 and 811. For the Rules of Reasoning, see ibid., 794–795. Below I will return to the role the Rules of Reasoning play in Newton's arguments.

40. The law of areas holds that a line between an orbiting body and its primary body sweeps out equal areas in equal times. For Propositions 2 and 3 of Book I, see Newton, Principia, 444–448.

41. The harmonic law holds that the periodic time of an orbiting body is as 3/2 power of its distance from the center of the primary body. For Corollary 6 of Proposition 4 of Book I, see Newton, Principia, 451.

42. Newton draws the same conclusion for Saturn's moons at the end of his argument for Proposition 1 using Phenomenon 2.

43. Newton, Principia, 943.

44. See ibid., 805–806. Although I am restating the second rule here instead of both the first and the second rules, Harper views the second rule (same effects same causes) simply as an implication of the first rule which cautions against the unnecessary multiplication of causes. See Harper, “Newton's Argument,” 183.

45. Newton, Principia, 796.

46. See Harper, Isaac Newton's Scientific Method, 36–37.

47. Newton, Principia, 589. Here, I am following Smith, “Newton's Principia Changed Physics.” Harper endorses Smith's approach. See Harper, Isaac Newton's Scientific Method, 45–47.

48. For example, the law of universal gravitation should be taken to hold exactly only when (1) there is some configuration of the parts of a body such that the macroscopic forces constructed from the forces of these parts would conform to the law exactly, and (2) there are identifiable circumstances in which the phenomena from which the law was inferred would hold exactly. See Smith, “Newton's Principia Changed Physics,” 374. To put Newton's approach in Kant's terms, holding a proposition as if it were exact is to employ the proposition in a regulative context. What is interesting, however, is that Newton believes the proposition can be held as if it were exact only if there is a situation where it would in fact hold exactly. In Kant's terms, the proposition can be deployed in a regulative context only if there is a situation where the proposition would hold constitutively. For Kant's version of the distinction, see Kant, Critique of Pure Reason, A671–673/B699–701.

49. These phenomena are second-order since they “presuppose specific theory, and they cease to have any meaning – they cease to exist – without that theory” (Smith, “Newton's Principia Changed Physics,” 377). Newton himself deploys this research strategy when trying to explain the non-Keplerian motion of the Moon. See Newton, Principia, 832–874.

50. Newton, Unpublished Scientific Papers, 281. This quote is from an expanded version of De Motu that did not become public until 1893.

51. Newton, Principia, 401. Emphasis is mine.

52. Pierre Duhem (and others) point out that there can be no deduction from consistent premises when what is deduced entails that one of these premises is false. In the case of Newton's argument for the law of universal gravitation, however, the application of the law to multi-body gravitational scenarios entails that Kepler's laws of motion are strictly speaking false. See Duhem, Structure of Physical Theory, 190–195. Smith notes that the approximate nature of Newton's inferences undercuts this objection since neither the premises nor the conclusions of his argument hold exactly, but only approximately. In a very important way, the approximate nature of Newton's reasoning is what keeps his argument from undermining itself. See Smith, “Newton's Principia Changed Physics,” 373.

53. See Smith, “Methodology of the Principia,” 160, and Friedman, Exact Sciences, 148 n19.

54. Newton, Principia, 795. For Newton's argument for Proposition 6 of Book III, see ibid., 806–810.

55. Harper, Isaac Newton's Scientific Method, 38. In my discussion of Proposition 6, I am following Harper.

56. For example, his pendulum experiments establish that the weights of different materials falling from equal distances in equal times are proportional to their masses, i.e., that the ratio of weight to mass of these different materials is the same. He then appeals to his moon-test, first introduced in Proposition 4, to establish the same ratio. I will return to the moon-test again below.

57. For Christian Huygens's canonical definition of the hypothetico-deductive approach from the Treatise on Light, see Matthews, Scientific Background, 126–127.

58. Harper makes this point. See Harper, “Newton's Argument,” 176–177 and Harper, Isaac Newton's Scientific Method, 43. It is also important to note that Newton's inferences (in these cases) rely upon modus ponens whereas hypothetico-deductive inferences do not.

59. Here I am following Smith's discussion of the differences between Newton's approach and Galileo's and Huygens's approaches. See Smith, “Methodology of the Principia,” 143.

60. See Newton, Principia, 803–805. From this hypothesis, we can deduce that the rate at which the Moon would fall to the Earth because the inverse-square force would agree with the rate at which heavy bodies actually do fall to Earth due to the force of gravity (15 and 1/12 Paris Feet per second). The key to this part of the argument comes with Newton's appeal to the first and second Rules of Reasoning in Philosophy (Principia, 794–795). Since we already know the force of gravity explains the fall of heavy bodies toward the Earth and the effect of the inverse-square force on the Moon is the same as the effect of gravity on heavy bodies, we can infer that this inverse-square force is itself the force of gravity. We can use this insight to identify the forces that maintain the Moon in its orbit around the Earth in Proposition 3 with the force of gravity in Proposition 4 of Book III.

61. Harper notes three ways in which Newton's approach is superior to the hypothetico-deductive model: (1) Newton has a richer conception of “empirical success” (as defined above). (2) Theory-mediated measurements provide empirical answers to theoretical problems. In the case of Proposition 6, the measurement is theory-mediated (i.e., assumes Newtonian theory for the purposes of measurement). Consequently, the converging measurements provide strong evidence for the theory. (3) Newton accepts theoretical propositions as guides to further research. This is an advantage that Newton's approach has over both inductive and hypothetico-deductive approaches. See Harper, Isaac Newton's Scientific Method, 43 and 375.

62. Jon Dorling goes so far as to claim that “nearly all theoretical advances in physics since Newton have depended partly or wholly on the use of arguments of this general form.” See Dorling, “Reasoning from the Phenomena,” 197. Although I only discuss a subset, Smith enumerates nine ways in which Newton's approach in the Principia fundamentally changed physics. See Smith, “Newton's Principia Changed Physics.”

63. See Smith, “Newton's Principia Changed,” 378–379, and Harper, Isaac Newton's Scientific Method, 191–193.

64. See Smith, “Newton's Principia Changed Physics,” 385–386. As Harper notes, not all of Newton's theory has been superseded. Newtonian calculations in applications of General Relativity to solar system motions have not yet been replaced by calculations carried out in the framework of Einstein's theory. See Harper, Isaac Newton's Scientific Method, 392–393.

65. As Smith and Harper note, Einstein's discovery of how to account for the additional 43 arc-seconds per century of Mercury's precession requires recovering the Newtonian limit (i.e., the 531 arc-seconds that Newton's theory already explained). For Smith, this means that Einstein's theory cannot undermine the evidence that supports Newton's theory (generated by his logic of discovery) otherwise “the specific value of 43 arc-seconds would be nothing but an artifact of an illusion.” See Smith, “Newton's Principia Changed Physics,” 385. For Harper, Einstein's theory does not undermine Newton's standard for empirical success (articulated by his logic of discovery), but rather does better than Newton's own theory by this standard. Harper thinks it is important that Einstein's discovery required no “question begging appeal to new standards.” See Harper, Isaac Newton's Scientific Method, 382. He goes on to show how modern advances in cosmology continue to reflect Newton's approach toward argumentation in natural philosophy. All of this provides strong support for the idea that scientists continue to employ Newton's logic of discovery up to the present day.

66. Kant, Metaphysical Foundations, 4:554–565. Friedman makes this observation. See Friedman, Exact Sciences, 141–152.

67. In the case of rectilinear motion, we can either view a body as moving relative to a space or the space moving relative to the body at rest. Since either description is consistent with the appearance, these are merely possible motions. In the second stage of the argument, Kant attempts to derive actual motions from relative motions using antecedently established laws of motion in conjunction with the appearance of circular motion. Finally, Kant uses the equality of action and reaction (third law of motion) to establish that for the actual motion of one body with respect to another it is necessary that there be an actual motion of the second body with respect to the first.

68. In this respect, one might contrast Newton's discovery of a new approach toward argumentation in natural philosophy with his discovery of the calculus which did not have the impact on future generations that Leibniz's version of the calculus had. Although both versions were developed independently and were underdetermined by earlier mathematical methods, Leibniz published before Newton (though Newton had made the discovery before Leibniz). For more on the history of the calculus, see Hall, Philosophers at War.

69. Before his discussion of genius, Kant mentions how ancient mathematicians' methods of proof correctly serve as examples to others insofar as others succeed and not imitate the ancients in the development of their own methods. The ancient methods “put others on the right path for seeking out the principles in themselves and thus for following their own often better course” (Kant, Critique of Judgment, 5:283). This suggests that Kant might well embrace the idea that second-order methodological discoveries (e.g., Newton's logic of discovery) could be indicative of genius insofar as these discoveries awaken the genius of others to make their own second-order methodological discoveries. Within mathematics, the creation of the calculus is a fine example of just this kind of methodological influence.

70. Kant, Critique of Judgment, 5:318.

71. Guyer, “Exemplary Originality,” 258.

72. Kant, Critique of Judgment, 5:211–219.

73. For the general distinction between determining and reflective judgment, see Kant, Critique of Judgment, 5:179–181. Kant uses the term “wit” to refer to reflective judgment in the Anthropology. As he says, “the faculty of thinking up the universal for the particular is wit (ingenium).” See Kant, Anthropology, 7:201. For Kant's discussion of how reflection is involved in aesthetic judgments, see the First Introduction to Critique of Judgment, 20:219–226. See also Kant, Critique of Judgment, 5:256, for a summary of how aesthetic judgments are not determining.

74. Kant, Critique of Judgment, 5:203–211.