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Always or Never: Two Approaches to Ceteris Paribus

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The Scientific Revolution spawned not just one methodology, but two. We have emphasized Bacon’s inductivism at the expense of Galileo’s more abstract, sophisticated method of successive approximation, and so have failed to appreciate Galileo’s contribution to the ceteris paribus problem in philosophy of science. My purpose here is to help redress this imbalance. I first briefly review the old unsolved problems, and then point out the Baconian basis of ceteris paribus, as this clause is conventionally understood, and its history from Aristotle to twentieth century Positivism. Then I explore Galileo’s method of dealing with unwanted impediments, and the more general problem of ‘accidents.’ I trace his methodology back to Archimedes and forward through the economic theories of Adam Smith (18th century), J. S. Mill (19th) and Milton Friedman (20th). Finally, I point out ways in which I think Galileo’s scientific method sheds light on, and provides a partial solution to, the ceteris paribus problem.

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  1. Newton (1995, 141, 197, 266 and passim).

  2. Caws (1967, 341). Herschel’s book also came out in Lardner’s Cyclopedia in 1831, which is sometimes given as the date of the work.

  3. There being no standard or well-known edition of Herschel’s Preliminary Discourse, I cite universal section numbers, rather than page numbers. For other historical sources I use both the original reference, where possible, and the modern edition’s page numbers.

  4. Cassirer (1942) gives a nice informal account of the Galilean methodological revolution.

  5. This is the conventional meaning of ‘induction,’ and the one I assume throughout this paper, although ‘induction’ was sometimes used as a catchall term for empiricism; and see below, n. 24. To be sure, in the New Organon (Aphorism 95; 1960, 93) Bacon does assert the need to combine ‘experimental’ and ‘rational.’ Scientists should not be like ants, which merely collect material, or spiders, which merely “make cobwebs out of their own substance,” but rather like bees, which produce something “altered and digested.” But this thought did not find its way to center-stage in Bacon’s system.

  6. See Joseph (1980, 777–778), Pietroski and Rey (1995, 104–105).

  7. See Oddie (1996).

  8. See Lewin (1935, 5 and passim), Hall (1954, 184), Laudan (1968, 20–21), Osler (1970, 3–4).

  9. Cf. New Organon, Book I, Aphorism 63 (1960, 60–61).

  10. Mill openly acknowledged his reliance on Herschel’s work (1973, 7: 414, and Introduction, xviii). Herschel, it should be said, was not a strict Baconian (Yeo 1989; Hankins 2006, 621). But then, contrary to popular belief, neither was Mill; see below, Sect. 5.

  11. See Cartwright (1980, 160).

  12. Well, hardly ever; see Asimov (1962, 72).

  13. Galileo’s mechanics “presupposes” that absent interference, bodies persist in a state of rest or uniform motion, according to Olschki, but “only once in a marginal note,” he says (1942, 264), is this principle actually stated.

  14. Pemberton (2005, 37), for example.

  15. And see Strong (1936, 8, 135 and passim), Drake (1967, 263–264).

  16. On this point, also see Friedman (1953, 10, 33–34).

  17. “We must assume that the plane is, so to speak, incorporeal, or at least that it is very carefully smoothed and perfectly hard …” Galileo, On Motion (sec. 298; 1960, p. 65).

  18. Wallace calls him an Aristotelian (1974, 79 and passim); Koyré calls him a Platonist (1943, 347–348).

  19. Nor does Bacon seem to have taken much interest in the scientific work being done in his own day, whether by Galileo, Kepler, or even his own physician William Harvey (Quinton 1980, 79).

  20. See Grendler (2002, 428), Drake (1970), Kuhn (1970, 119–120).

  21. Tellingly, the two scholars who squared off about whether Galileo was an Aristotelian or a Platonist (cf. note 18) agreed that he was an Archimedean. And Finocchiaro even asserts (2008, 834) that Galileo’s physics was not “designed to justify a prior commitment to Copernicanism,” but to put forward an “Archimedean science of motion.”

  22. In Wilber (1985, 60).

  23. Finocchiaro writes (1980, 152) that “the most striking fact about Galileo” in the “history-of-philosophy books” is “the neglect he receives” there.

  24. To be sure, even in the Principia Newton uses the term ‘induction’ in a way seemingly Baconian (e.g., 1995, 443, at the end of the General Scholium). But then, he uses the term ‘deduction’ (e.g., Preface, 1995, 4), to mean “any reasoning competent to establish a conclusion as warranted,” which includes induction (Harper and Smith 1995, 160, n. 100).

  25. Cohen thought Newton was overly generous in crediting Galileo with having grasped his own first two laws of motion (1960, 159). But Newton was not known for over-generosity in crediting others; and Cohen himself acknowledged (ibid. 151) that “the first workable physics for heaven and earth derived … from Galileo and attained its form under … Newton.” On Newton’s debt to Galileo, also see Funkenstein (2005, 54).

  26. Weisberg (2007, 645, 655) thinks Galileo’s aim was ultimately to de-idealize. He delineates three types of idealization, of which Galileo’s is only one; for our purposes, though, I think this one is enough.

  27. In fairness, Nagel (1963) fundamentally defends Friedman’s use of idealization in economics (see below).

  28. Hausman (1985, 235).

  29. Earlier in the twentieth century there was much emphasis on Marx and Keynes. I am not aware that Keynes made use of the method of idealization; but there is considerable literature on Marx’s use of it in the Poznań Studies series on idealization. Ronald Meek has written about the connection between Marx and Adam Smith (see Ross 1995, 417–418). According to Nowak (1992, 24), Marxism “went in the direction of either positivistic naturalism (‘Eastern Marxism’) or idealistic anti-naturalism (‘Western Marxism’).”

  30. She considers the former a subset of the latter (1989, 226–227).

  31. Mill, however, called it “in many parts obsolete, and in all, imperfect” (1965, xcii).

  32. Wealth of Nations I.vii.15, 30; Smith (1981, 75, 79). And see Schliesser (2005, 35). Much as he revered Newton, incidentally, Smith also owned Galileo’s Opere (Bonar 1932, 72), and compared Galileo favorably to Kepler. He also credited Galileo, rather than Newton, with recognizing the need to combine experience and reason, fact and theory (1982, 83–84, and Introduction, p. 1).

  33. “If a nation could not prosper without the enjoyment of perfect liberty and perfect justice,” Smith says in Wealth (IV.ix.28; 1981, p. 674), “there is not in the world a nation which could ever have prospered.”

  34. This Aristotelian, for-the-most-part bias leads us to emphasize the contrary-to-fact-ness of idealization, rather than its fruitfulness.

  35. That led one scholar to describe Galileo as “moving his experiment off the actual, physical inclined plane and into his mind” (Kolak 1993, 46). I would say he went less from external to internal than from perceptual to hypothetical.

  36. And see Gould (2000, 172) on this point.

  37. I am grateful to an Erkenntnis reviewer for raising this question, which had not occurred to me.

  38. Again, I am indebted to an Erkenntnis reviewer for a suggestion along these lines.

  39. Newton may be making a similar point in the Principia, saying: “It will be sufficient if the angle is found by a rude calculus in numbers near the truth” (quoted in Blake [1960, 322, n. 87], along with other, similar remarks by Newton).

  40. This implicitly places any ceteris paribus ‘laws’ still ‘impounded’ in a kind of scientific limbo, as temporary placeholders. See Glymour (2002, 403).


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I wish to thank the American Council of Learned Societies for a grant under which this study was begun, and Lorraine Daston, Arnold Koslow, Ernan McMullin, Joseph Pitt, Eric Steinberg, and my Erkenntnis referees for helpful criticisms and suggestions. The usual caveats, of course, apply.

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Carey, T.V. Always or Never: Two Approaches to Ceteris Paribus . Erkenn 77, 317–333 (2012).

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