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The Metaphysical Requirement for Models of Prediction and Explanationist Approaches to the Problem of Induction

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Abstract

David Armstrong once argued that to solve the problem of induction with inference to the best explanation we need an anti-Humean conception of law. Some Humeans have argued that this argument begs the question against Humeanism. In this paper, I propose a new argument for the same conclusion which is not vulnerable to this criticism. In particular, I argue that explanationist approaches to the problem of induction that are combined with Humeanism is internally incoherent.

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Notes

  1. Harman (1980).

  2. Armstrong (1983), BonJour (1998), Foster (1983) and Peacocke (2004).

  3. Armstrong, What Is a Law of Nature?, 52–53.

  4. Ibid., 40. For a similar argument, see Bird (2007), 86–90. The original characterization of what I call “Armstrong’s principle” is different from mine or, for instance, Bird’s. But these differences are of little import in the context of this study. I will use my characterization because it is the simplest and most straightforward one even though it might have some technical problems.

  5. Loewer (1996): 113, Lewis (1994): 478–479. By “Humean theories of explanation,” I mean roughly those theories of scientific explanation that do not appeal to any kind of necessary connection. (I will provide a better characterization of this term in Sect. 3.) Strictly speaking, we cannot say that the D-N model and unification account are Humean theories. For example, if someone accepts a non-Humean theory of law (e.g., Armstrong’s) and thinks that an explanation is a deductive inference of the explanandum from natural laws and some non-nomological facts, the resulting theory of explanation would be a non-Humean version of the D-N model. However, it is clear that Hempel and Kitcher had some kind of Humean theory of explanation in mind. See Hempel and Oppenheim (1948) and Kitcher (1989).

  6. For example, according to Roger White, Armstrong’s principle ignores an important distinction between instance explanation and regularity explanation. White (2005).

  7. Beebee (2011).

  8. I have already examined these criticisms elsewhere: Lee (2013a, c, 2015).

  9. Clark (2003), 4.

  10. “Leeway incompatibilism” is a view according to which the availability of alternative possibilities is crucial to explaining free will and moral responsibility. “Source incompatibilism” is a view according to which not the existence of alternative possibilities but the existence of a causal history of a sort that allows the agent to be the source of her action in a specific way is crucial. For the difference between leeway incompatibilism and source incompatibilism, see Pereboom (2007), 85–86.

  11. Beebee (2000): 579.

  12. Here, by saying that “an event is closed” I mean that alternatives of that event are closed. Similarly, I mean by “an event is open” that alternatives of that event are open.

  13. Beebee argues that the Humean notion of law is based on the descriptive conception of law, while Armstrong’s notion of law is based on the governing conception of law.

  14. In fact, this is John Stuart Mill’s insight when he writes, “It must be granted that in every syllogism, considered as an argument to prove the conclusion, there is a petitio principii” (Mill 1963, 184). Since a circular argument is not ampliative, it cannot be a predictive inference. According to Ruben, it was for this reason Mill accepted a down-graded notion of explanation according to which explanation has nothing to do with providing new information (Ruben 1990, 137).

  15. Hempel and Oppenheim claim, “Let us note here that the same formal analysis, including the four necessary conditions, applies to scientific prediction as well as to explanation. The difference between the two is of a pragmatic character.” Hempel, "Studies in the Logic of Explanation," 138. This claim is erroneous in dual sense. First, as many counterexamples against the D-N model have noted, there is a deep asymmetry between prediction and explanation. For example, irrelevancy is fatal to explanation yet harmless to prediction. Second, Hempel and Oppenheim’s version of the D-N model, which is combined with the Humean regularity notion of law, cannot serve as a model of prediction.

  16. Armstrong, What Is a Law of Nature?, 59.

  17. Note that if determinism is false, strong determinism is false as well. So, if there is no deterministic law, local strong determinism is false.

  18. This prediction is far from deterministic in the movie. But for the sake of argument, let us assume that it is a deterministic prediction.

  19. An anonymous reviewer raised this issue.

  20. Hume et al. (1978), 178.

  21. Lewis (1986), ix.

  22. Following Lewis, I mean by “chance” objective probability.

  23. This is in accord with Loewer, "Humean Supervenience," 113.

  24. Hempel, "Studies in the Logic of Explanation," Sec. 6.

  25. For the problems of naïve regularity theory, see Carroll (1994), Ch. 2. For the problems of the D-N model in its original form, see Salmon (1989), 46–50.

  26. Lewis (1973), 73.

  27. For Lewis (1983: 366), this question is misguided because he thinks that Armstrong’s N(F,G) is simply unintelligible. However, we are comparing Armstrong’s version of type-B approach with type-A approaches here, meaning we are assuming that his N(N,G) is at least intelligible. So, Lewis’s critique, or so-called “inference problem,” is irrelevant in our context.

  28. If by “best systematization” we mean best systematization of Humean facts, one might argue that this conclusion does not follow, claiming that since N(F,G) is not a Humean fact, it does not need to be systemized. I think this proposal is wholly unmotivated. Consider the following characterization of law by Ramsey, cited by Lewis:

    [Laws are] consequences of those propositions which we should take as axioms if we knew everything and organized it as simply as possible in a deductive system (Counterfactuals, 73. Italics mine.)

    There is no reason to think that N(F,G) cannot be included in “everything” even though it obtains.

  29. Strictly speaking, this argument by itself does not show that MRL has commitment to NNC, as there are non-Armstrongean versions of necessary connection. According to dispositional essentialists, we don’t need the N relation to explain observed regularities; first order universals themselves are capable to explain regularities because they have dispositional essences. However, since a similar argument can be made for dispositional essentialism, we may say that this argument shows that MRL has commitment to NNC. For the details of dispositional essentialism, see Ellis and Lierse (1994); Bird, Nature's Metaphysics: Laws and Properties. For a more detailed argument, see Lee (2013b).

  30. Psillos (2002), 274–275. Italics in the original.

  31. Loewer, "Humean Supervenience," 120. The same claim appears in Psillos, Causation and Explanation, 177.

  32. Van Fraassen (1989), 126.

  33. See footnote 4.

  34. See footnote 14. An interesting exception to this is A. J. Ayer. He shares Beebee’s intuition that determinism in Humean sense is perfectly compatible with the openness of future event. But he denies the analogy between free will and prediction. In my opinion, this fact does not undermine my claim, however, because he seems to be using a deflationary notion of prediction, according to which a prediction is nothing but a deductive argument which appeals to laws of nature, rather than a genuine one. See Ayer (1982), 22–23.

  35. I have replied to this criticism elsewhere. See Lee (2015).

  36. See White, "Explanation as a Guide to Induction," 12.

  37. John Foster has a weird position concerning this issue. He says, “There is a sense … in which to explain a fact is to subsume it under something more general. But it cannot be this sort of explanation which is involved in NES [nomological-explanatory solution].” Foster, "Induction, Explanation and Natural Necessity," 91; ibid. It seems that he thinks that we might have two different notions of explanation: one that can be used in explanationist approaches and one that cannot. I think this position is completely unmotivated.

  38. For Salmon’s criticism of IBE, see Salmon (2001).

  39. Ladyman (2002), 47.

  40. For example, Hempel and Oppenheim require that explanans be true. Hempel, "Studies in the Logic of Explanation," 137. No scientist would deny that a theory that contains references to theoretical entities could be used for genuine scientific explanation; thus Hempel and Oppenheim’s requirement results in scientific realism. For another example, Lewis’s Humean supervenience does not make sense if his “local matters of particular fact” contain only observable, macro-level facts. So it is quite obvious that he is assuming scientific realism. For the relation between scientific realism and IBE, see Psillos (1999), Ch. 4.

  41. Ladyman et al. (1997).

  42. Lewis writes, “If you’re prepared to agree that theorems of the best system are rightly called laws, presumably you’ll also want to say that they underlie causal explanations; that they support counterfactuals; that they are not mere coincidences; that they and their consequences are in some good sense necessary; and that they may be confirmed by their instances. If not, not.” Lewis, "Humean Supervenience Debugged," 478–479.

  43. Beebee, "The Non-Governing Conception of Laws of Nature (Ramsey-Lewis Theory, Thought Experiments)."

  44. Recently, a third area is growing among metaphysicians: that of metaphysical grounding. On this discussion, see Correia and Schnieder (2012).

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    Jaeho Lee

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Lee, J. The Metaphysical Requirement for Models of Prediction and Explanationist Approaches to the Problem of Induction. Axiomathes 27, 225–242 (2017). https://doi.org/10.1007/s10516-016-9299-x

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