Abstract
In this paper I adduce a new argument in support of the claim that IBE is an autonomous (indispensable) form of inference, based on a familiar, yet surprisingly, under-discussed, problem for Hume’s theory of induction. I then use some insights thereby gleaned to argue for the (reductionist) claim that induction is really IBE, and draw some normative conclusions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The D-N model (Hempel 1965, pp. 335–376) is an extreme special case. By deducing the explanandum from initial conditions and a set of laws, we show that it was certain to happen.
Fumerton (1980) shows how some causal inferences can be viewed as inductive ones (by making explicit tacit assumptions). But he doesn’t take up Harman’s detective case challenge, and here, it is not clear how the reduction is to be effected.
Unless otherwise suggested, references to, and quotes from, Hume pertain to the Treatise (1739).
I am here ignoring complications engendered by Goodman’s (1955) new riddle of induction. Let us assume that this is an instance of valid induction.
Hume (1777, p. 113) recognises yet another kind of less auspicious case, in which the observed regularity is perfect, but inadequate for complete confidence in the generalisation. Thus, an Indian prince, who has always lived in a warm climate, is justified in “refus[ing] to believe the first relations concerning the effects of frost [i.e., water freezing]”, but complete certainty that water never freezes would be rash for him. The freezing of water is not “contrary to his experience” or “miraculous”; it is merely “marvelous”, “amazing”, “not conformable to his experience”. He is reasoning—by analogy—about an unfamiliar situation, which imperfectly resembles the one he has experienced. “If you weaken the… resemblance, you weaken the principle of transition, and of consequence that belief, which arises from it” (p. 142).
Can I have an unfelt pain when I am unconscious or asleep? Maybe, but I am assuming that sometimes I am conscious—having eaten the cheese—and do not feel pain in my head.
Moore (1922, pp. 91–2) demurs, implausibly to my mind. “The question whether anything exists, when it is not perceived…seems to me to be one which can only be settled by observation…observation might justify us in concluding that…pains…do not exist, when they are not perceived”.
Fumerton (1980, p. 597) defends the opposite suggestion: that every IBE is, in fact, a case of induction. But his argument is a non sequitur. Even if (contentiously) IBE must be defended by invoking its success in cases where the conclusion is observable and then reasoning inductively to its success tout court, this doesn’t show that IBE does not invoke explanatory considerations that are irreducible to induction.
For Lycan (1988, p. 130), too, simplicity, coherence, fruitfulness and initial plausibility all contribute to the explanatoriness of a hypothesis. Confusingly, Lycan’s list of the features which enhance explanatory goodness (1988, p. 130) includes explanatoriness (in addition to simplicity and fitting what else one already believes). Here, Lycan seems to be using the term ‘explanatoriness’ more narrowly.
In a somewhat similar vein, but in a different context (rebutting the regularity theory of causation), Strawson (1989, p. 30) claims it is absurd that “there is, quite definitely, no reason at all” for the fact that “these massy physical objects…[behave] in perfectly regular ways”. The explanation (to whose truth we may reasonably infer) is that “there definitely is something about the nature of the world given which it is regular” (1989, p. 22).
How are we to construe the claim? According to Lange (2000, p. 111), it means we can only be justified in believing an accidental generalisation if we have checked all the instances. But the accidental generalisation may be very probable even before we check its instances (‘All the people in this room weigh less than 300 lb’, e.g.). Neither does it mean that the probability of the generalisation isn’t increased when an instance is encountered (Goodman 1955), since the positive instance rules out one way in which the generalisation could be false (Lange 2000, p. 113). If P((x)(Ax → Bx)) > 0, then
P((x)(Ax → Bx)/(Aa^Ba)) > P((x)(Ax → Bx)). The correct explication of the intuition is that a positive instance does not increase the probability of an unexamined case satisfying the generalisation, and doesn’t increase the probability of the generalisation over and above that engendered by eliminating a falsifier (Dretske 1977, p. 256).
We ignore gaps if they can be explained away in a sufficiently simple and plausible manner. IBE also yields an adequate response to Goodman’s riddle. The green and grue hypotheses both explain our experience. But the former is simpler (Hesse 1969).
I take it that Popper’s attempt isn’t successful (Newton-Smith 1981, ch. III).
Ladyman, Douven, Horsten and van Fraassen (1997, p. 316) argue that IBE to the unobservable involves added ontological commitments. Hume (1777, p. 153) argues that “here experience is, and must be entirely silent. The mind has never anything present to it but the perceptions, and cannot possibly reach any experience of their connexion with objects”.
I am persuaded by Weisberg’s (2009) response to van Fraassen’s claim that IBE violates the Bayesian rule of conditionalisation. If, as subjective Bayesians think, any prior probability distribution is permissible, then, to be sure, P(T1/E) may be smaller than P(T2/E) even if T1 better explains E than does T2, and assigning it higher credence in response to E because it better explains it is incompatible with conditionalising. But, Weisberg (2009, p. 137) replies, for an objectivist Bayesian, explanatory considerations constrain permissible conditional probabilities. So if T1 better explains E than does T2, P(T1/E) will be greater than P(T2/E).
References
Armstrong, D. M. (1983). What is a law of nature? Cambridge: Cambridge University Press.
Baier, A. C. (1991). A Progress of sentiments. Cambridge, MA: Harvard University Press.
Bartelborth, T. (1999). Coherence and explanation. Erkenntnis, 50, 209–224.
Berkeley, G. (1710). Principles of human knowledge. In A. A. Luce and T. E. Jessop (Eds.), The works of Georg Berkeley, 9 vols. (pp. 1948–1957). London: Nelson.
Bridgeman, P. W. (1927). The logic of modern physics. New York: MacMillan.
Cartright, N. (1983). How the laws of physics lie. Oxford: Clarendon.
Day, T., & Kincaid, H. (1994). Putting inference to the best explanation in its place. Synthese, 98, 271–295.
Dray, W. (1957). Laws and explanation in history. Oxford: Oxford University Press.
Dretske, F. (1977). Laws of nature. Philosophy of Science, 44, 248–268.
Ennis, R. (1968). Enumerative induction and best explanation. Journal of Philosophy, 64, 523–529.
Falkenstein, L., & Welton, D. (2001). Humean contiguity. History of Philosophy Quarterly, 18, 279–296.
Feigl, H. (1970). ‘The “orthodox” view of theories’. In M. Radner and S. Winokur (Eds.), Minnesota studies in the philosophy of science. vol. IV, Minneapolis, MN: University of Minnesota Press.
Foster, J. (1983). Induction, explanation and natural necessity. Proceedings of the Aristotelian Society, 83, 87–101.
Friedman, M. (1974). Explanation and scientific understanding. Journal of Philosophy, 71, 5–19.
Fumerton, R. (1980). Induction and reasoning to the best explanation. Philosophy of Science, 47, 589–600.
Gomberg, P. (1976). Coherence and causal inference in Hume’s treatise. Canadian Journal of Philosophy, 6, 693–704.
Goodman, N. (1955). Fact, fiction and forecast. New York: Bobbs-Merrill.
Harman, G. (1965). The Inference to the best explanation. Philosophical Review, 74, 88–95.
Harman, G. (1968). Enumerative induction as inference to the best explanation. Journal of Philosophy, 64, 529–533.
Hempel, C. G. (1942). The function of general laws in history. Journal of Philosophy, 39, 35–48.
Hempel, C.G. (1965). ‘Aspects of scientific explanation’. In Aspects of scientific explanation. New York: Free.
Hesse, M. (1969). Ramifications of grue. British Journal for the Philosophy of Science, 20, 13–25.
Howson, C. (2000). Hume’s problem. Oxford: Clarendon.
Hume, D. (1739). A treatise of human nature. In: L. A. Selby-Bigge (2nd ed.) (p. 1978). Oxford: Clarendon.
Hume, D. (1777). Enquiries concerning human understanding. In: L. A. Selby-Bigge (3rd ed.) (1975). Oxford: Clarendon.
Humphreys, P. (1989). The chance of explanation. Princeton, NJ: Princeton University Press.
Kim, J. (1992). Multiple realization and the metaphysics of reduction. Philosophy and Phenomenological Research, 52, 1–26.
Kitcher, P. (1989). Explanatory unification and causal structure. In P. Kitcher & W. C. Salmon (Eds.), Minnesota studies in the philosophy of science (Vol. XIII). Minneapolis, MN: University of Minnesota Press.
Kneale, W. (1949). Probability and induction. Oxford: Clarendon.
Kuipers, T. (2004). ‘Inference to the best theory, rather than inference to the best explanation—kinds of abduction and induction’. In: F. Stadler (Ed.),Induction and deduction in the sciences. Dordrecht: Kluwer.
Ladyman, J., Douven, I., Horsten, L., & van Fraassen, B. (1997). A defence of van Fraassen’s critique of abductive inference. Philosophical Quarterly, 47, 305–321.
Lange, M. (2000). Natural laws in scientific practice. Oxford: Oxford University Press.
Lehrer, K. (1970). ‘Justification, explanation, and induction’. In: M. Swain (Ed.). Induction, acceptance, and rational belief. Dordrecht: Reidel.
Lewis, D. (1986). ‘Causal explanation’. In: D. Lewis (Ed.). Philosophical papers vol. 2. Oxford: Oxford University Press.
Lipton, P. (1991). Inference to the best explanation. London: Routledge.
Lycan, W. G. (1988). Judgement, and justification. Cambridge: Cambridge University Press.
Mendelson, E. (1979). Introduction to mathematical logic (2nd ed.). New York: D. van Nostrand.
Miller, R. W. (1987). Fact and method. Princeton: Princeton University Press.
Moore, G. E. (1922). Philosophica studies. London: Routledge.
Moore, G. E. (1962). Common-place book (pp. 1919–1953). In: C. Lewy (Ed.). London: Allen–Unwin.
Newton-Smith, W. (1981). The rationality of science. London: Routledge–Kegan Paul.
Niiniluoto, I. (2004). Truth-seeking by abduction. In F. Stadler (Ed.), Induction and deduction in the sciences. Dordrecht: Kluwer.
Okasha, S. (2001). What did hume really show about induction? Philosophical Quarterly, 51, 307–327.
Peirce, C. S. (1966). ‘Abduction and induction’. In: Collected papers (2nd ed.) Cambridge, MA: Harvard.
Popper, K. R. (1972). The logic of scientific discovery (4th ed.). London: Hutchinson.
Price, H. H. (1940). Hume’s theory of the external world. Oxford: Clarendon.
Reid, T. (1785). Essays on the Intellectual Powers of Man. In: A. D. Woozley (Ed.). London: MacMillan, 1941.
Salmon, W. C. (1984). Scientific explanation and the causal structure of the world. Princeton, NJ: Princeton University Press.
Scheffler, I. (1964). The anatomy of inquiry. London: Routledge–Kegan Paul.
Schurz, G. (1999). Explanation as unification. Synthese, 120, 95–114.
Scriven, M. (1970). Explanation, predictions, and laws. In H. Feigl & G. Maxwell (Eds.), Minnesota studies in the philosophy of science (Vol. III). Minneapolis, MN: University of Minnesota Press.
Sober, E. (1988). Confirmation and law-likeness. Philosophical Review, 97, 93–98.
Stebbing, S. (1933). Modern introduction to logic (2nd ed.). London: Methuen.
Strawson, G. (1989). The secret connexion: Causation, realism, and David Hume. Oxford: Clarendon Press.
Swinburne, R. (1974). The justification of induction. Oxford: Oxford University Press.
van Fraassen, B. C. (1989). Laws and symmetry. Oxford: Oxford University Press.
Weisberg, J. (2009). Locating IBE in the Bayesian framework. Synthese, 167, 125–143.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Weintraub, R. Induction and inference to the best explanation. Philos Stud 166, 203–216 (2013). https://doi.org/10.1007/s11098-012-0034-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11098-012-0034-1