Abstract
While Chap. 6 discussed the role of abduction in the confirmation of hypotheses by their success in explanation and prediction, in this chapter we turn to the notion acceptance which is a stronger form of justification than confirmation. Section 7.1 gives a survey of inductive acceptance rules, and following Gilbert Harman formulates inference to the best explanation (IBE) as a rule of acceptance: a hypothesis H may be inferred from evidence E when H is a better explanation of E than any other rival hypothesis. The notion of “best explanation” is explicated by measures of explanatory power, with a comparison to Lipton’s distinction between “lovely” and “likely” explanations. In the special case with only one available explanation, IBE reduces to inference to the only explanation. Section 7.2 deals with the question of justifying IBE by giving replies to Bas van Fraassen’s “bad lot” and “incoherence” arguments. It is concluded that under certain conditions an explanatory hypothesis may be so successful that its tentative acceptance as true is warranted.
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Notes
- 1.
Convergence theorems of de Finetti and Savage show that under some conditions researchers, who update their personal degrees of beliefs by the same evidence , are eventually led from different prior probabilities to the same posterior probabilities. See Howson and Urbach (1989) and Earman (1992) . Objective Bayesians suggest that there are unique ways of fixing the prior probabilities.
- 2.
Similarly, low probability is not a sufficient condition for rejecting a hypothesis.
- 3.
For example, in a language with two monadic predicates F and G, the Q-predicates are Q1x = Fx & Gx, Q2x = Fx & ¬Gx, Q3x = ¬Fx & Gx and Q4x = ¬Fx & ¬Gx. The generalization g = (∀x)(Fx → Gx) states that the cell Q2 is empty, so that it can be expressed as a disjunction of seven constituents which leave Q2 empty. (The constituent which leaves all four Q-predicates empty is excluded, since the universe cannot be empty.) If the probabilities of finding an individual b in the four Q-predicates are equal, then we have 1/3 = P(Fb/g) < P(Fb/Gb & g) = ½, which shows that Gb confirms Fb relative to g (cf. (6.5)). But to formalize singular abduction (1.3), so that Fb is acceptable on Gb and g, we need to assume that the probabilities the Q-predicates are non-symmetric, i.e. P(Q1b) is much larger than P(Q3b).
- 4.
- 5.
In Risto Hilpinen’s (1968) modified version, the expected utility is P(H/E) – qP(H), where 0 < q ≤ 1 is an “index of boldness” in Levi’s sense. Thus, for (3), this index of boldness is maximal. However, even the boldest application of Levi’s rule is cautious in the sense that it always prefers truth to falsity. In Chap. 8, we shall introduce measures of truthlikeness which admit that some false statements may be so close to the truth that they are cognitively better than weak uninformative truths like tautologies.
- 6.
Levi (1979) restricts the task of abduction to the formulation of potential hypotheses, without reference to explanation, but here we are interested in the role of abduction in the selection of the best hypothesis.
- 7.
For discussion of this thesis, see Sect. 1.4.
- 8.
See also formulations of abduction as a rule of inference in Chap. 3.
- 9.
Bird (2010) , who calls such deduction “Holmesian inference”, argues that Lipton’s (1991) historical example of Ignaz Semmelweis’s study of childbed fever (see Hempel, 1966) is an eliminative abduction in this strong sense. But one may doubt that the list of potential explanations that Semmelweis considered was exhaustive.
- 10.
If the coroner is asked to identify the cause of death, a disjunction of even two alternative causes may be too weak.
- 11.
It is questionable whether IBE can be saved from these troubles by joining it with simplicity considerations, such as “consilience ” in Thagard (1978) and “explanatory unification ” in Friedman (1974) or with additional penalties for “conceptual problems” (cf. problem-solving ability in Laudan, 1977) .
- 12.
For an attempt to find objective prior probabilities for IBE, see Weisberg (2009) . In Carnap’s and Hintikka’s systems of inductive logic, there are canonical ways of giving prior distributions and likelihoods , but they are open up to the choice of one or two parameters.
- 13.
An important contemporary example of the power of explanatory considerations is the postulate of dark matter. The majority of physicist accept the existence of dark matter as an abductive solution to the problem of “missing masses”, since it explains anomalous observations about galaxies, even though dark matter by definition is invisible (does not interact with electromagnetic radiation), and experimental attempts to verify or test its existence have failed. Therefore, some philosophers have claimed that it is an untestable ad hoc hypothesis (see Merritt, 2017). See also Sect. 8.5.
- 14.
- 15.
Another case which guarantees that P(H/E) is close to one is that H has a unique novel deductive prediction E which no rival of H is able to predict (see Leplin 2004) .
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Niiniluoto, I. (2018). Inference to the Best Explanation. In: Truth-Seeking by Abduction. Synthese Library, vol 400. Springer, Cham. https://doi.org/10.1007/978-3-319-99157-3_7
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