Abstract
Motivated by examples, many philosophers believe that there is a significant distinction between states of affairs that are striking and therefore call for explanation and states of affairs that are not striking. This idea underlies several influential debates in metaphysics, philosophy of mathematics, normative theory, philosophy of modality, and philosophy of science but is not fully elaborated or explored. This paper aims to address this lack of clear explanation first by clarifying the epistemological issue at hand. Then it introduces an initially attractive account for strikingness that is inspired by the work of Paul Horwich (1982) and adopted by a number of philosophers. The paper identifies two logically distinct accounts that have both been attributed to Horwich and then argues that, when properly interpreted, they can withstand former criticisms. The final two sections present a new set of considerations against both Horwichian accounts that avoid the shortcomings of former critiques. It remains to be seen whether an adequate account of strikingness exists.
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Notes
For an elaboration of this point, see Baras, D., A strike against a striking principle, (unpublished).
For instance, Good (1984, 164), Schlesinger (1991, 99), Manson (2003) and Mogensen, A. L., Ethics , evolution , and the coincidence problem : A skeptical appraisal, (unpublished) attribute competing hypothesis (the first account that I will introduce shortly) to Horwich and make no mention of disconfirmation (the second account). Manson (1998) and Bostrom (2002, 30) both slightly misquote Horwich, and each of them attributes to Horwich a slightly different mixed account. Bostrom’s interpretation of Horwich is logically equivalent to competing hypothesis.
In private correspondence, Horwich explained that disconfirmation is his official account, whereas competing hypothesis was meant to be just one unnecessary way in which the account can be realized.
In later editions van Inwagen revises his principle without explaining why. The existence of a potential explanation remains a core feature in his most recent revision (van Inwagen 2015, 205). However, the revised principle is presented as only a sufficient condition and it introduces new elements, some of which require disambiguation. Unfortunately, I cannot discuss van Inwagen’s revision as it would lead us too far astray from the focus of this article.
Example: Suppose there is only one competing hypothesis K, so that K ≡ ¬C. Suppose that (E) = 0.001, P(C|E) = 0.5 and P(C) = 0.9. Plausibly, these numbers fulfill Horwich’s conditions for strikingness. They imply though that P(E|¬C) = 0.005. Surely that doesn’t count as high.
Example: Again, for simplicity, suppose there is only one competing hypothesis K, so that K ≡ ¬C. Suppose further that P(C) = 0.999; P(E|K) = 0.9; P(K) = 0.001 and P(E) = 0.01. It follows that P(C|E) = 0.91. Arguably, that does not count as a significant decrease in the probability of C.
For a discussion of Schlesinger and Harker’s alternative accounts of strikingness, see Baras, D., Do extraordinary types call out for explanation?, (unpublished).
Schlesinger and Harker use different examples to make the same point.
Manson (1998) makes a similar point.
Good (1956) also has this restriction. An interesting consequence of the restriction to non-negligible hypotheses is that necessarily anything satisfying this version of Alternative Hypothesis will also satisfy Disconfirmation, because E will raise the probability of K, which is contrary to a relevant background belief. The converse is false because E can disconfirm C even if all alternative hypotheses have negligible prior probability, for instance, if P(C) ≈ 1.
Here’s the proof:
- 1.
\( P\left(E|K\right)=P\left(K|E\right)\frac{P(E)}{P(K)} \) [Bayes’ theorem]
- 2.
P(K| E) ≤ 1 [probability axioms]
- 3.
\( P\left(K|E\right)\frac{P(E)}{P(K)}\le \frac{P(E)}{P(K)} \) [from 2]
- 4.
\( P\left(E|K\right)\le \frac{P(E)}{P(K)}\kern1em QED\kern0.5em \) [from 1, 3]
- 1.
I thank Blake McAllister for pressing me here.
Notice though that in order for this account to give the correct predictions, the terms ‘low probability’, ‘non-negligible probability’ and ‘high probability’ should be interpreted not as fixed ranges of numbers, but rather as relative to each other. For example, the lower the prior of E, the lower K can be and still be confirmed by E. I thank an anonymous referee for this comment.
For this reason, Harker’s suggestion to Horwich is ruled out as well. Harker (2012, n. 1) suggests that we ‘limit admissible alternative circumstances to those that we might reasonably expect to know or discover.’ However, we can only reasonably expect to know or discover hypotheses that we can reasonably expect to be true. Harker’s suggestion fares even worse than Horwich’s because we can easily come up with counterexamples. Suppose that an omniscient god revealed to you that you have no way of knowing or discovering the explanation for why a particular die landed 3535353535. Alternatively, suppose that the die fell into the ocean, so you cannot reasonably expect to be in a position to examine it ever again. It would be unreasonable to expect to know or discover any alternative hypotheses in such circumstances, yet the sequence seems no less striking.
Although their wording is vague, it seems that Leslie (1989, 10) and van Inwagen (1993, 135) think along similar lines. Leslie indicates that the potential explanation must be a ‘tidy’ explanation. However, what does tidiness mean in this context? The same problems that I raise for Schechter’s restriction to salient hypotheses apply to Leslie’s restriction to tidy hypotheses so I do not see a need to discuss Leslie’s idea separately.
Adherents of this account may want to allow the set of alternative hypotheses to include hypotheses with initial probability zero, since, plausibly, hypotheses that are conclusively ruled out can still be salient. Even if the tooth fairy hypothesis were conclusively ruled out, one might still believe that the replacement of the tooth calls for explanation because of the tooth fairy hypothesis. If so, we will have to make some amendments to the formal account because conditionalizing on probability zero propositions is undefined in the standard Bayesian framework. Note that some philosophers believe that the lack of definition of conditional probability for probability zero propositions is a flaw in the standard Bayesian analysis of conditional probability (Hájek 2003).
White (2007) makes this point. He argues that if we rule out the intelligent design hypothesis, we no longer have reason to rule out the hypothesis that we owe our existence to mere chance. This argument seems to me to be in tension with White’s claims elsewhere in which he seems to imply that something can call for explanation even if the most salient explanations have been ruled out (White 2005, 2015).
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Acknowledgements
Whatever merits this paper may have, they are most definitely explainable: Very helpful comments I received from Ron Aboodi, Sharon Berry, David Enoch, Yehuda Gellman, Alan Hájek, Paul Horwich, Ofer Malcai, Neil Manson, Blake McAllister, Eli Pitcovski, Joshua Schechter, Miriam Schoenfield, Orly Shenker and Martin Smith on previous drafts have contributed significantly to improving this paper. I also wish to thank the participants at my presentations at Ben Gurion University’s philosophy department colloquium, the 2016 Eastern Regional Meeting of the Society of Christian Philosophers at Rutgers University and at the 2nd Jerusalem-MCMP Workshop on Explanatory Reasoning in the Sciences at the Munich Center for Mathematical Philosophy for very helpful discussions. During the various stages of writing, my work was supported by Ben Gurion University and later by the Center for Moral and Political Philosophy at the Hebrew University of Jerusalem.
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Baras, D. Why Do Certain States of Affairs Call Out for Explanation? A Critique of Two Horwichian Accounts. Philosophia 47, 1405–1419 (2019). https://doi.org/10.1007/s11406-018-0047-x
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DOI: https://doi.org/10.1007/s11406-018-0047-x