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Where are the chances?

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Abstract

Not all probability ascriptions that appear in scientific theories describe chances. There is a question about whether probability ascriptions in non-fundamental sciences, such as those found in evolutionary biology and statistical mechanics, describe chances in deterministic worlds and about whether there could be any chances in deterministic worlds. Recent debate over whether chance is compatible with determinism has unearthed two strategies for arguing about whether a probability ascription describes chance—that is, to speak metaphorically, two different strategies for figuring out where the chances are: find the chances by focusing on chance’s explanatory role or find the chances by focusing on chance’s predictive role. These two strategies tend to yield conflicting results about where the chances are, and debate over which strategy is appropriate tends to end in stalemate. After discussing these two strategies, I consider a new view of chance’s explanatory role. I argue that one theoretical advantage of this new view is that allows us to make progress on the question of where the chances are by providing a principled way of determining which probability ascriptions describe chances. From the vantage of this new view, the correct application of both strategies involves figuring out where the chances are by figuring out where the probabilistic scientific explanations are and what those explanations are like.

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Notes

  1. For recent examples of this kind of argument for compatibilism, see Loewer (2001), Glynn (2010) and Emery (2013).

  2. For recent examples of this kind of argument for incompatibilism, see Hoefer (2007) and Sober (2010) (wherein the argument is described) and Schaffer (2007) (wherein the argument is endorsed).

  3. It might nevertheless be true that chances are ultimately grounded in facts about relative frequencies, as on David Lewis’s popular Humean treatment of objective chance (Lewis, 1980). Furthermore, history does contain authors who have defended the view that chances simply are the frequencies with which events occur relative to a reference class (e.g., Venn, 1876). However, I assume that frequentism is incorrect, for reasons such as those detailed in Hájek (1996). I additionally assume that at least some objective chances are “single-case” chances: chances of a particular event occurring. Some philosophers are skeptical of single-case chances (e.g., Gillies, 2000; Howson and Urbach, 1993; von Mises, 1957), but the authors I discuss in the main text all allow that chances can attach to particular events.

  4. Frequencies do have the power to explain things. For example, the fact that I’ve lost all of the thousands of lotteries I’ve entered helps to explain why I’m not rich. Nevertheless, the frequency with which an event of some type has occurred seems incapable of explaining why that very event, whose occurrence (or non-occurrence) helps constitute that frequency, occurred. For example, the fact that the frequency with which I have won the lottery is equal to 0 seems to report that, rather than to explain why, I have lost each of the lotteries I’ve entered.

  5. The question of what kind of information goes into an ideal explanatory text is just the question of what is the correct theory of scientific explanation.

  6. Thanks to an anonymous referee for pressing me to clarify this point.

  7. Well-known discussions of chance’s unique predictive role appear in, e.g., Butler (1736), Salmon (1967) and Lewis (1980).

  8. Hoefer (2007) denies that the conjunction of the laws and history of the world is admissible in a deterministic world on the grounds that that conjunction implies the truth of every proposition about the future and thus contains information that does not “go by way of” the chances. Perhaps that is right, but without some independent account of which information, in fact, “goes by way of” the chances, Hoefer’s rejection of the PP-based argument for compatibilism—unlike Loewer’s and Glynn’s—does not motivate an alternative prediction-based test of which probability ascriptions model chance.

  9. Sometimes events that occur by chance counterfactually depend on their causes, but sometimes causes merely change an event’s chance of occurring.

  10. The distinction between mediate and immediate explanatory information is crucial to this view. In contrast, the view that scientific explanation is transitive functionally collapses this distinction by implying that mediate explanatory information is, ipso facto, immediate explanatory information. In my experience, the alleged transitivity of explanation is typically assumed rather than supported by argument. At any rate, this essay is meant to push back on the transitivity assumption by demonstrating one of the theoretical advantages that comes with preserving the distinction between mediate and immediate explanations of an event’s occurrence.

  11. That is, it is a serious epistemic possibility that the “standard” interpretation of quantum mechanics is correct.

  12. Importantly, my view should be interpreted as a view about the structure of scientific explanation rather than as a view about acceptable answers to why-questions. Many philosophers have pointed out that a sentence might be part of an ideal explanation of an event’s occurrence yet not be part of an appropriate answer to a question about why the event occurred in a particular context. (See, for example, Railton 1978, Lewis 1986) For example, it might be true that the presence of oxygen helps to explain a fire even though it is inappropriate to cite the presence of oxygen when answering the question, “Why was there a fire?” across a wide variety of standard contexts. Similarly, it may be that there are many contexts in which the question, “Why did this [chance] event occur?” is appropriately answered by mediate explanatory information about laws, prior conditions or causes, rather than by immediate explanatory information about the event’s chance of occurring.

  13. Thanks to an anonymous referee for pressing this point, which Hempel called “the problem of explanatory ambiguity” (Hempel 1695, p. 709).

  14. See my manuscript Chance Explanation.

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Correspondence to Katrina Elliott.

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Thanks to Pamela Hieronymi, Michaela McSweeney, Seana Shiffrin and two anonymous referees for their helpful comments on earlier drafts.

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Elliott, K. Where are the chances?. Synthese 199, 6761–6783 (2021). https://doi.org/10.1007/s11229-021-03092-w

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