Abstract
This paper shows how a particular resiliency-centered approach to chance lends support for two conditions characterizing chance. The first condition says that the present chance of some proposition A conditional on the proposition about some later chance of A should be set equal to that later chance of A. The second condition requires the present chance of some proposition A to be equal to the weighted average of possible later chances of A. I first introduce, motivate, and make precise a resiliency-centered approach to chance whose basic idea is that any chance distribution should be maximally invariant under variation of experimental factors. Second, I show that any present chance distribution that violates the two conditions can be replaced by another present chance distribution that satisfies them and is more resilient under variation of experimental factors. This shows that the two conditions are an essential feature of chances that maximize resiliency. Finally, I explore the relationship between the idea of resilient chances so understood and so-called Humean accounts of chance—one of the most promising recent philosophical accounts of chance.
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Notes
Famously, Lewis (1986) claimed that his Principal Principle is the sole condition on chance: it captures all we know about chance. But, as shown by Arntzenius and Hall (2003), Lewis’s claim cannot be rationally sustained. Similarly, Schaffer (2007) has argued that besides the Principal Principle, there is a number of equally plausible conditions that inform our understanding of chance.
Here, the original formulation of these conditions is slightly rephrased to fit in with the framework presented in this paper.
As explained in Sect. 2, \({\mathcal {C}}_{\mathcal {F}}\) is understood as a set of Ch’s refinements that accommodate information about experimental factors from the set \({\mathcal {F}}\).
Notice that there are several methods by which one can show how \(C_{ch_{w}}\) is part of \({\mathcal {A}}\), and so how our two conditions are meaningful expressions in the sense of probability theory. Most notably, one can use the theory of higher-order probabilities developed in Gaifman (1988) and take \({\mathcal {A}}\) to be an element of a higher-order probability structure. Or, following Rédei and Gyenis (2016), one could take \({\mathcal {A}}\) to be an extension of some underlying algebra \({\mathcal {B}}\), which is the domain of \(ch_{w}\), and require certain consistency conditions to hold. For the purposes of this paper, I follow the approach developed in Bana (2016) in the context of the Principal Principle. That is, I take it that C1 and C2 are themselves consistency conditions that we have to require for Ch on \({\mathcal {A}}\) when prior chances are assigned to propositions about posterior chances. Therefore, there is only one algebra \({\mathcal {A}}\) that includes propositions like \(C_{ch_{w}}\), and Ch and \(ch_{w}\) are defined over this algebra.
Let me mention two successful applications of Humean accounts of chance. Loewer (2001) uses Lewis’s conception of Humean chance to resolve what he calls the paradox of deterministic probabilities, to wit, the problem of reconciling the fact that some theories posit non-trivial probabilities for events not to occur with the fact that those events are determined to occur. In a similar vein, though more specifically, Frigg and Hoefer (2015) use their Humean account of chance to explain the nature of probabilities posited by classical statistical mechanics in deterministic settings.
Also, following the approach developed in Bana (2016), I take this assumption to express a consistency condition that we have to require for \(ch_{v}\) on \({\mathcal {A}}\) when it assigns chances to propositions about later chances.
Lewis (1994, p. 482) gave the following example of an undermining future: “For instance, there is some minute present chance that far more tritium atoms will exist in the future than have existed hitherto, and each one of them will decay in only a few minutes. If this unlikely future came to pass, presumably it would complete a chancemaking pattern on which the half-life of tritium would be very much less than the actual 12.26 years.”
References
Arntzenius, F., & Hall, N. (2003). On what we know about chance. British Journal for the Philosophy of Science, 54(2), 171–179.
Bana, G. (2016). On the formal consistency of the principal principle. Philosophy of Science, 83(5), 988–1001.
Banerjee, A., Merugu, S., Dhillon, I. S., & Ghosh, J. (2005). Clustering with Bregman divergences. Journal of Machine Learning Research, 6, 1705–1749.
Bigelow, J., Collins, J., & Pargetter, R. (1993). The big bad bug: What are the humean’s chances? British Journal for the Philosophy of Science, 44(3), 443–462.
Briggs, R. (2009). The big bad bug bites anti-realists about chance. Synthese, 167(1), 81–92.
Frigg, R., & Hoefer, C. (2015). The best humean system for statistical mechanics. Erkenntnis, 80(3), 551–574.
Gaifman, H. (1988). A theory of higher order probabilities. In B. Skyrms & W. Harper (Eds.), Causation, chance, and credence (Vol. 1, pp. 191–219). Dordrecht: Kluwer Academic Publishers.
Ismael, J. (1996). What chances could not be. British Journal for the Philosophy of Science, 47(1), 79–91.
Lewis, D. (1986). A subjectivist’s guide to objective chance. In D. Lewis (Ed.), Philosophical papers, (Vol. 2, pp. 83–132). Oxford: Oxford University Press.
Lewis, D. (1994). Humean supervenience debugged. Mind, 103(412), 473–490.
Loewer, B. (2001). Determinism and chance. Studies in History and Philosophy of Science Part B, 32(4), 609–620.
Lyon, A. (2011). Deterministic probability: Neither chance nor credence. Synthese, 182(3), 413–432.
Mitchell, S. D. (2000). Dimensions of scientific law. Philosophy of Science, 67(2), 242–265.
Pettigrew, R., & Titelbaum, M. G. (2014). Deference done right. Philosophers’ Imprint, 14(35), 1–19.
Predd, J., Seiringer, R., Lieb, E., Osherson, D., Poor, H. V., & Kulkarni, S. (2009). Probabilistic coherence and proper scoring rules. IEEE Transactions on Information Theory, 55(10), 4786–4792.
Rédei, M., & Gyenis, Z. (2016). Measure theoretic analysis of consistency of the principal principle. Philosophy of Science, 83(5), 972–987.
Schaffer, J. (2003). Principled chances. British Journal for the Philosophy of Science, 54(1), 27–41.
Schaffer, J. (2007). Deterministic chance? British Journal for the Philosophy of Science, 58(2), 113–140.
Skyrms, B. (1977). Resiliency, propensities, and causal necessity. The Journal of Philosophy, 74(11), 704–713.
Skyrms, B. (1978). Statistical laws and personal propensities. In PSA: Proceedings of the Biennial meeting of the philosophy of science association (pp. 551–562).
Skyrms, B. (1980). Causal necessity: A pragmatic investigation of the necessity of laws. New Haven: Yale University Press.
Skyrms, B. (1984). Pragmatism and empiricism. Yale: Yale University Press.
van Fraassen, B. (1989). Laws and symmetry. Oxford: Oxford University Press.
Vranas, P. (2002). Who’s afraid of undermining? Why the principal principle might not contradict humean supervenience. Erkenntnis, 57(2), 151–174.
Woodward, J. (2003). Making things happen. Oxford: Oxford University Press.
Acknowledgements
I would like to especially thank Jan-Willem Romeijn, Richard Pettigrew, and Rafal Urbaniak for incredibly helpful comments on earlier versions of this paper. I am also indebted to the anonymous referees of Erkenntnis for detailed comments.
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Dziurosz-Serafinowicz, P. Chance, Resiliency, and Humean Supervenience. Erkenn 84, 1–19 (2019). https://doi.org/10.1007/s10670-017-9944-9
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DOI: https://doi.org/10.1007/s10670-017-9944-9