Abstract
I defend a threefold form of pluralism about chance, involving a tripartite distinction between propensities, probabilities, and frequencies. The argument has a negative and a positive part. Negatively, I argue against the identity thesis that informs current propensity theories, which already suggests the need for a tripartite distinction. Positively, I argue that that a tripartite distinction is implicit in much statistical practice. Finally, I apply a well-known framework in the modelling literature in order to characterize these three separate concepts functionally in terms of their roles in modelling practice.
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Notes
- 1.
Lewisian analyses of chance in the spirit of Hume may be regarded as a variety of frequency accounts for the purposes of this paper.
- 2.
One may in turn wonder whether all bona fide chances ultimately reduce to physical chances. The answer turns on the thorny question of whether the “special” sciences, and indeed ordinary cognition of macroscopic objects and phenomena, ultimately reduce to physics. I very much doubt such reduction is possible or desirable, but my claims in this paper are independent and require neither reductionism to physical chances, nor its denial.
- 3.
Some of Hájek’s arguments (1997) rely on the well-known reference class problems. I am not so interested in them here because they leave open any claim regarding a reduction to propensities, and I am arguing for a full tripartite distinction.
- 4.
- 5.
For a very nice treatment of this issue in connection with Renyi’s axiom system, see Lyon (2013).
- 6.
- 7.
Consider as a rudimentary example two fair coins, each independently obeying a binomial distribution. Suppose that the coins are then physically connected in accordance to a dynamical law that implies correlations amongst them (you can imagine some kind of invisible thread connecting both tail sides). They are thereafter always tossed simultaneously and more likely to fall on the same side. The sample space in the statistical model for this phenomenon must then include both outcome events (“head” and “tails”) for each of the coins, as well as all the joint events (“heads & heads” “heads & tails”, etc). And the probability distribution function defined in this formal model must be consistent with these underlying dynamical facts.
- 8.
A referee helpfully points out that Spanos (2006) defends a similar distinction between structural theory models, statistical models, and observational data, with similar consequences regarding the role of “chance set-ups”.
- 9.
I do not thereby endorse here any of their epistemological claims beyond the tripartite distinction. My account of statistical modelling, for instance, is also consistent – at least for the purposes of the present essay – with the widely accepted claim that models are autonomous relative to both theory and data. See the essays in Morrison and Morgan (1999) for an articulation and defence.
- 10.
They derive the example from Ernst Nagel’s (1961) discussion. One of Bogen and Woodward’s main claims is that the logical positivist accounts of explanation and confirmation suffer from oversimplification of the empirical content of science. The logical positivist emphasis on “observable phenomena” is, according to Bogen and Woodward, an oxymoron. As explained in the text, phenomena are on their account never observable, but always the result of some low level generalizing inferences.
- 11.
In our rudimentary two-coin system example, the theory that describes the dynamics of the system (including the hidden mechanism, such as the connecting thread) is not meant to account for, or explain, any particular two-coin outcome. It is only meant to explain the probability distribution that appears in the formal statistical model for the phenomenon. Similarly no particular outcome may refute this theory other than by compromising the distribution function in the model – for which much more than just one observation will certainly be needed.
- 12.
How would a subjectivist try to account for these distinctions? One way that occurs to me is via Skyrms’ (1977) notion of propensity as resilient subjective probability. Roughly, a probability is resilient if it is immune to (or invariant under) further conditionalization by admissible evidence. While this type of stability strikes me as a good way to mark out one difference between what I call chances and frequencies (the former being stable in a way the latter are not), I do not see how it can possibly account for the robust form of explanatory power that I here ascribe to propensities in relation to chances.
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Acknowledgements
I thank audiences at the BSPS 2015 conference in Manchester and the EPSA15 conference in Dusseldorf for their comments and reactions. Thanks also to the other members of the symposium panel at EPSA15: Luke Fenton-Glynn, Aidan Lyon, and Philip Dawid, as well as two anonymous referees. Research towards this paper was funded by a Marie Curie personal grant from the European Commission (FP7-PEOPLE-2012-IEF: Project number 329430), and research project FFI2014-57064-P from the Spanish Government (Ministry of Economics and Competitiveness).
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Suárez, M. (2017). Propensities, Probabilities, and Experimental Statistics. In: Massimi, M., Romeijn, JW., Schurz, G. (eds) EPSA15 Selected Papers. European Studies in Philosophy of Science, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-53730-6_27
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