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Powers, Probabilities, and Tendencies

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Abstract

In this article, I aim at showing how powers may ground different types of probability in the universe. In Section 1 I single out several dimensions along which the probability of something can be determined. Each of such dimensions can be further specified at the type-level or at the token-level. In Section 2 I introduce some metaphysical assumptions about powers. In Section 3 I show how powers can ground single-case probabilities and frequency-probabilities in a deterministic setting. Later on, in Section 4, I move to a theoretical framework where the falsity of determinism is assumed. Within such a framework, I first argue that some probabilities are grounded on basic powers (i.e., powers whose activation is not determined by anything else). Moreover, in Section 5, I introduce tendencies and suggest that they are endowed with specific degrees of activation that may change over time. Such degrees explain why tendencies are more likely to be activated than non-activated, or vice versa. In Section 6 I compare my account of tendencies with other accounts. Finally, in Section 7, I anticipate some general objections against my account – objections that it shares with propensity-accounts of probability – and against degrees of activation of tendencies.

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Notes

  1. Similar projects have been pursued by Barker (2009) and Anjum and Mumford (2021). Barker takes dispositional properties as grounding particular chance assignments, where chances are distinguished from other kinds of probabilities. However, dispositional properties (and their strength) are founded in turn on chances. Anjum and Mumford hold that non-deterministic powers (i.e., tendencies and powers with equal distributions of outcomes as their manifestations) ground all kinds of probabilities, including frequencies. The distinctions between my account and these accounts will emerge from what follows.

  2. The locus classicus for these theories is Ramsey (1926).

  3. On these issues and for further introductory issues on probability, see Gillies (2000), Mellor (2005), Handfield (2012), Childers (2013) and Hájek (2019).

  4. On the varieties of ontological dependence, see Tahko and Lowe (2020).

  5. I do not rule out here the possibility that one and the same token-effect can occur at distinct places taken together at one and the same time.

  6. Again, I do not rule out here the possibility that one and the same token-trial can occur at distinct places taken together at one and the same time.

  7. As we shall see, if we consider basic powers, trial-probabilities reduce to effect-probabilities. For basic powers do not have distinct activation conditions (i.e., distinct trials) in virtue of which their effects are reached.

  8. This is the classical definition of causal determinism (see Hoefer, 2016). I do not rule out that there are also other forms of determinism. However, for what concerns probabilities and powers, I shall only be concerned with causal determinism.

  9. Classical frequency theories have been expounded by Reichenbach (1949) and Von Mises (1957).

  10. Again, even if I use the verb “ground” here and elsewhere, I am not committed to the acceptance of any recent theory of metaphysical grounding. On the contrary, my use of “ground” only points to some generic enough notion of ontological dependence, to be further specified according to the preferences of my readers.

  11. The most relevant propensity theories of probability have been presented by Popper (1957, 1959, 1990), Mellor (1971), Giere (1973), Fetzer (1974, 1981), Jackson and Pargetter (1982), Miller (1991), Gillies (2000).

  12. See Paolini Paoletti (2020, 2021a). With respect to passive powers, I argued that they are redundant, as active powers are enough in order to account for whatever happens in the universe. For a similar conclusion, see also Wahlberg (2019). In Paolini Paoletti (2021a) I also argued that someone’s power to learn may be seen as an active power or as a way of describing an active power. Therefore, when I shall introduce below my power to learn Japanese, such a power will count as a bona fide one in my perspective.

  13. This gives rise to a well-known problem discussed, among others, by Molnar (2003): a power may exist and be what it is even if and when it does not manifest itself, i.e., even if and when its manifestation does not exist/occur. How can the former depend on the latter? I discussed this problem in Paolini Paoletti (2016). Roughly, I defended the view that existing powers may depend for what they are even on non-existing/non-occurring manifestations, insofar as the latter are endowed with definite identity conditions. Obviously, this does not imply that the former also depend on the latter for their existence.

  14. In Paolini Paoletti (2020, forthcoming), I criticised those models of causation in which causal processes result from the joint manifestations of several powers (e.g., the vector model of Mumford & Anjum, 2011) or from the mutual manifestations of active and passive powers taken in pairs (see Heil, 2003; Martin, 2008).

  15. I expanded on this point in Paolini Paoletti (2020).

  16. Even if I always use “F1”, …, “Fn” for features circumscribing type-effects, type-bearers and type-trials, this does not imply that one has to choose the same features for the sake of circumscribing all the latter dimensions. Namely and for example, the feature of being a golden coin does not have to circumscribe the type-bearer, the type-trial and the type-effect.

  17. An interesting project that is connected with the ideas presented in this Section is the one pursued by Barton et al. (2012). The authors show how one may determine the probability ascribed to a certain universal disposition possessed by a certain type of bearers with a certain type of trial and a certain type of realization and the probability ascribed to some specific disposition possessed by some specific bearer with a certain type of trail and a certain type of realization. They also argue that the former can be used in order to determine the latter. However, both kinds of probabilities have type-dimensions. Moreover, even the probability ascribed to specific dispositions is determined by appealing to hypothetically infinite sequences of trials. This is in contrast with my project, in which the type-dimensions of probability are ultimately based on highly specific powers or on specific activations of powers with ‘repeatable’ or ‘universal’ features.

  18. More on this point in Paolini Paoletti (2021b).

  19. Additionally, please note that tendencies can also acquire a 0,5-degree of activation, though they turn out to have the latter in a different way in comparison with the basic powers of Section 4. See Section 7 for a discussion on this point.

  20. See also Schmidt-Petri (2008).

  21. I argue for this controversial thesis in Paolini Paoletti (forthcoming). However, I admit that a certain power may be activated in virtue of the activation of other powers.

  22. Degrees or strengths of propensities are also considered by Giere (1973), Fetzer (1974) and Sapire (1992).

  23. For an overview, see Mellor (2005), Childers (2013) and Hájek (2019).

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Acknowledgements

I am grateful to one reviewer for her helpful comments that contributed to improving this work. This study received financial support from the Italian “Ministero dell’Istruzione, dell’Università e della Ricerca”, as part of the PRIN-2017 Project “The Manifest Image and the Scientific Image” (prot. n. 2017ZNWW7F).

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Paolini Paoletti, M. Powers, Probabilities, and Tendencies. Philosophia 50, 2035–2067 (2022). https://doi.org/10.1007/s11406-021-00467-8

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