Abstract
Epistemic theories of objective chance hold that chances are idealised epistemic probabilities of some sort. After giving a brief history of this approach to objective chance, I argue for a particular version of this view, that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. The main argument for this view is the demonstration that it entails all of the commonly-accepted properties of chance. For example, this analysis entails that chances supervene on the physical facts, that the chance function is an expert probability, that the existence of stable frequencies results from invariant chances in repeated experiments, and that chances are probably close to long-run relative frequencies in repeated experiments. Despite these virtues, epistemic approaches to chance have been neglected in recent decades, on account of their conflict with accepted views about closely related topics such as causation, laws of nature, and epistemic probability. However, existing views on these topics are also very problematic, and I believe that the epistemic view of chance is a key piece of this puzzle that, once in place, allows all the other pieces to fit together into a new and coherent way. I also respond to some criticisms of the epistemic theory that I favour.
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Notes
For example, when Hoefer (2007) surveys the existing views of chance, and finds them all wanting, he does not mention the epistemic view.
See for example Franklin (2009, pp. 161–2) for a statement of this argument.
Of course one can explain human behaviour in epistemic terms, but here we are talking about inanimate processes.
Here I just mean that, had the building not been given any rating, its performance during the earthquake would not have been any different. The assignment of a low rating did not help to destroy it.
A passionate defense of this view is given by Frege in his introduction to the Grundlagen (1884). For an opposing view see Cooper (2001) who proposes an evolutionary origin not just of human cognition, but also of the laws of logic themselves. He writes (p. 5) “The laws of logic are neither preexistent nor independent. They owe their very existence to evolutionary processes, their source and provenance.” I agree with Frege (1884) that if views like Cooper’s were correct then “... there would no longer be any possibility of getting to know anything about the world and everything would be plunged in confusion ... this account makes everything subjective, and if we follow it through to the end, does away with truth.” (p. VII).
The causal context includes not just the things that will actually cause E, but also all factors that might help to bring E about. For example, flipping two coins rather than one increases the chances of getting at least one head, even in cases where the extra coin lands tails.
Event C may ‘partially’ cause E in the sense that C may be merely part of the total cause of E. But a total cause cannot (concretely) cause E merely to a certain degree.
In medicine, for example, double-blind experimental studies are designed to measure such chance increases and reductions.
I am aware that such composition inferences are not all valid, but this one surely is. It is no different from the following: If every person in this room is from Portugal, then the aggregate of the people is also from Portugal.
This was one of the objections made in Lewis (1980) to his own (quickly dismissed) epistemic theory of chance.
“In this paper I do not consider regularity or “best system” accounts of laws, or the theories of chance developed along similar (Humean) lines. The conceptual chasm between these views and mine so wide that there is little common ground on which to base an argument. This is not to say that there can be no rational grounds for choosing one camp or another, for one see can how successful (fertile, intellectually satisfying, etc.) each approach is and judge between them on those grounds.
In making this point, David Lewis (1983, p. 366) nicely quipped that being called ‘Armstrong’ doesn’t give a person big biceps.
‘Consequentialist’ might be better, but this word is too strongly associated with a view about ethics.
Impervious events are often misidentified as being necessary. Consider, for example, the so-called “necessity” of the past, which is really just the causal independence of the past from present events.
In a similar way, the inferentialist view of laws is consistent with theological voluntarism concerning natural laws, as espoused by William of Ockham for example.
The Lagrangian and Hamiltonian are different mathematical functions that express essentially the same information about the system, in the sense that either can be derived from the other.
It should be noted that the epistemic view of chance is one according to which, as Lewis (1980, p. 112) put it, “the complete theory of chance for every world, and all the conditionals that comprise it, are necessary”. (Thus, Lewis’s problem of undermining futures does not arise for the epistemic view.) The causal context M consists of the past history of the world together with D (the dynamical nature), and all chances logically follow from M.
Or almost certain. It is shown in Johns (2002, pp. 31–32) that the rational number (quotient) 1 represents actual certainty, whereas the real number (Dedekind cut or Cauchy sequence) 1 represents a degree of belief that is either certain or very close to certainty. The same distinction applies to probability zero.
This understanding of deference to experts agrees with the account given in Joyce (2007).
I note that an incomplete description of a pair <X, Y> will not factorise into a conjunction, in some cases, and argue that this fact can account for the existence of quantum-mechanical correlations, such as in the famous EPR experiments. My view is that the quantum state vector represents maximal-yet-incomplete information about the system. Generally speaking, epistemic views of chance go hand-in-hand with epistemic interpretations of quantum states, such as those of Spekkens (2007) and Bub (2007).
As stated in the introduction, I take the view that to explain an event is to infer it (to some degree, not necessarily with certainty) from a hypothesis about the concrete causes of the event.
The description of a particular experiment will involve various parameters such as lengths and angles, and the chance of a given outcome in that experiment may be determined by some algebraic expression involving these parameters.
See van Fraassen (1989, pp. 78–81) for a summary of the difficulties.
See van Fraassen (1989).
The ‘properties’ of objects in an epistemic state are also subjective, as internal objects may have magical powers, be made of the celestial aether, and so on.
That is the point of the following joke: A farmer had two horses, and for years he couldn’t tell them apart, until one day he noticed that the black one was an inch taller than the white one.
As mentioned above, I take it that explaining a datum requires predicting to some degree from a theory about its causes.
More precisely, diffusion is far more likely to occur in that direction of time than in the reverse direction.
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Johns, R. Epistemic theories of objective chance. Synthese 197, 703–730 (2020). https://doi.org/10.1007/s11229-018-1719-6
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DOI: https://doi.org/10.1007/s11229-018-1719-6