Abstract
Many philosophers think that part of what makes an event lucky concerns how probable that event is. In this paper, I argue that an epistemic probability account of luck successfully resists recent arguments that all theories of luck, including probability theories, are subject to counterexample (Hales in Noûs 50(3):490–508, 2016). I argue that an event is lucky if and only if it is significant and sufficiently improbable. An event is significant when, given some reflection, the subject would regard the event as significant, and the event’s epistemic probability, determined by the subject’s evidence, is the only kind of probability that directly bears on whether or not the event is lucky. I conclude with some lessons that are applicable to probability theorists of luck generally, including those defending non-epistemic probability theories.
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Notes
Depending on how one interprets ‘probability account of luck’, Steglich-Petersen’s account may not be a probability account. The notion of probability seems to have no direct role in his analysis, which is stated in terms of knowledge. I discuss the details of his account in section three. In any case, Steglich-Petersen is certainly defending an epistemic account of luck: whether it is an epistemic probability account of luck is disputable.
Hales acknowledges this. “...[M]y concern here will be with what is added to the significance condition to have a complete theory of luck” (pp. 491–492). Nevertheless, his challenges to theories of luck generally ignore the significance condition.
For example, Pritchard (2005) endorses what I call a counterfactual subjectivist significance condition, while Coffman (2007) endorses an objective significance condition. Pritchard recently (2014) denied that significance is necessary for luck. Ballantyne (2012) has the best discussion of significance in the literature.
That is not to say the epistemic probability of being shot in the head must be 1/6. The a priori probability of an event does not always equal the epistemic probability of the event. Perhaps I have evidence that the event is rigged: my friends, knowing that I am foolhardy but not wanting to hurt me, have not loaded the gun. They just want to see if I will pull the trigger. Or perhaps I have evidence that someone related to the event set-up has recently taken out a very large life insurance policy on me, and the gun feels a bit too heavy to be holding just one bullet. Such considerations could easily make the epistemic probability of death-upon-trigger-pull closer to or further from 1/6.
The distinction drawn here between objective and subjective accounts is useful, but I am unconvinced that the divisions lie where Broncano-Berrocal suggests. Many epistemologists think evidential probabilities are logical truths, which suggests that they are objective, not subjective. And epistemological externalists characteristically take evidential relations to be contingent, determined by features of the world, which points toward categorizing that view of probability as an objective probability account. However, what counts as lucky for a subject according to an epistemic probability account depends upon what evidence a subject possesses, which tells in favor of treating any epistemic account as a subjective account, even if epistemological notions used to define the view are apparently ‘objective’ notions. In sum, take the subjective versus objective division lightly. Also see footnote 14.
One could specify a probability condition for a confidence account of luck that (i) defines how lucky an event is in terms of how confident the subject is that the event will occur and that (ii) claims that how confident one is that an event will occur is determined by one’s evidence. But that would just be an epistemic probability account with an unnecessary part.
As stated, this is only a necessary condition on Steglich-Petersen’s view.
This phrasing suggests that Steglich-Petersen holds that knowledge is directly affected by stakes. In the quote above, he claims both that knowledge and the truth of knowledge attributions are directly affected by stakes. Invariantists about knowledge attributions accept that “S knows that p” is true when S knows that p; so, it is unimportant whether we attribute to Steglich-Petersen a view about knowledge or about knowledge attributions.
(Stoutenburg 2015, p. 328) contains a similar argument.
In my (2015) I defined the condition this way: “Event E is lucky to some degree for subject S only when E was/is not epistemically guaranteed for S.” My new formulation is an improvement for a few reasons. First, it is clearer to make temporal references explicit, as I do here. Second, the locution “epistemically guaranteed” that I used in my (2015) is slightly unfortunate, as one may reasonably object that when one knows that p, p is epistemically guaranteed for one. But if that view is combined with a view that allows that one’s knowledge is constituted by factors in addition to belief and the probability of a proposition on one’s evidence—as every fallibilist view must—then those accounts eliminate more luck than I think is plausible. So, it is better to state unequivocally that luck is possible whenever one’s evidence does not rule out the event’s occurrence. Third, I previously defined the probability condition as a necessary condition on luck rather than as a biconditional for analyzing probability for luck. I here define the probability condition as necessary and sufficient for probability for luck, and explicitly add that this biconditional and the significance biconditional jointly analyze luck. The view is the same, but the presentation of the conditions is clearer here.
First, Steglich-Petersen could, in principle, make the same claim. However, as I have argued above, incorporating an interest-relative conception of knowledge into one’s probability condition for luck problematically separates an event’s epistemic probability from how probable the event is on one’s evidence.
Second, this account of luck implies a kind of infallibilist conception of knowledge, in that one knows that an event will occur or that a proposition is true only when one’s evidence guarantees it. Infallibilists about knowledge have been a minority for a while, but are starting to reappear, especially thanks to the defense of infallibilism in Williamson (2000). Nevertheless, infallibilist conceptions of knowledge are a minority view. Third, one might argue that a proposition being certain on one’s evidence is insufficient for knowledge, perhaps because one must also not be subjected to higher-order defeat of the sort that may occur in a case of peer disagreement. The issue is difficult and a serious treatment is beyond the scope of this paper, so I will simply state my preferred view without arguing for it. I think that if one really has evidence that guarantees the truth of a particular proposition, then one is justified in rejecting further evidence against that proposition, including higher-order evidence like testimony from a disagreeing peer (Unger 1975). If one were to encounter further evidence, including higher-order evidence, that really did reduce the probability that the proposition is true, then one would not know the proposition, and it would be reasonable to say that one never did know it. I recognize that all of those claims are highly controversial. I should also point out that someone interested in accepting EAL but who does not want to accept all of these claims about knowledge could respond to the concern about defeat by simply conceding that certainty on one’s evidence is insufficient for knowledge. I thank an anonymous referee for encouraging me to discuss this issue.
Those sympathetic with an epistemic analysis of luck will likely let their metaepistemological views determine their analyses of epistemic probability for luck. One might be an actual frequentist reliabilist and understand ‘E makes probable P’ in terms of the actual frequency of events described by P happening when E in the actual world. E.g. the probability of a coin toss landing heads is .5 if, in the actual world, coins land heads half of the time they are tossed. (Cf. Alston’s 1988 reliable indicator theory of justification.) Or one might be a transglobal reliabilist and understand E making probable P as a matter of the percentage of E-worlds that are P-worlds among worlds very much like ours as far as experience is concerned (cf. Henderson and Horgan 2006). And so on. See Conee and Feldman (2008) and Comesaña (2010) for discussion of the flexibility of evidentialist views in epistemology. The flexibility owes to the need to analyze ‘evidence’ and ‘epistemic probability’ in order to get a complete theory of justification. While I prefer the account described in the main text (and supplemented in the next footnote) to these alternative epistemic accounts, I still think that these epistemic accounts are superior to non-epistemic accounts of luck.
In addition to an account of evidence, a fully worked-out epistemic probability account of luck needs an account of the evidential relation. I accept that the epistemic making-probable relation that holds between a body of evidence and an event (or proposition) is a logical relation. See Fumerton (1995), where a logical interpretation of probability is put to work for a theory of epistemic justification, and of course (Keynes 1921), where the idea is first proposed. I think that only a logical conception of epistemic probability can be used to satisfactorily address deep skeptical concerns (Fumerton 1995). However, one could in principle incorporate a different conception of probability into an epistemic probability account of luck.
One might further worry that my account requires too much cognitive sophistication of subjects like small children who are nevertheless intuitively beneficiaries of luck. Small children are more cognitively sophisticated than they get credit for, and consequently such objections are questionable, as I argue in Stoutenburg (2017).
Steglich-Petersen’s epistemic probability account can also handle the case as follows. The stakes for getting the answer correct are very high, which makes it difficult to know what the correct answer is. Since your evidence does not make it probable enough for you to know in this situation, answering correctly is lucky for you.
Note also that if some accepted principles of modal logic are interpreted as epistemic principles, with the ‘necessity’ operator interpreted as ‘knowledge’, then necessary truths should count as known because they are necessary. I reject that consequence, thus I also deny that these principles of modal logic describe the same property that we express when we use the word “knowledge”, rather than some idealized epistemic property. This denial is motivated. For instance, traditional epistemologists overwhelmingly reject the principle that if one knows that p, one knows that one knows that p: but that principle is a straightforward application of the principle that if it is necessary that p, then it is necessary that it is necessary that p, given an epistemic interpretation. I thank an anonymous reviewer for prompting me to discuss this.
For a helpful discussion of ways to understand degrees of luck, see Church (2013).
Steglich-Petersen’s account could say the same thing: since Cobb could not know that any individual at-bat would be a hit, a hit is always a little lucky.
I take the fact that “You are lucky to X” and “I am lucky to X”—when they are attributions of the same property to the same individual regarding the same event from different perspectives—vary in communicative content to suggest that there is a negative implicature correlated with second-person and third-person luck attributions. We get offended if someone says we are lucky for something we think we have earned, even if we are prepared to attribute luck to ourselves. Given that evidence, it is a mistake to think there is an entailment from “You are lucky to X” to “You do not deserve credit for X,” because, again, you might be willing to call yourself lucky while still thinking that you deserve credit.
Because Steglich-Petersen does not have a separate significance condition, his account, unlike EAL, is open to the problem of diachronic luck. Note, furthermore, that a counterfactual subjective significance condition is needed to account for the problem of diachronic luck, because only that sort of significance condition can account for how seemingly contradictory attributions of significance by a single individual to a single event at different times can both be true.
I thank Brian Collins and anonymous reviewers for comments on drafts at various stages.
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Stoutenburg, G. In defense of an epistemic probability account of luck. Synthese 196, 5099–5113 (2019). https://doi.org/10.1007/s11229-018-1699-6
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DOI: https://doi.org/10.1007/s11229-018-1699-6