Abstract
I argue that inferences from highly probabilifying racial generalizations (e.g. believing that Jones is a janitor, on the grounds that most Salvadoreans at the school are janitors) are not solely objectionable because acting on such inferences would be problematic, or they violate a moral norm, but because they violate a distinctively epistemic norm. They involve accepting a proposition when, given the costs of a mistake, one is not adequately justified in doing so. First I sketch an account of the nature of adequate justification—practical adequacy with respect to eliminating the \(\lnot p\) possibilities from one’s epistemic statespace. Second, I argue that inferences based on demographic generalizations tend to disproportionately expose group members to the risks associated with mistakenly assuming stereotypical propositions, and so magnify the wrong involved in relying on such inferences without adequate justification.
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Notes
Gendler (2011), p. 3. The case is taken from Franklin (2005)’s memoir, Mirror to America (p. 340). Notice that we can make the evidential likelihood that Franklin is staff arbitrarily high by increasing the number of black staff members. If your first reaction to this case is to think that the woman doesn’t have good evidence, it cannot be because she lacks information on which it is highly probable that Franklin is staff.
‘Acceptance’ as I am using it is thus broadly like the notions defended by Cohen (1989) and Bratman (1992), namely an attitude of ‘taking for granted’ to frame deliberation that is incompatible with thinking p to be false. It is importantly unlike Stalnaker (1984)’s notion of acceptance, which resembles supposing or pretending in allowing that an agent may accept p in one domain while simultaneously rejecting it in another; it is also unlike the notion in Engel (1998) which explicitly aims only at utility and permits agents to accept propositions they take to be false. My thanks to Julianne Chung for encouraging me to explicitly characterize the attitude.
‘Belief’ names two different attitudes: degrees of belief, or credences, are the epistemic probability that p for S, while all-out or full belief is an all or nothing attitude of confidence in the proposition. Since acceptance is a binary attitude, it should be distinguished sharply from the degreed notion; in what follows, I’ll use ‘credences’ to refer to degrees and reserve ‘belief’ for full belief. Whether acceptance in my sense amounts to belief depends on the theoretical role assigned to full belief. If we characterize the attitude as something like a disposition to ‘treat as true’, to ‘premise’, or to ‘take for granted’ [as Ross and Schroeder (2014) do], then acceptance and belief appear to be the same attitude. Alternatively if we insist on distinguishing premising from ‘feeling to be true’ or credence 1, and take only the latter to be belief [as Cohen (1992) does], then acceptance cannot be the same attitude as belief. But insofar as the two differ, it is acceptance, rather than belief, that implies willingness to act as if p, and so it is acceptance that, together with her credences, guides an agent’s action in a context.
gatecrashers, also known as the ‘paradox of the rodeo’ is based on hypothetical given by Cohen (1977), The Probable and the Provable, pp. 70–83. The buses case is based on Smith v. Rapid Transit, Inc. (317 Mass. 469, 58 N.E.2d 754 (1945).
In her analysis of the problem of statistical evidence, Thomson (1986) says something along these lines, suggesting that legal findings are subject to a norm like ‘Assert p only if the expected costs to the hearer of relying on p are low enough.’
We can model this either as contracting the epistemic space \(\Omega \) by removing all possibilities incompatible with p, or as setting the probability of those possibilities to 0. The differences between the two will likely have no effect for our purposes, but the former is more realistic as a model of how actual agents allocate cognitive space. The models diverge where there are uncountably infinite alternatives or in a system that doesn’t validate countable additivity. One cannot have positive credence in a disjunction all disjuncts of which have been excluded from the epistemic space (the disjunction will be undefined), but one can when all the disjuncts are just set to 0 [see Arntzenius et al. (2004)].
A prominent view in contemporary epistemology holds that in general, pragmatic concerns about the potential costs of error and the benefits of success encroach on knowledge: it is harder to know or have adequate evidence to justify believing p in ‘high stakes’ contexts. Regardless of its merits as a view about knowledge, something like this picture is attractive for acceptance. Beyond concerning acceptance rather than knowledge, the account I offer departs from standard articulations of pragmatic encroachment in two key ways. First, standard pragmatic encroachment proposals remain thoroughly probabilistic: the effect of high stakes is just to raise the minimum threshold of how probable the evidence must make p in order to justify accepting p. I advocate modeling the demand not as a difference in probability threshold, but strength: you need evidence that can function to dismiss a salient error possibility, and even extremely high probability generalizations often can’t play this role. Second, I replace the somewhat mysterious talk of ‘stakes’ with the comparatively tractable notion ‘practical adequacy.’ Worsnip (2015) and Anderson and Hawthorne (forthcoming) show that it is non-trivial to define a decision-theoretic notion of stakes that will play the role needed to underwrite the classic judgments of pragmatic encroachment. Russell (forthcoming) suggests that while we can define a consistent notion, it will be sensitive only to ratios, not to raw magnitudes of outcomes and thus will diverge at crucial points from the rough intuitive notion. Practical adequacy escapes these difficulties.
On this sort of ranking, the value of an action is determined by the sum of the values of each possible outcome weighted by its probability on S’s evidence. Actions that are top-most in the ranking count as ‘best’, though because a partial ordering allows for ties and permits some alternatives to be incommensurable, there can be multiple ‘best’ actions. The rankings may be made sensitive to rights and other classically deontological concerns by invoking a dual-ranking evaluative scale [like the one proposed by Portmore (2008)], and can allow agents to discount costs to themselves, or allow personal costs to weigh against supererogatory moral values, if desired.
Roughly this notion of practical adequacy is articulated in Anderson and Hawthorne (forthcoming), who offer the following definition: “S is practically adequate with respect to p iff the top-ranked element(s) in S’s actual preference ranking do not differ from the top-ranked element(s) in her ranking conditional on p.” Locke (2013)’s notion of ‘practical certainty’ is also very similar, but he offers it as a necessary and sufficient condition for rational acceptance (in his terminology, ‘premising’), while I am proposing it only as a necessary condition. The standard can be made more stringent, if desired, by requiring minimal divergence in the n top-most actions.
Enoch et al. (2012) favor sensitivity; Pritchard (2017) advocates safety. Smith (2010) advocates Normic Support, on which e is strong evidence for p if p is more normal, given e, and we require an extra explanation to make e compatible with \(\lnot p\). [Gardiner (2018) also favors a variant of normic support, while Peet and Pitcovski (2018) defend something similar.] Haack (2012) offers a conception grounded in explanatory power and coherence. On any of these, evidence like eyewitness testimony will be stronger than even high-probability generalizations, since the latter are easily consistent with \(\lnot p\) even at the actual world.
If the costs of error are high enough, it may be that no merely probabilistic evidence (short of certainty) can justify S in accepting p, in which case to accept she’ll need strong evidence that p.
If we allow a policy of relying on the market-share evidence to determine fault, we would hold the Blue Bus co. liable for every crash in this region for which we lack more specific evidence, whereas the eyewitness’ risk of false-positive error is not similarly concentrated on one party.
Where a ‘stereotypical proposition’ is roughly that A has some property stereotypically had by his group.
Oberdiek (2008) argues that this modal restriction is how pure risk imposition can harm agents. In that it reduces the space of valuable deliberative alternatives, risk undermines the necessary conditions for the agent’s exercise of autonomy in deciding how to shape her life. It therefore can be a setback to the agent’s strong interest, and thus a violation of his right.
(Parfit 1984, p. 80). In Parfit’s case, “Each of the thousand torturers presses a button, thereby turning the switch once on each of the thousand instruments. The victims suffer the same severe pain. But none of the torturers makes any victim’s pain perceptibly worse.”
Obviously not all operable social signals are adequately avoidable to have this moral effect, and so not all have these epistemic ‘licensing’ effects. To fully address the moral significance of voluntary risk, or thoroughly characterize the conditions under which social signals are morally active in this way would require a longer discussion than I have space for here. I have, however, begun to address this question in other work; see ‘The Case for Conventional Defensive Permissions’, (ms).
In both cases, the woman also disregards a property he has that is lacked by all the staff (wearing a non-uniform in cosmos, being non-white in alibi.) Not all accounts of non-probabilistic evidential strength will consider the woman’s evidence in alibi strong: since p is false, the woman’s evidence is not sensitive, and since the fact that some people are wearing costumes is already part of her total evidence, she needs no additional explanation to make Franklin’s attire consistent with his being a guest. So the fact that he’s wearing a uniform doesn’t normically support p. It’s less clear whether the evidence satisfies a safety standard.
This ‘Problem of the Reference Class’ most famously affects frequentist interpretations of probability, but as Hájek (2007) demonstrates, it is not unique to it.
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Acknowledgements
This work grew out of conversations with Rima Basu, John Hawthorne, and Mark Schroeder, who each also generously gave me comments on several drafts, and to whom I owe particular gratitude. Thanks also to Michael Ashfield, Julianne Chung, Justin D’Ambrosio, Kenny Easwaran, Georgi Gardiner, Alan Hájek, Elizabeth Jackson, Ethan Landes, Dustin Locke, Jonathan Quong, and James Willoughby for helpful comments, and to Matthew Babb, Maegan Fairchild, Sahar Joakim, Colin Klein, Jeremy Strasser, Jake Ross, and the audiences at the 2016 Arché Epistemology Workshop at St. Andrews, the Talbot Philosophical Society at Biola University, and the 2017 St. Louis Annual Conference on Reasons and Rationality, for fruitful discussion of earlier versions of this material.
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Work on this paper was supported by ARC Grant D170101394.
Appendix: Credences and reference classes
Appendix: Credences and reference classes
Arguments that a generalization e justifies accepting a proposition p can be divided into three claims:
- 1.
e yields a high conditional probability for p,
- 2.
So e justifies high credence in p,
- 3.
So e justifies accepting p.
In the main paper I objected only to the move from (2) to (3), but it is worth briefly noting that the move from (1) to (2) is not unproblematic. The following discussion draws heavily on Moss (2018) and Hájek (2007).
The setup of cases like cosmos invites us to assume that one’s credence that a given member of F has a further property G should be roughly equal to the ratio of Fs that are G. The cases mention only a single salient group (race, or presence in the stands, or buses in a city), so the inference seems straightforward. But objects and individuals can be sorted into indefinitely many groups, each of which may have a different ratio of members that are G. To rationally match one’s credence to the ratio of Fs, we need some justification for taking F to be uniquely relevant to whether a thing is G. To illustrate, consider a slight variant on Gatecrashers case:
Gate Crashers 2 — Of the 1,000 people in F, only 10 paid the fare. Of the ten former Boyscouts in F, 9 paid the fare; of the 3 Canadians in F, 2 paid. Alfred is a Canadian former boyscout in F.
Let Ga be the proposition ‘Alfred failed to pay’. Conditional on being in F, P(Ga) \(=\) .99; conditional on Alfred’s being a former boyscout, P(Ga) \(=\) .1; conditional on Alfred’s being Canadian, P(Ga) \(=\) .33. With this as evidence, what credence should a rational agent have in Ga? Presumably in asking this question, we think that credences should be substantially constrained by one’s evidence; the problem is that the evidence is not univocal. It supports multiple, competing probability assignments, depending on which reference class we attend to. To identify what credence is rational, we’ll first need to determine whether being a member of F, or former Boyscout, or Canadian, is most relevant to determining whether Alfred failed to pay.Footnote 21
The justificatory hurdle can be skirted only if we lack any information about alternative classes, so that F is the relevant class simply by being the only class we have any evidence about. While the stipulatively sterile environments of puzzle cases sometimes give information only about one group, the actual world is positively buzzing with detail, giving agents a wealth of classificatory information about the people who are the subjects of their inferences. So in the kinds of inferences the puzzle cases are supposed to be about, the justificatory challenge must be faced head-on: we must have a reason for taking F to be the relevant class before we can assume it is rational to set one’s credences in Ga to match the ratio of Fs that are G.
In other contexts, we justify relying on a particular class by appeal either to the naturalness of the properties on which it is based, or to the causal relationship between those properties and the target property. For instance, though we could divide precious stones by color into any number of classes, including <grue, bleen>, division into <green, blue> is natural in a way that the other alternatives are not. Similarly, though a biopsy reveals many properties about a growth, our knowledge of relevant causal patterns allows us to select some features (size and shape) as relevant and dismiss others (e.g. being discovered on a Tuesday).
Each of these appeals is more dubious when the class we want to rely on is based on a social category like race. Appeals to the naturalness of the property feel out of place, and prospects for a causal connection depend very much on the nature of the target property. This may explain why there seems to be something epistemically objectionable even when racial generalizations are only used to ground credences. Doing so presupposes that race is explanatorily relevant to the target property, which, depending on the property, may be both false and insulting. Some (including Moss) argue that when anticipating the properties of autonomous agents, we must always be sensitive to the fact that A may choose to act differently from others in the reference class. If so, it will take more to justify the relevance of a class for claims about agents than about objects, and demographic generalizations will rarely ground either high credence or acceptance of p.
So it is worth distinguishing three possible cases in which S has a generalization e that yields a high conditional probability for p. There are the two that were the focus of the main paper,
- 1.
e justifies high credence in p, and justifies accepting p,
- 2.
e justifies high credence in p, but not accepting p,
but there are likely also many cases in which
- 3.
e neither justifies high credence in p nor accepting p, because S lacks justification for taking the reference class for e to be uniquely relevant.
I am inclined to think that though statistics about demographic groups will very often lack relevance and hence fail to justify high credence, this need not always be so. Plausibly there are some properties that tend to arise from causal forces (social or natural) that converge on members of these groups, such that group membership is strongly predictive of having the further property. If so, the demographic statistics may justify high credence in these cases, while still failing to justify acceptance.
On the view I have offered, the downstream effects on evidence-gathering and action explain this asymmetry. While accepting involves treating the question whetherp as closed, simply having a high credence in p is compatible with continuing to seek stronger evidence whether p and considering the possibility that \(\lnot p\) when choosing one’s action. It seems morally and epistemically permissible to increase your credence in proportion with your (properly justified) statistical evidence; this credence will still be sensitive to reform in the face of additional evidence. Furthermore, in being attentive to the possibility that \(\lnot p\), agents’ reasoning takes into account the cost of being mistaken whether p; when these costs are high, even agents with high credence will be cautious when making p-dependent decisions.
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Bolinger, R.J. The rational impermissibility of accepting (some) racial generalizations. Synthese 197, 2415–2431 (2020). https://doi.org/10.1007/s11229-018-1809-5
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DOI: https://doi.org/10.1007/s11229-018-1809-5