Abstract
Various sexist and racist beliefs ascribe certain negative qualities to people of a given sex or race. Epistemic allies are people who think that in normal circumstances rationality requires the rejection of such sexist and racist beliefs upon learning of many counter-instances. This is a common view among philosophers and non-philosophers. But epistemic allies face three problems. First, sexist and racist beliefs often involve generic propositions. These sorts of propositions are notoriously resilient in the face of counter-instances. Second, background beliefs can enable one to explain away counter-instances to one’s beliefs, thus making it rational to retain one’s beliefs in generics in the face of many counter-instances. The final problem is that the kinds of judgements epistemic allies want to make about the irrationality of sexist and racist beliefs upon encountering many counter-instances is at odds with the judgements that we are inclined to make in seemingly parallel cases about the rationality of non-sexist and non-racist generic beliefs. Thus epistemic allies may end up having to give up on plausible normative supervenience principles. In what follows I explain how a Bayesian approach to the relation between evidence and belief can neatly untie these knots. The basic story is one of defeat: Bayesianism explains when one is required to become increasingly confident in chance propositions, and confidence in chance propositions can make belief in corresponding generics irrational.
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Notes
Q1 is an epistemically important question in thinking about the epistemology of sexist and racist beliefs. But it’s not the only important question. For example, consider the following questions:
Q2. In normal circumstances is it irrational to maintain one’s belief that women are less intelligent than men given the fact that one ought to be aware of many intelligent women?
Q3. In normal circumstances is it irrational to maintain one’s belief that women are less intelligent than men given all the reliable testimony one has, or could easily have, to the effect that it’s false.
Space unfortunately prohibits me from discussing these questions in further detail. For more on Q2 see Goldberg (2016) and Benton (2016).
We regularly ascribe properties to kinds, e.g. the dodo bird is extinct, a duck is a biological organism, coffee beans are small, etc. Notice that the truth of such statements doesn’t depend on any member of the kind existing. ‘a duck is a biological organism’ is true even if ducks ceased to exist, and ‘Dodo birds are extinct’ is true in part because no dodo exists.
This is not the only explanation for why encountering so many intelligent women ought to lead Solomon to reject X. Perhaps, as Pace (2011) and Basu (2018) argue, moral considerations can encroach on rational belief even as more familiar pragmatic considerations can. But this does not seem to be the kind of explanation Arpaly and Fricker invite us to consider here, and those resistant to pragmatic encroachment will obviously take issue. It would also be surprising if there were no purely evidential justification for epistemic allies. So my hope is that some kind of purely evidential story can be told even if epistemic allies can help themselves to further resources.
Cf. footnote 3.
To say that theaverage F is G is not to say Fs are G. Suppose every blonde-haired human died. Then it would be true that the average human is not blonde-haired; but it doesn’t follow from this that humans are not blonde-haired. The reason for this is that statements about averages are mathematical functions over a population, but generics are about kinds. Begby (2013) sometimes wrongly treats generic claims as claims about averages.
Since I will resolve this problem we can set aside questions about just how the intuitive advice to “evaluate like cases alike” should be precisely formulated. I’m grateful to Begby (2013) for drawing my attention to the need to treat sexist/racist generics and non-sexist/non-racist generics alike, and thus the puzzle allies face in this regard.
Under the assumption that learningthat P is distinct from having an experienceas of P, this rule for updating is consistent with allowing agents to update in other ways (Miller 2016). The ‘just’ in ‘just upon learning new information’ is meant to exclude complications where an agent might simultaneously learn that P and and have an experience that would somehow conflict with updating on P.
I’m grateful to Alan Hinkle for drawing my attention to some of the implications of this condition in the present discussion.
If an agent can rationally update in ways other than conditionalization (Miller 2016), then being certain that P can be undermined by one’s future experience. But I don’t want to defend epistemic allies on these grounds here.
This point is incompatible with extreme subjective Bayesianism. But even if extreme subjective Bayesianism were the correct account of the kind of rationality epistemologists tend to care about, I suspect that in most practical cases people who believe X will have some degree of doubt in X. And that’s enough to enable extreme subjective Bayesians to make use of the remarks to follow.
Extreme subjective Bayesians reject this, requiring only that agents have coherent credences and conditionalize. But even so, agents have a tendency to be sensitive to their views about the chances even if they’re not required to be. So extreme subjective Bayesians can still make some use of the justification of epistemic allies to follow. Though it will be somewhat more limited. For they will have to hold that if Solomon choses not to calibrate his credences to the chances, then he might well be rational in retaining his belief in X-depending on his priors.
...where ‘random’ is to imply not at the university or any other circumstance that screens for intelligence and an equal ratio of men to women.
That is, we reach p(E1) = .22 with an application of the law of total probability:
\(\hbox {p(E1)} = \hbox {p(E1}|\hbox {H9)p(H9)} + \hbox {p(E1}|\hbox {H8)p(H8)} + \hbox {p(E1}|\hbox {H7)p(H7)} + \hbox {p(E1}|\hbox {H6)p(H6)} + \hbox {p(E1}|\hbox {H5)p(H5)}\).
Because H9-H5 specify the chances that a randomly encountered intelligent person is a man, it follows that the chances for encountering an intelligent woman are 1- the chances of randomly encountering a man as specified by H9-H5. Since Solomon has calibrated his credences to the chances, \(\hbox {p(E1)} = \hbox {.1x.35} + .\hbox {2x.3} + .\hbox {3x.2} + .\hbox {4x.1} + .\hbox {5x.05} = .22\).
These are easy to calculate. For by conditionalization \(\hbox {p}^{+}\hbox {(Hn)} = \hbox {p(Hn}|\hbox {E1}) = \hbox {p(E1}|\hbox {Hn)p(Hn)}/\hbox {p(E1)}\), and since Solomon has set his conditional credences in E1 given Hn to the chances, \(\hbox {p(E1}|\hbox {Hn)} =\) the chances that E1 obtains given Hn. Solomon’s priors for H9-H5 are given above, and we’ve already determined that his credence in E1 is .22.
Since H9-H6 are mutually exclusive and X is the disjunction of them, p(X) = p(H9) + p(H8) + p(H7) + p(H6).
For if Solomon has randomly encountered 42 recognizably intelligent individuals–half of which are men and half of which are women–and if he conditionalizes on each encounter, then his credence in H5 after learning \(\hbox {E}_{42}\) will be \(\hbox {p(H5}|\hbox {E}_{42}) = \hbox {p(E}_{42}|\hbox {H5)p(H5)/p(E}_{42}) \approx .512\). And his credence in X will be \(\hbox {p(X}|\hbox {E}_{42}) = 1 --\hbox {p(H5}|\hbox {E}_{42}) \approx .488\).
These values are easy to calculate. Since H5 implies that the chances that a randomly selected intelligent person is a woman or a man is .5, it follows that \(\hbox {p(E}_{42}|\hbox {H5}) = .5^{42}\). It’s already part of Solomon’s credence distribution that \(\hbox {p(H5)} = .05\). And \(\hbox {p(E}_{42}) = \hbox {p(E}_{42}|\hbox {H5)p(H5)} + \hbox {p(E}_{42}|\hbox {H9)p(H9)} + \hbox {p(E}_{42}|\hbox {H8)p(H8)} + \hbox {p(E}_{42}|\hbox {H8)p(H8)} + \hbox {p(E}_{42}|\hbox {H7)p(H7)} + \hbox {p(E}_{42}|\hbox {H6)p(H6)}\). Which is: \((.5^{21}\hbox {x.5}^{21}\hbox {x.05}) + (.9^{21}\hbox {x.1}^{21}\hbox {x.35}) + (.8^{21}\hbox {x.2}^{21}\hbox {x.3}) + (.7^{21}\hbox {x.3}^{21}\hbox {x.2}) + (.6^{21}\hbox {x.4}^{21}\hbox {x.1})\). Thus, \(\hbox {p(H5}|\hbox {E}_{42}\)) \(\approx \) .512. Thus, \(\hbox {p(X}|\hbox {E}_{42}) = 1 - \hbox {p(H5}|\hbox {E}_{42}\)) \(\approx \) .488.
To calculate this just take the formulas from the previous footnote and replace the relevant values.
For example, it makes it seem as if Solomon, if he’s rational, is bound to converge on H5 and relatively quickly. That’s a function of our model’s setup. Were Solomon to assign a non-trivial credence to more chance hypotheses, he’d converge so quickly only on a clump of hypotheses surrounding H5 upon encountering many intelligent women about half of which are women–e.g. hypotheses that say the chances that the next encountered intelligent person is a man are either, say, .48 or .49 or .5 or .51 or .52. But which clump of hypotheses near .5 and how quickly is all a function of the priors. I’ll say a bit more about why this doesn’t compromise some of the epistemic lessons I draw in footnote 29.
Notice also that Solomon’s sexism could be more extreme in the sense that he might be very confident that women are objectively far less likely to be as intelligent as men (e.g. he might assign a much higher credence to H7-H9 than to H6). On the other hand, Solomon’s sexism can be less extreme in the sense that he is very confident that women are just somewhat less likely to be as intelligent as men (e.g. he might assign a low to credence to H7-H9 and a very high credence in H6). This is approximately the difference between Distribution 6 and Distribution 3 on the graph above, where Distribution 3 is the original, more extreme form of sexism we assigned Solomon at the beginning. But from the graph it’s easy to see that being less of a sexist in this sense entails that it will take many more encounters with intelligent people for one to assign a credence of less than .5 to H9vH8vH7vH6– it will take approximately 150 encounters where about 50% are women. This is about 3.5 times more encounters than the 42 it would have taken Solomon to reach the same credence in H9vH8vH7vH6 on his original, more sexist distribution. So, surprisingly, being more sexist (i.e. assigning a higher credence to H7-H9) entails that one’s sexism can be moreeasilycorrected than if one is less of a sexist. So the less of sexist one is the less lucky one is in the sense that one’s sexism will be harder to correct. This fact is also perspicuous in the case of Distributions 7 and 8.
This is also true of women at the high school level. That is particularly of note for someone like Solomon since the vast majority of high schools, unlike most universities, do not have admission requirements that exclude unintelligent people. So were someone like Solomon to learn of these studies he’d not be able to appeal to the screening off condition that he did above. For some discussion of the closing of the performance gap in math and science between men and women in high school and college see Goldin et al. (2006).
One referee pointed out that the prejudice and stereotyping literature (Fiske 1998) strongly suggests that stereotypes and prejudices persist because these attitudes are highly resistant to counter-evidence. Plausibly, this is because subjects have something like further information in a variety of these circumstances which screens-off the relevance of the counter-evidence.
Whether or not this observation about human psychology impacts the epistemological points I’m making depends on whether the actual resistance we witness to revising beliefs in claims like X in light of counter-evidence E is rational. This in turn depends on (i) whether or not one’s belief in X was rational to begin with, and on (ii) whether or not one has–in an epistemically relevant sense–further information that screens-off E from X. But regarding (i), it’s not clear that people tend to have nearly the sort of strong evidential support for high credence in X to begin with (recall how carefully constructed Solomon’s case was). And regarding (ii), it is not obvious that people ‘have’–in a relevant sense–further information that allows for screening-off. For in order to have further information in a sense that’s relevant to preserving the epistemic rationality of one’s belief in the face of counter-evidence, it is not enough that one merely believe further propositions. They have to rationally believe them, or be in a position rationally believe them, or stand in some other positive epistemic relation to that further information. So the ‘have’ in “having further information” that’s relevant in thinking about the epistemology of sexist/racist beliefs is itself hiding a normative element. And observing that as a matter of fact people act as iftheyhave further information in an epistemically relevant sense is not enough to show that they do have such information.
Leslie (2008), for example, argues against associating generics with probabilities too closely. In his book on the psychology of stereotypes Schneider (2004, p. 206) also warns against treating agents as if their stereotype beliefs (=beliefs with generic content) involved probabilistic content, even though doing so enables efficient mathematical representations. I’m grateful to Begby (2013) for drawing my attention to this.
Premise 2 didn’t explicitly figure into Solomon’s reasoning. But we should grant it. For without Premise 2 Solomon’s reasoning to the conclusion would be quite poor. For, other things being equal, encounters with many Fs that are G doesn’t give one reason to think most or all or onaverage Fs are G if one has some reason think their encounters fail to accurately represent the Fs. The fact that Solomon, as imagined in the narrative, is sensitive to this kind of concern is evident in the fact that he takes U to screen off X from E (see above).
When considering further chance hypotheses convergence on H5 will take longer. Does that imply that in such cases an agent like would lack a defeater for Premise 2? Not necessarily, for suppose Solomon did not have a .5 credence in H5, but the following disjunctive chance claim:
(NearH5) The chances that the next intelligent person encountered are a man are either .48 or .49 or .5 or .51 or .52.
Suppose his credence in each disjunct here is spread evenly, or near enough. (That is, he’s not, say, .49 confident in the hypothesis that says the chances are .52, and thus he does not have a high credence in a disjunctive claim that say that one’s more likely to encounter an intelligent man than a woman.) In such a case where his .5 credence is spread evenly enough around the cluster of hypotheses specified in (NearH5), it’s still intuitive to think that Solomon would continue to have significant reason to think Premise 2 is false and so should not be highly confident in Premise 2. Accordingly, his credence in the conclusion, X, should not be high either.
One way of explaining this tension is to argue that generics (or at least comparative generics) have probabilistic truth conditions (cf. Cohen 1999). Another way of explaining the rational tension is to argue that comparative generics, like G, have non-probabilistic truth conditions; but that claims about the objective probabilities, like O, can be evidence that those non-probabilistic truth conditions don’t obtain. But we needn’t settle on an explanation of the tension to recognize the tension.
Notice that having a tail is an easily discernible property of animals; we know more or less just what we’re talking about when we are talking about having a tail; and we’re very reliable at discerning among the animals we encounter which have tails–especially when it comes to dogs who have rather obvious tails. But our judgements about intelligence are not at all like this. While we have a vague idea of what intelligence is, it’s not clear exactly what intelligence is; our tests for intelligence are certainly more fallible than our tests for having tails; and the kind of averaging we implicitly engage in thinking about men’s intelligence versus women’s intelligence is surely very imprecise. So while (I think) a reasonable case can be made for idea that we can be rationally certain (or quite close to it) that dogs have tails, there’s no parallel case to be made for thinking anyone in even semi-realistic circumstances can be rationally certain of X.
Technically, tailless breeds of dogs typically just have naturally very short tails relative to their body size. We can ignore this empirical wrinkle in the example, however, and treat having a tail as having a sufficiently long tail relative to one’s body size.
One referee asked whether we could “explain the irrationality of believing that Blacks are more criminal than Whites on strictly evidentialist grounds. Since Blacks are strikingly overrepresented among both perpetrators and victims of homicide, and are overrepresented at every level of the criminal justice system; while Whites, comparatively, are underrepresented.”
Like all beliefs, when it comes to evaluating the rationality of this racist belief a lot turns on a thinker’s over all epistemic situation. That said, I’m inclined to think (of course a lot turns on the envisioned details) that the Bayesian explanation of why this racist belief tends to be epistemically irrational for thinkers in the envisioned circumstances will be similar to why it tends to be irrational to believe that the most intelligent women are less intelligent than the most intelligent men. Basically, we know (or at least have strong evidence in support of the idea) that in the United States black people are overrepresented in the indicated ways in part because of their differential treatment in socio-economic systems and the justice system. If one has this kind of further information, it will screen-off the relevance of the statistical overrepresentation of black people just as having information about the differential treatment of women screens-off the relevance of the underrepresentation of women in social roles that demand high intelligence. If someone lacks this further information about the differential treatment of black people, then it’s information that they arguably ought to have and it’s this that defeats the rationality of their belief that black people are more criminal than white people (cf. Q2 in footnote 2).
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Acknowledgements
Endre Begby and Nicholas Fillion were instrumental in getting this paper off the ground. I’m indebted to their kindness in reading rough drafts and offering penetrating comments. Likewise the referees at Synthese were thorough and thoughtful in their remarks and the present paper has been much improved as a result. Many others contributed to this work, including: Dan Singer, Julia Staffel, Karen Frost-Arnold, Alan Hinkle, Rima Basu, Gregory Phelan, Joseph Shieber, Max Lewis, Grace Boey, Kai Draper, and audiences at Washington University in St. Louis, the University of Cologne, the University of Delaware, and the University of Connecticut.
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Silva, P. A Bayesian explanation of the irrationality of sexist and racist beliefs involving generic content. Synthese 197, 2465–2487 (2020). https://doi.org/10.1007/s11229-018-1813-9
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DOI: https://doi.org/10.1007/s11229-018-1813-9