Abstract
Value-based epistemology sees epistemic norms as explained by or grounded in distinctively epistemic values. This paper argues that, no matter what epistemic value is, credences or beliefs about some topics have at most infinitesimal amounts of this value. This makes it hard to explain why epistemic norms apply at all to credences or beliefs on these topics. My argument is inspired by a recent series of papers on epistemic versions of Parfit’s Repugnant Conclusion. The discussion in those papers parallels work in ethics, because it focuses on an epistemic value—accuracy—that shares features with ethical values like well-being. I argue that, because of this focus, this discussion is inconclusive and only relevant to accounts of epistemic value that share those features. My argument is more general and more conclusive. It uses four types of problem cases that have no parallel in ethics. It applies to all extant accounts of the value of individual beliefs or credences and all extant accounts of the value of total doxastic states.
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Notes
Carr and Pettigrew do not use the term “barely accurate.” They speak in terms of “neutral” credences (Pettigrew 2018, pp. 341–342) or credences that are “no closer to truth than falsehood” or “no better than chance.” (Carr 2015, pp. 232–233). Barely accurate credences are just slightly better than these. Both give more precise accounts than I do here, but what they say fits with my rough-and-ready treatment. Carr, Pettigrew, and I all argue previously that barely accurate credences have some positive epistemic value. I show in Sect. 4 why my arguments in this paper do not need this.
This deals with the case I used to illustration the Conclusion, which compares credences about wisdom to those about boring propositions. It does not, however, deal with all of the versions of the Conclusion that Pettigrew discusses, since the topics of the beliefs are not specified. See my previous paper for discussion of this, but it is irrelevant to my arguments in this paper.
There’s another error theory discussed in ethics: Repugnant Conclusions involve too large of sets of things for us to reliably have intuitions about. I won’t discuss this in the main text for two reasons. First, it piggy backs on an error theory I do discuss. If we could clearly think about the value had by a few barely accurate boring credences, then we should be able to compare this to the expected value of accuracy improvements to credences about interesting topics, or see their trend in total value as the numbers of them add up. This would give us useful information about the value of boring credences, so our inability to think about large sets is only an error theory if we also are not good at imagining the value of smaller sets of barely accurate credences. Second, humans for all of our history have had doxastic states consisting of immense numbers of credences, whereas it is only very recently that humans have had to think about immense human populations. Even if we are bad at thinking about the total values of large human populations, I don’t see good reason to think that we can’t fathom the value of even very large doxastic states.
This may need qualification—depending on what forms of closure one endorses, and whether one thinks that credal states have to be partitions or Boolean algebras, it could be that losing certain credences would be problematic. But those qualifications don’t matter for my points here.
Can we base requirements on boring credences in instrumental value? Most boring credences have no actual instrumental value. To explain requirements on these credences, we’d have to appeal to their expected instrumental value. Expectation is defined in terms of probabilities of outcomes. To get plausible norms from expectations, we must appeal to the rational probabilities of outcomes. Where do the rational constraints on these probability assignments come from? Credences about the instrumental value of boring credences must themselves be boring. If they weren’t, then massive sets of such credences would be superior to wisdom. This is a problem: to use expected instrumental value to explain requirements on boring credences, we need some way of constraining credences about their instrumental values, but we do not have any such way, because these credences about instrumental value are themselves boring. See Talbot (2019) for more discussion.
This assumes that some infinitesimal values are greater than others.
One may prefer some alternate model for arithmetic involving infinitesimal values. The problematic models (for finite satisficing) would be ones that allow infinitesimal values to add up to very large totals at their limit. But, if that’s how infinitesimals work, then we won’t be able to use infinitesimal values to deal with either the Epistemic Repugnant Conclusion or the problems I go on to discuss. We’d have to instead say that boring credences have no epistemic value.
Arntzenius et al. discuss infinite series of decisions such that: standard causal decision theory says that a certain choice is rational for each individual decision, but if the agent were able to make all of these decisions at once, they would be rationally required to not make these choices. That’s quite similar to what we may see for finite satisficing: each sub-optimal choice looks intuitively fine, but the collection of choices together looks intuitively wrong. Arntzenius et al conclude that causal decision theory is issuing the correct verdicts in each individual case—the decisions are individually rational, even though taken together they would be irrational—suggesting that the objection to finite satisficing may not be so serious.
As presented, neither W nor R is a Boolean algebra, since they don’t include the negations, conjunctions, and disjunctions of the propositions I’ve mentioned. That’s just to make things easy to follow. We can make them into algebras if one likes, and if we did, R would still have a greater number of accurate credences than W in each case. We could make this greater number as large as we like, and it would still be obvious that R cannot be more valuable than W. I won’t go through the process, as it would be tedious, but it should be clear how it goes: since each R starts with a greater number of accurate credences than the relevant W, extending each R and W into algebras will just continue this trend.
An anonymous reviewer suggested that we could get an ethical analog by considering non-human animals. To illustrate, let’s say that an ant can suffer in a way that is at least somewhat morally bad, but they cannot suffer to the same degree as a human. Intuitively, the suffering of any number of ants is less important than the great suffering of one human.
Some may say that our curiosity would be satisfied just by thinking we have knowledge. If that were so, then in cases 3 and 4, an agent in W would have their curiosity more satisfied than an agent in R, even if R were epistemically better than W. That’s because in these cases W contains as many or more maximal credences as R; thus, in these cases an agent in W would think they knew as much or more than the agent in R. However, in case 2, R contains more maximal credences than W. Yet in case 2 the credences in W still clearly satisfy our curiosity more than those in R. All that can explain this is that the maximal credences in W are together more epistemically significant than those in R.
Carr, Pettigrew, and I each argued that accuracy-first epistemology cannot adopt an account of total value that avoids the Repugnant Conclusion. These arguments relied on the distinctive features of accuracy that I discuss below. Accounts of epistemic value that don’t share these features can adopt these different accounts of total epistemic value.
We need case 4, and not just case 2, for views that say only full beliefs, and not suspensions of judgment, have value or disvalue.
To restate case 4 in terms of knowledge, when R contains knowledge that p, W would have to contain the belief that not p. So R and W must have beliefs with different content. But any tenable view of epistemic norms based on knowledge has to say that, for the purposes of determining what we ought to believe, knowledge that p is superior to a false belief that not p. Otherwise no doxastic state would be better than any other.
What if the different forms of epistemic value were incomparable, or on a par? When we say that two types of value are incomparable, or on a par, we are positing a sort of rough equality (Chang 2002). We might say, for example, that Mozart’s music is incomparable to Michelangelo’s. But we wouldn’t say that Michelangelo’s art is incomparable to my music, because I am a just-barely-competent musician. So, to say that there is value that R has more of than W, and this value is incomparable or on a par with values that W has more of than R, is just another way to bite the bullet on cases 1–4.
There are variants of the average utility view which say that the utility of a state is additive for small worlds, and average utility for large (see e.g. Temkin 2012). Since average utility views don’t avoid the Epistemic Repugnant Conclusion, these variants do not either.
There are a number of other variants on critical level views in the ethics literature. That’s because critical level views, in their simplest form, have untenable consequences. These variants add features to block these consequences, generally having to do with fairness or equality (e.g. Asheim and Zuber 2014). None of these impact the key features of critical level views that are relevant to the discussion here. Since critical level views in the simplest form don’t avoid cases 2–4, neither do these variants.
Temkin (2012) suggests some version of this view, although he suggests combining it with pluralism. One can combine what I say about pluralism and diminishing marginal utility to apply to Temkin-style views.
I’m assuming that the utility each boring credence contributes diminishes as a function of the number of boring credences in one’s credal state. But there is a different approach to diminishing utility: the utility of each boring credence diminishes as a function of the credence’s place in a sequence (e.g. a temporal sequence), with later credences contributing less than earlier ones. This view is implausible. It means that a handful of early credences can contribute more to total epistemic value than an infinite number of later credences. I can’t see why that would be so. But let’s say we like the view. It does avoid some of my arguments. Infinite series of boring credences can diminish towards a limit without having to have infinitesimal values. But this view ultimately doesn’t avoid the main problem I discuss in Sect. 2.1. Boring credences will still have to have very minimal epistemic utility. And their total utility must still approach a low limit. Given this, we can still adopt a form of satisficing consequentialism that allows us to ignore boring credences, and this form of satisficing will not be open to objections.
Dispositional beliefs are subject to epistemic evaluation. For example, Rose and Schaffer (2013) have recently argued that knowledge entails dispositional belief, not non-dispositional belief, and evaluating as knowledge is the paradigmatic form of epistemic evaluation.
You may wonder if I’m being hypocritical. In discussing finite satisficing consequentialism (section 2.1), I said it might be acceptable for it to say implausible things about infinite series of choices. Yet, here I am saying that a view must say plausible things about infinitely large doxastic states. What’s the difference? We probably don’t make infinite series of choices. But we may very well have infinitely large doxastic states, and some ideal agents almost definitely do. Epistemic consequentialists want a theory that applies to ideal agents, and (typically) also want a theory that applies to us as well. So, while it might not be so bad were consequentialism to generate implausible implications for infinite series of choices, it would be bad if consequentialism had implausible implications for infinitely large doxastic states.
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Acknowledgements
This paper was inspired by an exchange with Geoff Keeling, who also gave me helpful feedback on it. My thanks as well to Julia Staffel and anonymous referees for their comments on the paper.
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Talbot, B. Epistemic repugnance four ways. Synthese 199, 3001–3022 (2021). https://doi.org/10.1007/s11229-020-02919-2
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DOI: https://doi.org/10.1007/s11229-020-02919-2