Abstract
According to epistemic utility theory, epistemic rationality is teleological: epistemic norms are instrumental norms that have the aim of acquiring accuracy. What’s definitive of these norms is that they can be expected to lead to the acquisition of accuracy when followed. While there’s much to be said in favor of this approach, it turns out that it faces a couple of worrisome extensional problems involving the future. The first problem involves credences about the future, and the second problem involves future credences. Examining prominent solutions to a different extensional problem for this approach reinforces the severity of the two problems involving the future. Reflecting on these problems reveals the source: the teleological assumption that epistemic rationality aims at acquiring accuracy.
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Notes
Hereafter, by ‘rational’, I mean epistemically rational (instead of, for example, practically rational).
This view isn’t unanimously held, though. See Konek & Levinstein (2019) for a version of EUT where credences are not evaluated on the condition that they’re adopted.
More precisely, the inaccuracy of a credence at a world is equal to the squared distance between the credence and the maximally accurate credence at the world. The shorter the distance, the less inaccurate the credence is; the longer the distance, the more inaccurate it is. Multiplying the inaccuracy score by -1 results in an accuracy score for the given credence. The closer the score is to 0, the more accurate the credence is, and the farther it is from 0, the less accurate it is. A perfectly accurate credence in a true proposition is the maximal credence in it. A perfectly inaccurate credence in a true proposition is the minimal credence in it. The overall accuracy for a set of credences (i.e. a credal state) is the average of the accuracy scores for the given credences.
For a discussion of these additional norms, see Pettigrew (2016).
Those who accept a causal maximization norm think that the principle should take into account the probability of worlds if the agent were to occupy the given credal state. Those who accept an evidential maximization norm think that the principle should take into account the probability of worlds if the agent in fact comes to occupy the given credal state. While there’s this difference between causal and evidential CEUT, they agree in thinking that an agent’s occupation of a credal state should bear on the probability of worlds. For the rest of the paper I will be focusing on causal CEUT, but the success of the arguments below does not hinge on which version of CEUT is correct. It’s worth noting that the leading defenders of CEUT (e.g. Pettigrew (2018), and Joyce (2018)) subscribe to causal versions of it.
The accuracy score at each world: -(1 – (1/2))2 or -(0 – (1/2))2, according to the Brier Score.
Carr (2017) also presents a case involving self-fulfilling credences to argue that CEUT clashes with Bayesianism’s central diachronic norm: Conditionalization. While we won’t be relying on the opposite kind of case (involving self-frustrating credences), she uses it—employing Caie’s (2013) argument—to show that CEUT clashes with Bayesianism’s central synchronic norm: Probabilism. Now although we both use self-fulfilling cases to arrive at similar conclusions, we rely on different premises and there’s an important evidential difference between our cases. To illustrate the first difference, while Carr leverages our beliefs about the epistemic rationality of credal-state transitions via Conditionalization, we rely on our intuitive judgments about the epistemic rationality of credal states at a single time. Shifting to the second difference, in Carr’s case it’s not obvious what credence in p the evidence points toward when the agent learns that her future credence in p will match p’s future objective chance. The situation of Sony in Painful Prep differs in that his evidence obviously points toward a credence of .5 in B. Finally, this paper attempts to illuminate just how unintuitive CEUT’s verdicts are in a plethora of ordinary situations.
Greaves (2013) uses a case involving self-fulfilling credences too. However, in her case, the agent’s evidence doesn’t point towards a particular credence in the relevant proposition. Instead, the agent knows that whatever credence she comes to have in it, her credence will be in accord with the objective chance that it is true. This is noteworthy since if we’re dealing with this (or Carr’s) case where there’s no fact of the matter concerning (or it’s unclear) which credence is supported by the evidence, we don’t have a strong intuitive reaction (about epistemic rationality) to the case. So, this type of case won’t pose an intuitive problem for CEUT. But if we’re dealing with our type of self-fulfilling case where there’s a fact of the matter (and it’s clear) which credence is supported by the evidence, we do have a strong intuitive reaction to it. These cases can be used to—as we do in this paper–generate an intuitive problem for CEUT.
Berker (2013a, 2013b) similarly uses a self-fulfilling example to target epistemological accounts that resemble reliabilism—where beliefs are justified if they’re formed in a truth-conducive way, even if the agent has no idea that it is truth-conducive. So the patient who believes against her evidence that she will recover, in a situation where (unbeknownst to her) that belief will make her recovery likely, is justified. This is clearly counterintuitive—but it doesn’t apply to cases where the agent has evidence to think that she will recover if she believes she will. Berker (2013b) says, in a footnote, that he believes one could construct troubling cases where the agent is aware of the self-fulfilling nature of believing in her recovery, but adds that arguing for this “takes a bit of care,” and doesn’t pursue it. However, from the perspective of CEUT, it is precisely the (rational) expectation of self-fulfilling credal states that is crucial to epistemic rationality.
Imps is reminiscent of similar trade-off cases used to argue against epistemic consequentialism as applied to beliefs rather than credences. In these cases the agents can sacrifice the EU of a particular belief in order to acquire a collection of beliefs that has an unsurpassed amount of EU. Imps is an instance of this general problem for epistemic consequentialism. For more on trade-off cases, see: Berker (2013a, 2013b), Caie (2013), Firth (1981), and Jenkins (2007).
The evidence-disrespecting credal state in Imps is the one consisting of a credence of 0 in the proposition that there is now a child before her and a credence of 1 in the other five propositions.
For more on the direction-of-fit metaphor, see Anscombe (1957).
Now you might raise the following worry about these cases: do we really find it intuitive that the evidence-disrespecting credences are epistemically irrational? Clearly, it’s intuitive that they’re irrational in some way. But maybe our intuitions are tracking practical rationality (or all-things-considered rationality) instead. While some may find it intuitive that the evidence-disrespecting credences are practically irrational, it’s also intuitive that they’re epistemically irrational. To see this, let’s consider a case that disentangles these intuitions. So suppose it’s quite unlikely that there will be a really loud noise soon. But it’s quite likely that if I were certain that there would be a really loud noise soon, then I would warn my partner by shouting across the room. So it’s quite likely that if I were to be certain that there would be a really loud noise soon, then there would be a really loud noise soon. Now is it epistemically rational to be certain that there will be a really loud noise soon? Clearly, it isn’t. And given that there are virtually no costs associated with this credence, it doesn’t seem to be practically irrational to adopt it. At the very least, the intuition is much weaker that the credence is practically irrational.
The same point holds concerning evidence-respecting credences. Accordingly, it’s implausible that our intuitions concerning evidence-respecting credences and evidence-disrespecting credences in the self-fulfilling cases are about practical rationality rather than epistemic rationality.
For a quite different extensional problem concerning causal CEUT, see Caie (2018). Caie argues that in a great number of situations, there’s an infinite number of credal states that lack well-defined expected epistemic utilities (EEUs), and that if this is so, causal CEUT delivers incorrect verdicts in these situations. By contrast, I argue that even if every credal state were to have a well-defined EEU in the self-fulfilling cases, both causal and evidential CEUT would deliver incorrect verdicts.
One might object that the evidentialist heuristic actually satisfies the value-requirement. After all, as Pettigrew (2018) notes, the heuristic has always been available, and it’s easy to use, too. While this is true, these features don’t suffice to make a heuristic a good heuristic—in fact, they count for very little if a heuristic often yields the wrong verdicts. But as we’ve seen, if CEUT were correct, there would be an abundance of cases in which the evidentialist heuristic would yield the wrong verdicts. For this reason, it seems implausible that a defender of CEUT can plausibly hold that the evidentialist heuristic satisfies the value requirement. Thanks to an anonymous referee for bringing up this concern.
While Joyce (2018) isn’t entirely clear on which probability function is to be used when calculating the objective expected accuracy of C’’ on the condition that C’ is adopted, it’s plausible that the agent’s evidential probability function is to be used.
While Joyce (2019, p. 259) considers a self-fulfilling case from Greaves (2013, p. 916), her case is importantly different from our self-fulfilling cases, as I explain in fn. 8. After all, her case is silent on which credence is supported by the evidence. But in our cases we know that the evidence supports a middling or low credence in the relevant propositions even though the agents know that if they were to have a high credence in the propositions, then these propositions would be true. So even though Joyce acknowledges (and argues) that the self-fulfilling credence in Greaves’ case is rational to adopt, the intuitive cost of embracing this claim as applied to our cases is much higher.
For another solution to the Trade-Off Problem, see Joyce & Weatherson (2019). According to their solution, it turns out that certain versions of CEUT are consistent with our intuitive verdict in Imps. That said, they concede that different trade-off cases can be constructed where CEUT licenses adopting evidence-disrespecting credal states. Another limitation with their solution is that it only helps with trade-off cases, which the Problem of Self-Fulfilling Credences doesn’t rely on.
The quotation appears in a previous draft of Pettigrew (2020).
At the very least, it’s plausible that there’s a serious explanatory problem here for CEUT. While Joyce & Weatherson (2019) acknowledge and reject versions of CEUT that are sensitive to future EU, they make no attempt to explain how CEUT’s teleological foundation is consistent with CEUT discriminating against future EU.
While you wouldn’t think that diachronic trade-off cases pose a problem for CEUT—since it doesn’t take into account future EU—I’m arguing that well-motivated versions of CEUT turn out to be vulnerable to such cases. See: Berker (2013a, 2013b), Firth (1981), and Jenkins (2007) for a similar problem—also using diachronic trade-off cases—for belief versions of epistemic consequentialism.
See Nozick (1993, p. 69), for the inspiration for Too Bad to be True.
See Berker (2013b, p. 372, fn. 16), for the inspiration for The All-Consuming Fad.
Encountering people such as Dr. Aker is one way that we can expectedly worsen our epistemic futures. We can also do so through encountering putative gurus concerning politics, religion, self-help, and personal finance.
While Joyce discusses a related notion (being a ‘sham’ credence), the fundamental notion behind epistemic ratifiability is usability.
Joyce uses t0 to refer to a previous time where the agent can choose the credal state she will have at t.
Berker (2013a) and Talbot (2014) also argue that the source of the counterintuitive verdicts of views like CEUT (e.g. belief versions of epistemic consequentialism) is not their theories of EU. While Berker and I think this gives us a good reason to reject such views, Talbot argues that we’re committed to accepting these counterintuitive verdicts.
Thus the problems we’ve been examining relate to another sort of problem that’s been discussed in the literature. As others have pointed out, if epistemic rationality is teleological, then epistemic rationality should apply to non-doxastic acts such as eating sandwiches or building the Large Hadron Collider, since such acts can be expected to do better or worse in terms of acquiring EU. This worry concerning CEUT also seems to come from CEUT’s teleological foundation. While the problems may be similar in this way, some might reply to the ‘sandwich’ problem by claiming that it is definitional of epistemic norms that they only apply to doxastic options, not to lunch options. This reply is of no help in solving the problems in this paper, since the problems concern doxastic options. See Greaves (2013, p. 922), for this “definitional” response. For more on this worry concerning teleological theories of epistemic rationality, see: Arpaly (unpublished Ms.), Horowitz (2019), and also Konek & Levinstein (2019, p. 100).
See Marxen (2021) for an alternative account of the connection and for a different argument—which appeals to a connection between epistemic rationality and practical rationality—for the conclusion that potentially self-fulfilling credences are not thereby rational to have.
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Acknowledgements
Many thanks to Zach Barnett, Jamie Dreier, Adam Pautz, Richard Pettigrew, an anonymous referee for Synthese, and the audience at Pepperdine’s Philosophy Colloquium Series in 2017. I’m especially grateful to David Christensen and Josh Schechter for their many helpful suggestions.
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Marxen, C. Epistemic utility theory’s difficult future. Synthese 199, 7401–7421 (2021). https://doi.org/10.1007/s11229-021-03120-9
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DOI: https://doi.org/10.1007/s11229-021-03120-9