Abstract
There are currently two robust traditions in philosophy dealing with doxastic attitudes: the tradition that is concerned primarily with all-or-nothing belief, and the tradition that is concerned primarily with degree of belief or credence. This paper concerns the relationship between belief and credence for a rational agent, and is directed at those who may have hoped that the notion of belief can either be reduced to credence or eliminated altogether when characterizing the norms governing ideally rational agents. It presents a puzzle which lends support to two theses. First, that there is no formal reduction of a rational agent’s beliefs to her credences, because belief and credence are each responsive to different features of a body of evidence. Second, that if our traditional understanding of our practices of holding each other responsible is correct, then belief has a distinctive role to play, even for ideally rational agents, that cannot be played by credence. The question of which avenues remain for the credence-only theorist is considered.
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Notes
Ramsey (1926).
Here is another example to illustrate the difference between objective and epistemic chance. One may believe that a coin has an objective chance of either 80 or 20 % of landing heads, and have symmetric evidence with respect to each bias; as a result, one can believe that the coin has an epistemic chance of 50 % of landing heads, but one will not believe that it has an objective chance of 50 % of landing heads.
See, e.g., Fantl and McGrath (2010, p. 141).
Two prominent theories that claim rational agents act only on what they know (rather than only on what they believe) include those of Fantl and McGrath (2002) and Hawthorne and Stanley (2011). See also the debate about norms of assertion, where Douven (2006) argues that the norm of assertion is not (as the consensus view holds) “assert only what you know” but rather “assert only what is rationally credible to you,” where what is rationally credible to one is what one can or could rationally believe.
Scoring rule arguments for probabilism have made use of the idea that it is an epistemic virtue to have cr(p) closer to 1 in worlds in which p is true and closer to 0 in worlds in which p is false. See Pettigrew (2011) for an overview of these arguments.
Authors generally focus on objecting to the claim that cr(p) = 1 is necessary for belief. Nonetheless, the claim that cr(p) = 1 is sufficient for belief has also met with challenges: see Maher (1993) and Hájek (ms.). For an alternative picture on which full beliefs have maximal credence, see van Fraassen (1995), who takes conditional credences to be basic and full beliefs to be derived from them.
That justified belief requires credence over a threshold, which is relative to the stakes involved, is motivated in Fantl and McGrath (2002) by consideration of the phenomenon of “pragmatic encroachment.” One kind of Modified Threshold View is what Ross and Schroeder (2012) call Pragmatic Credal Reductivism, spelled out in Weatherson (2005), and (under one interpretation) Fantl and McGrath (2010). (See also Harsanyi (1985) for a view of this type.) This view also fits with the general spirit of Hawthorne (2004) and Stanley (2005), although they both formulate their views in terms of epistemic probability rather than subjective probability or credence.
A more recent argument against Threshold Views that I won’t discuss, but that is worth examining, is Jane Friedman’s (2013) argument from the rationality of suspending judgment on high-credence propositions.
Kyburg (1961).
Presentation based on Schauer, Chapter 3. See that chapter for further details of the actual case.
But see Cohen (1977) for arguments (in addition to the one considered here) against the thesis that evidential standards can be cashed out in terms of credences or other “Pascalian” notions of probability.
See Cohen (1977, p. 82).
In any event, if “preponderance of the evidence” sometimes requires only that the claim is more probable than not, we could tweak the information given so that it would license the same credence as in this hypothetical case and also license a court verdict. Since the argument in this section only hinges on what we ought to believe in these cases, the complexities of the actual legal system are unimportant to the discussion here.
See also Thomson (1986), who argues that in the Blue Bus case, we don’t know whether the blue bus hit the woman.
I thank the students in Robert Audi’s graduate seminar at Notre Dame for suggesting this case.
These accounts have come under fire. See, for example, Douven’s (2003) reply to Nelkin. Douven’s reply is specifically aimed at Nelkin’s claim that the “One False Belief” accounts of Bonjour (1985) and Ryan (1991) cannot handle an additional case she proposes. The cases here, however, have a different structure than Nelkin’s cases.
For an outline of the disagreement about why they don’t give rise to a guilty verdict in the legal case, see Redmayne (2008).
I’m leaving open how we want to represent the statistical evidence in the credal framework, as cr(p(Js) = 0.9 | Jm) ≈ 1, or as cr(Js | Jm) = 0.9. The latter seems more straightforward, but if we want to interpret statistical evidence as being evidence about epistemic probabilities, we might want to employ the former. As for the suggestion that believing or having a high credence in an epistemic-chance proposition blocks outright belief, this won’t work because epistemic-chance propositions are not believed only in response to statistical evidence: presumably one also believes that there is a high epistemic chance Jake stole in the “guilty look” case—that is just what it means to believe the guilty look is evidence of Jake’s guilt in this case.
See Spites et al. (1993). There are a few exceptions to this general claim but they are not relevant to the present case. Perhaps an objector could claim there will be a difference in one’s credences in the relevant counterfactuals. But I doubt that an agent needs to formulate a credal opinion about counterfactuals in order to count as rational. Alternatively, one could try to add more to structure to credence functions. If one wants to take these escape route, it will be an interesting upshot of the argument here that rational agents need to have much more complex credences than is ordinarily supposed.
I thank Brian Weatherson and Roger White for raising this point.
In the Blue Bus case, where E is the new eyewitness’s testimony and S is the statistical evidence, cr(BB | E & S) = cr(E | BB)cr(BB | S)/[cr(E | BB & S)cr(BB | S) + cr(E | ~BB & S)cr(~BB | S)] = (0.25)(0.8)/[(0.25)(0.8) + (0.75)(0.2)] = 0.2/0.35 ≈ 0.57. In the Green Bus case, where E is the new eyewitness’s testimony and O is the old eyewitness’s testimony, cr(GB | E & O) = cr(E | GB & O)cr(GB | O)/[cr(E | GB & O)cr(GB | O) + cr(E | ~GB & O)cr(~GB | O)] = (0.25)(0.75)/[(0.25)(0.75) + (0.75)(0.25)] = 0.5.
Theories that seek to eliminate belief altogether include Jeffrey (1970) and Christensen (2004). The latter argues that the notion of binary belief is useful, though “may not in the end capture any important aspect of rationality” (p. ix). Theories in which belief and credence play different roles in the same domain include the “reasoning disposition account” of Ross and Schroeder (2012). Theories in which credence and belief play the same role but occupy a different discourse include that of Frankish (2009). Sturgeon (2008) is a difficult theory to categorize, since he thinks that everyday evidence does not always rationalize sharp credence, and fuzzy confidence of a certain sort is identical with belief, but I tentatively place his theory in the category of theories in which credence and belief play a role in the same domain. Two theories that do recognize different primary roles for credence and belief are Kaplan’s (1996) Assertion View and Maher’s (1993) notion of “acceptances.” Both Kaplan and Maher claim that our ordinary notion of belief is not coherent, and each propose to replace it by a notion that shares many of the features of belief and does much of the same work. (Therefore, there is a sense in which these theories are eliminativist.) These theories are not reductionist in the sense that they don’t reduce assertions or acceptances to credence, but they are reductionist in that they reduce the rationality of assertions or acceptances to facts about the agent’s credences plus something else: for example, according to Maher, one rationally accepts a proposition if doing so maximizes expected “cognitive” utility. I think these theories are on the right track in their recognition of two very different kinds of activity, one which involves credence and one which involves something else.
See Fermat and Pascal (1654).
I note that on a view that has become fairly standard in decision theory (the constructivist view), one does not have a utility function independent of one’s preferences, so the norm of decision theory is technically to have preferences that obey particular axioms, from which it will follow that you are representable as preferring the act with the highest expected utility value. So a rational individual will not and cannot explicitly consider the utility of various outcomes. See, e.g., Dreier (1996). The difference, however, won’t matter for our purposes—we will primarily be considering whether the norm of decision theory can capture certain intuitive decisions concerning our moral practices of blame—and so I will continue to speak in terms that make the discussion less cumbersome.
If there are no ties, this norm reduces to: “Perform an act if and only if that act has the highest expected utility among the available acts, given your credences in the events which bear on the utility of the acts.”
Though Ross and Schroeder (2012) argue that its application rests on belief: belief plays a role in setting up decision problems, about which we can then reason using credences.
This isn’t to say we can’t explain actions in lottery cases using beliefs: they can perfectly well be explained using beliefs about objective chances. The point is just that we can also explain them using credences.
Additionally, although this isn’t the subject of this paper, the “belief-only” theorist who wants to eliminate the need for credences but doesn’t think they can be reduced to beliefs, would need a way to capture the Action Norm and the interaction between the epistemic and value facts, using just beliefs and chance-beliefs as epistemic facts—or would need to argue that this norm is not the correct norm for personal action.
I am presupposing the common view that having a reactive attitude toward someone is sufficient to praise or blame him, in the tradition of Strawson (1962). While I note that there is some disagreement with this claim, it is a natural view to take, as reactive attitudes appear to be an important component of our moral responsibility practices. Further, even if this turns out to be incorrect, the points I make here hold under any reasonable understanding of blame.
A few caveats are necessary. First, on some views, there is a distinction between when we ought to blame someone and when we ought to find them blameworthy, and theorists adhering to these views may think that the above norm should concern when to judge someone blameworthy—whether to blame her will be a matter of whether some additional condition (e.g. concerning my relationship to her) is fulfilled. However, this distinction will not matter for the discussion here, since in all cases we may simply assume that the additional condition is met. Second, this norm might be thought of as defeasible, for example if the individual is believed to have transgressed but is judged not to be a member of the moral community. A final complication arises from the possibility that we believe an individual committed a transgression, but we are unsure about the exact badness of the transgression. How to in general handle examples in which the uncertainty is not about whether the agent performed the act but about the status of the act itself is beyond the scope of this paper. It is possible that these examples are best handled by introducing a decision-theoretic calculus into the assessment of the severity of the transgression itself, so that the norm is “Blame someone if and only if you believe (or know) that she transgressed, and blame her in proportion to the expected severity of the transgression.” Nonetheless, the main point is that the norm concerning blame has the general form given above: an epistemic component which must be satisfied if blame is to be apportioned at all, and a separate component describing the amount of blame to be apportioned.
Nesson (1985, p. 1382).
Nesson (1985, p. 1359).
I thank Sarah Moss and David Christensen for raising this objection.
See Colyvan et al. (2001) for a discussion of the relationship of reference classes to the use of bare statistics in the law.
Perhaps condemning on the basis of merely statistical evidence has a high disutility even if the person is in fact guilty. If so, then the utility of correctly blaming someone for an act could in principle outweigh this disutility, but again, I submit that it does not.
Note that this situation and the situation in the previous paragraph do not have the same structure. In the Blue Bus case, there are two different actions in one situation (rendering a verdict and betting), and in the shoplifting case, there is a single action (keeping an eye on the teenager) that is subject to two different norms: the action norm and the blame norm.
We could add that stopping an impaired individual would have much better expected consequences for her, given the likelihood of injuring oneself while impaired.
This is true even if the standard for stopping someone is “reasonable suspicion” rather than outright belief: I would explain this by pointing out that reasonable suspicion cannot be cashed out in terms of credences either. Thanks to Jennifer Nagel for raising this point.
I thank Matt Smith for this suggestion.
In particular, the “continuity axiom.”
An analogous problem is discussed in Hájek (2003).
I thank Jonathan Weisberg for this suggestion.
I thank Jada Twedt Strabbing for this suggestion.
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Acknowledgments
I would like to thank Matt Benton, Lindsey Crawford, Julien Dutant, Jane Friedman, Julian Jonker, Matthew Lee, Jennifer Nagel, Ted Poston, Jada Twedt Strabbing, and Jonathan Weisberg for comments on earlier versions of this paper. I would also like to thank Sherri Roush’s graduate seminar, Robert Audi’s graduate seminar, the philosophers at Leeds, and participants in Epistemology Above the Arctic Circle (sponsored by the Oslo Center for the Study of Mind and Nature) and the Harvard Workshop on Belief for helpful discussions of earlier versions of this paper.
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Buchak, L. Belief, credence, and norms. Philos Stud 169, 285–311 (2014). https://doi.org/10.1007/s11098-013-0182-y
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DOI: https://doi.org/10.1007/s11098-013-0182-y