Abstract
This paper explores ‘reasonable doubt’ as an enlightening notion to think of reasoning and decision-making generally, beyond the judicial domain. The paper starts from a decision-theoretic understanding of the notion, whereby it can be defined in terms of degrees of belief and a probabilistic confirmation threshold for action. It then highlights some of the limits of this notion, and proposes a richer analysis of epistemic states and reasoning through the lens of ‘reasonable doubt’, which in turn is likely to supplement the DT framework. The strategy consists in fighting on two fronts: with DT, the paper claims that there is no absolute (i.e. decision-independent) notion of ‘reasonable doubt’ but, pace DT, it shows that reasonable doubt cannot be accounted for only in terms of degrees of belief and probabilistic threshold. We argue that the lens of reasonable doubt sheds light on aspects of belief dynamics, as well as of the nature of epistemic attitudes, which are often obscured by belief-centred approaches. In particular, when it comes to acknowledging the necessary ignorance and irreducible uncertainty that we face in our everyday-life decisions, studying the various facets of doubt rather than focusing on what can be believed, enables one to do justice to the richness and diversity of the mental states in play.
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Notes
As Stephen John emphasised in a personal communication, it is very important to keep the issues of rejecting a theory and of accepting another separate, since it is possible to undermine, e.g., climate science without providing an alternative positive theory. Many conspiracy theories thus rest on an illegitimate assumption that the burden of proof is on the side of the official theory. See Hahn and Oaksford (2007) for reflection on the use of the notion of burden of proof in argumentation beyond the legal domain.
Movie by Sidney Lumet (1957), from a TV play by Reginald Rose (1954).
See footnote 34 below.
One contemporary exception is Thagard (2004), but this paper remains marginal, and his definition of doubt is all in all quite cursory. To our knowledge, the most in-depth recent analysis of doubt is Salmon’s (1995), but his proposal makes sense against the background of issues in the philosophy of language and logic, rather than in an epistemological and psychological framework as ours. Jane Friedman’s (2017, 2019) works linking inquiry with suspension of judgement notably put an emphasis on the importance of those epistemic states and actions that are generally ignored by belief-centred approaches. Finally, it is worth mentioning that, while the present paper was under review, two papers on doubt have appeared (Lee 2018; Moon 2018). The conceptions of doubt that they defend are different from ours, but the issues they address are mostly orthogonal to the main focus of the present paper, which places discussion of their views beyond its scope.
Section 5 will develop on the variety of what accepting non-H might imply.
As one anonymous referee suggested, one may also want to include some notion of partial acceptance (as distinct from acceptance of H-in-full); for example, if one’s evidence is not great, one may take the lighter of two umbrellas. However, we suspect that this could be accounted for in terms of full acceptance by clearly specifying the decisional context: there may be one decision that concerns the heavier (and safer) umbrella, regarding which one does not accept H (because, given the respective costs of false negatives and false positives, one does not evaluate H as likely enough to carry the umbrella—just as for the decision whether to take one’s plants out or not), and another one involving the lighter umbrella, regarding which one actually (fully) accepts H (concluding H is likely enough for one to decide to carry the lighter umbrella).
Another, related problem is that there seems to be something inconsistent in saying that the BARD standard is the highest standard of proof, used in criminal cases because stakes are particularly high in those cases, and to defining reasonable doubt as a threshold depending on the utilities. If one defines ‘reasonable doubt’ in BARD as set on the utilities, then BARD should apply to any case—‘balance of probabilities’ corresponding to what counts as ‘reasonable doubt’ in the contexts of civil law. This might offer grounds for a criticism to DT accounts of the BARD standard of proof, and one might have to admit of two uses of ‘reasonable doubt’, one in terms of utilities, and one more specific as used in the BARD legal standard (thanks to Stephen John for helping us clarifying this).
As a matter of fact, since the turn of the twenty-first century, the Crown Court has given up the very phrase “beyond a reasonable doubt” in its guidance to trial judges in directing the jury, in favour of a mention that “the prosecution must make the jury sure that [the defendant] is guilty” to prove guilt, and that “nothing less will do”. (Judicial College, The Crown Court Compendium – Part I: Jury and Trial Management and Summing Up (February 2017), 5-8 (on line at www.judiciary.gov.uk/publications/crown-court-bench-book-directing-the-jury-2/). Note that such a restatement of the criminal standard of proof makes it considerably closer to the French rule of ‘innermost conviction’ (intime conviction).
There are of course several hypotheses to examine on which the final hypothesis rests. See Schum (1994) for a thorough analysis of the “cascaded inference” at play in (legal) evidential reasoning.
Indeed, the question is not only whether it is true that greenhouse gases can be harmful, but how much. On the contrary, the accused is guilty or not of the charge—that being independent from the epistemic fact that the hypothesis of guilt is doomed, as any other empirical hypothesis, to be never 100% confirmed.
But see below footnote 33.
As suggested by one anonymous referee, this ‘verdictive’ aspect of verdicts might be a reason not to take the figure of the juror as paradigmatic. As our referee emphasizes, this contrasts with most other cases: for instance, accepting that climate change is anthropogenic might play a role in various practical decisions, but there is a gap between the acceptance and the subsequent action (of, say, imposing a limit on greenhouse gases emissions), which is often taken by another agent (here, governments). However, given our views on acceptance, and of assertion as a kind of acceptance (see Sect. 3.2), this makes the juror’s case even more interesting, by highlighting the essential link between acceptance, assertion, and action.
In Sect. 3, we clarify some assumptions and implications of such a view.
We do not claim that no occurrence of the notion of doubt in ordinary language corresponds to lack of certainty, but rather that the cases where it makes sense to ask whether doubt is reasonable are not of this kind. Our proposal is not intended as accounting for all the meanings that the word ‘doubt’ may have in different contexts; see Moon (2018) for such a proposal.
Such a stake-related aspect of doubt has been acknowledged by Thagard (2004), after Peirce (1877). However, it is not necessary, as Thagard does, to appeal to incoherence (according to him, doubt arises from the hypothesis’ conflicting with one’s background beliefs). Moreover, Thagard uses this idea to reject the probabilistic account of reasonable doubt; we however argue that they are compatible.
This is the reason why it is not relevant, in the framework of the present analysis, to include in the definition of doubt acceptance of the complement to the hypothesis at stake (as does Salmon (1995) at the onset his paper): when one accepts non-H, it makes no big sense to say that one doubts H.
Certainly, as one anonymous referee emphasized, we can, and often do, have “idle doubts”, namely doubts regarding a past decision, even though that decision is irreversible. That is however compatible with our view of doubt as decision-relative and dynamical: after the defendant was acquitted, the juror may doubt whether she has made the right choice. That hypothesis (let us call it H’) is different from both the guilt (H), and the innocence (-H) hypothesis (which she may also doubt). The fact that she cannot come back on the decision on which it bears (which itself depended on H) does not imply that accepting or doubting H’ has no relevance whatsoever for the ex-juror. Indeed, as the anonymous referee insightfully suggests, such alertness to the choices one should have made in the past may be a useful skill to cultivate if one wants to make better decisions in the future. One may account for the need to clarify whether one has made the right choice as an epistemic decision to be made, which might have practical consequences in the future.
True, presumption of innocence may suggest that the per default hypothesis should be innocence. But as soon as there is trial, it is clearly acknowledged that one should doubt innocence, and what becomes at stake is whether there is any doubt about guilt. This is one among other difficulties with how to account for presumption of innocence in a Bayesian framework (see Dahlman 2017; Fenton et al. 2017).
In particular, raising the issue of whether it is reasonable to doubt makes particularly good sense when doubting would consist in actively questioning a hypothesis that the subject herself would be naturally inclined to accept.
As suggested by an anonymous reviewer, the general picture of inquiry sketched here could be nicely complemented analyses of the relationships between Inference to the Best Explanation and Bayesian accounts.
Not believing H may imply having no idea, but that doesn’t correspond to a degree of belief either.
Note that our view of acceptance is compatible both with cases of belief without acceptance, and with cases of acceptance without belief. In fact, as an anonymous referee emphasized, the notion of “acceptance” in the philosophy of science literature is most typically used as a way of understanding cognitive attitudes which, in some sense, fall short of “full belief” (see Jeffrey 1956; Levi 1960).
They would not be related in any way to rational action.
Thanks to Stephen John for helping us clarify this.
The goal of Lackey in that paper is to show that norms of assertion are different from norms of belief (that it is neither necessary, nor sufficient to believe p in order to be entitled to assert p).
Supposing that the case imagined by Lackey correspond to a real situation, a Bayesian account would consist in considering the juror’s belief (which he refuses to base his verdict on) as actually updated in front of the evidence presented in court, but starting from a pathologically high prior — or that his evidence evaluation is biased by racist prejudices and that he gives more weight to incriminating evidence. Being aware of that, the juror would correct this bias by the establishment of a higher threshold for reasonable doubt. In fact, the DT framework is able to account for prejudice-based priors and wrong evaluation of evidence. From that perspective, having explicit rules of evidence, and basing verdicts on collective decision, as well as the practice of peer-reviewing and standards of scientific proof, would in fact be a way to compensate for the irreducible subjectivity of belief.
Indeed, at the end of the day, jurors only have two options. There is certainly time for deliberation, but, when the verdict is brought, rejecting H implies accepting non-H.
However, acceptance as we think of it has to be based on evidence. Cohen, who emphasises the difference between belief and acceptance, is surprisingly unclear about that: in order to emphasise the voluntary character of acceptance as an action, as opposed to the passivity of belief, he claims that a juror bringing a verdict of acquittal because he sees the penalty as “being too severe”, or the alleged crime as “an honourable deed or a public service” (Cohen, 2002, pp. 298–299), “would then be accepting, on ethical or pragmatic grounds rather than on cognitive ones, that the accused is not guilty, while believing perhaps quite firmly in his or her guilt. So the verdict would declare what the jury accepts; not what it believes.” However, if the juror does so independent from any consideration of the evidence, then he does not accept the hypothesis of innocence in our sense—the question of guilt and its probability is simply not relevant to his verdict. In divorcing acceptance from belief, Cohen misses the evidential grounding of the latter.
The verdict’s taking a linguistic form (typically the form of an assertion about guilt) may be misleading, but the question asked to jurors is whether guilt has been proven beyond a reasonable doubt — not whether they ‘believe’ that the defendant is guilty (as Cohen rightly acknowledges, although we disagree with his definitions of belief and acceptance). Interestingly, as a way to prevent from confusing rejection of guilt and belief in innocence, juries in Scotland have a choice between three verdicts: ‘guilty’, ‘not guilty’, and ‘not proven’, the last two equally imply acquittal. Although this can be thought of as a protection of the defendant, this was heavily criticized (Walter Scott called it the bastard verdict), as stigmatizing defendants for which the verdict was ‘not proven’, since they are not freed from any suspicion.
There exist several attempts at conciliating a graded view of beliefs (especially in the Bayesian perspective), as being the most likely account of rational belief change, with the notion of full belief, as both highly intuitive and corresponding to the folk psychology view of mental states and the representationalist view of mental life, as well as largely assumed by most mainstream epistemology. Those attempts have given rise to a debate in epistemology and the philosophy of mind about the relation between full beliefs (also called ‘categorical’ or ‘outright’ beliefs) on the one hand, and graded beliefs, on the other (see Ebert and Smith eds. (2012), as well as the online bibliography available at https://natureofrepresentation.wordpress.com/2013/09/27/bibliography-on-belief-and-degrees-of-belief/. For a more formal approach of the question by a Bayesian who nevertheless keeps room for full belief, see Leitgeb (2013). This debate is sometimes practically undistinguishable from the discussion on the relations between belief (categorical or probabilistic) and acceptance [see Engel, ed. (2000)]—those notions being diversely construed by different authors—and on the norms of assertion (for a recent contribution, see Hawthorne et al. 2016). We will not present those debates, and the various arguments pro and contra the reduction of full beliefs to graded beliefs (or vice versa). We nevertheless take for granted that full belief cannot be equated in any simple and general way to a specific degree of belief, whether very high, or simply above 0.5.
On sincerity, and how it is not the right value for understanding scientific claims and many speech acts, see (John 2018). Although our view is compatible with this claim, it makes finally hard to grasp what a ‘sincere’ speech act would amount to, as we will shortly see.
Moreover, it would be a naïve idealization not to acknowledge that one’s attribution of mental states to others impacts one’s conveying one’s own mental states (even sincere).
In fact, many philosophers and psychologists claim that we do not access to our beliefs through introspection. See Mandelbaum (2014, pp. 75–76) for references.
It is a hard question what actually determines the threshold for full beliefs so construed, and we can only draw conjectures about empirical issues. One can for instance suppose that the juror’s “full belief” is not independent from the fact that she otherwise has a verdict to bring. Maybe her threshold for belief would be high, so as to avoid cognitive dissonance; conversely, she might react to the uncomfortable feeling of bringing a verdict of acquittal while being far from convinced of innocence by acknowledging (at least for herself) that she believes the defendant is guilty… In all those (putative) cases, the threshold for reasonable doubt as far as the verdict is concerned would not be free from consequences on the threshold for what the juror identifies as her “belief”. More generally, it seems hard to ask oneself what one believes, without considering any of the decisions that are likely to result from the answer, or without imagining a possible interlocutor. Not only is it difficult to imagine an entirely non-contextual assertion, but also can we hypothesise that, for what might be the closest to such an ideally sincere assertion, the threshold for belief might vary along various parameters. Among other things, what (one believes) others believe about a given issue might make one’s own answer vary. The threshold might also vary according to the threshold for a decision that is typically associated to a question (which may vary between subjects). For instance, is it really possible to consider the question of what one believes regarding the potential harmfulness of vaccines without the debate on obligation to vaccinate, and the various opinions expressed around this entering into one’s assessment of one’s own belief? Is it possible to entirely dissociate the issue of the guilt of a defendant from the typically associated decision that is verdict — even though one does not have to actually bring a verdict? Those are psychological issues, whose answer can only be empirical, but raising them here enables us to highlight that full belief, as distinct from acceptance, is a very hard to grasp entity. The closest thing we have seems to vary depending on the context, just as any other act of acceptance.
As one anonymous reviewer notes, there should be a way to develop our account of doubt as essentially decision-relative in a way that makes room for a general disposition to doubt—by contrast with active doubting—as valuable, insofar as it warrants openness to potential alternative hypotheses.
This argument is different from Huneman’s (2015), who suggests that adopting some conspiracy theories might result very costly from an epistemic point of view, because of the radical revision of one’s web of belief it implies. This approach rather applies to the adoption of fanciful theories than for doubt. Indeed, doubting a theory does not imply accepting another one. Hence, doubting well entrenched theories does not necessarily lead to incoherence. At any rate, our argument is not incompatible with Huneman’s.
See Hardwig (1985).
One could even add some global coherence constraints on thresholds, whereby one should doubt any claim that is less confirmed than a given claim I doubt. However, such constraints seem to conflict with others, having to do with social norms. For instance, imagine a person who has no a priori reason to believe that she has a certain disease that is relatively rare (let’s say a 1 on 3000 incidence in global population). If that person decides to take the diagnostic test that no one takes unless one has some reason to suspect that one is ill, one would think this person is unreasonable (she unreasonably doubts that she is healthy to this respect and search more evidence). Now imagine another person who is considered at risk for an extremely rare disease: the incidence in general population is 1 on 1,000,000, but that person has 1 on 3000 chance to suffer from this disease. She will be considered totally reasonable to take some test to know whether she has this disease (even though we assume same costs for test, and same gravity of disease, and equal opportunity to cure it).
Alice Dreger’s inquiries, as she tells them in Galileo’s middle finger (2015) embody this kind of intellectual (and more general) courage. This leads her to deep reflections on whether any hot question is worth debating, raising both the question of whether one should address any question whatever one may find (even if that might somehow be detrimental for social justice) but also because one may initially think that there is no chance to find anything on such a route.
This issue is related to another one, which we will not address here, about whether statistical evidence is enough to convict—such as the so-called “gate-crasher paradox” (Cohen 1981).
See Schum (1994) on the irreducible subjectivity of the evaluation of the relevance of evidence.
As emphasized by Stephen John in personal communication, this is well exemplified by debates over climate modelling: one can have some degree of belief in some claim generated by a model, but also have reasons to worry the model itself is partial.
This is object of Hahn and Hartmann (in preparation).
This is far from a rare situation. Most application of the precaution principle consists in acting as if H was the case, without necessarily searching an explanation for a specific phenomenon.
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Acknowledgements
The authors wish to thank Anouk Barberousse, Denis Bonnay, Isabelle Drouet, Adam J.L. Harris, Philippe Huneman, Stephen John, David Lagnado, as well as two anonymous reviewers for useful discussions and/or comments on earlier drafts of this paper.
Funding
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 660187.
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Vorms, M., Hahn, U. In the Space of Reasonable Doubt. Synthese 198 (Suppl 15), 3609–3633 (2021). https://doi.org/10.1007/s11229-019-02488-z
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DOI: https://doi.org/10.1007/s11229-019-02488-z