What is Doubt and When is it Reasonable?
Paul Thagard
University of Waterloo

Thagard, P. (forthcoming). What is doubt and when is it reasonable? In M. Ezcurdia & R. Stainton & C. Viger (Eds.), New Essays in the Philosophy of Language and Mind. Canadian Journal of Philosophy, Supplementary Volume. Calgary: University of Calgary Press.


Descartes contended that "I am obliged in the end to admit that none of my former ideas are beyond legitimate doubt" (Descartes 1964, p. 64). Accordingly, he adopted a method of doubting everything: "Since my present aim was to give myself up to the pursuit of truth alone, I thought I must do the very opposite, and reject as if absolutely false anything as to which I could imagine the least doubt, in order to see if I should not be left at the end believing something that was absolutely indubitable" (p. 31). Similarly, other philosophers have raised doubts about the justifiability of beliefs concerning the external world, the existence of other minds, and moral principles; philosophical skepticism has a long history (Popkin 1979).

The concept of doubt is not only of philosophical interest, for it plays a central role in the legal system when jurors are instructed not to convict an accused criminal unless they are convinced of guilt beyond a reasonable doubt. Surprisingly, however, there is little consensus in the theory and practice of law concerning what differentiates reasonable from unreasonable doubt. Faust (2000a, p. 229) reports a "firestorm of controversy" concerning the proper legal meaning of the term "reasonable doubt," and furnishes an extensive annotated bibliography.

My aim in this paper is to propose (1) a descriptive theory of doubt as a cognitive/emotional mental state and (2) a normative theory of the conditions under which doubt can be viewed as reasonable. After describing previous philosophical accounts of doubt, I develop an account of doubt as emotional incoherence that provides a framework for a general account of when doubt is reasonable or unreasonable in philosophical, legal, and scientific contexts.

Cold and Hot Doubt

Social psychologists distinguish between cold cognition and hot cognition, where the latter involves emotions tied in with personal goals and motivations (Kunda, 1999). Similarly, I shall distinguish between cold doubt and hot doubt, where the latter involves an attitude toward a proposition that is emotional as well as cognitive. Most philosophers and legal theorists have discussed cold doubt, but I shall follow Charles Peirce in treating doubt as hot, that is as involving an attitude toward a proposition that has a central emotional component. First let us consider accounts of cold doubt.
Nathan Salmon (1995) proposes the following definition for the word "doubt":

A doubts p =def (A disbelieves p) or (A suspends judgment concerning p)
A disbelieves p =def A believes not-p
A suspends judgment concerning p =def not-(A believes p) and not-(A disbelieves p)

Salmon acknowledges that this definition constitutes a departure from standard usage in that it does not require that a believer has a grasp of a proposition and has attempted consciously to choose between the proposition and its negation. It follows from his definitions that for any proposition p, either A believes p or A doubts p. This is a very odd result: it implies that a person who has never even considered a proposition, for example, that there are more than a million trees in Newfoundland, either believes it or doubts it. Salmon's definition of doubt also does not take into account the contention of Bertrand Russell (1984, p. 142) that doubt "suggests a vacillation, an alternate belief and disbelief." For both Salmon and Russell, doubt is an entirely cognitive rather than emotional phenomenon, a matter of belief and disbelief.

Similarly, Jennifer Faust's (2000b) discussion of reasonable doubt in the law assumes that it is a purely cognitive matter. She distinguishes two senses of doubt that generate two senses of reasonable doubt:

S doubts1 that p =def S believes that not-P.
S doubts2 that p =def S does not believe that P.
S reasonably doubts1 that p =def S has sufficient reason to believe that not-p.

S reasonably doubts2 that p =def S does not have sufficient reason to believe that p.
Faust makes a convincing case that some prevalent legal instructions concerning reasonable doubt mistakenly confuse the first and second senses, so that jurors are told that acquitting an accused person requires having sufficient reason to believe that the accused was not guilty (sense 1 of "doubt" and "reasonable doubt"). The more appropriate instruction is that acquitting an accused person requires only not having sufficient reason to believe that the accused was guilty (sense 2). As for Salmon and Russell, Faust's doubt is a matter of cold cognition.

An alternative hot conception of doubt was developed by Charles Peirce in the 1860s and 1870s. He attacked Descartes' method of doubt by arguing that complete doubt is a mere self-deception: "Let us not pretend to doubt in philosophy what we do not doubt in our hearts" (Peirce 1958, p. 40). According to Peirce, beliefs are habits of mind that guide our desires and shape our actions. Doubt is not merely a matter or belief or disbelief, but is an irritation that causes inquiry, which is a struggle to attain a state of belief (p. 99). The Cartesian exercise of questioning a proposition does not stimulate the mind to struggle after belief, which requires a "real and living doubt" (p. 100). According to Peirce, "the action of thought is excited by the irritation of doubt, and ceases when belief is attained" (p. 118). Doubt is not the result of an internal exercise: "Genuine doubt always has an external origin, usually from surprise" (p. 207). For Peirce, doubt is intimately tied with goals and motivation to increase knowledge, as well as with emotional states involving irritation, excitement and surprise. Doubt is a matter of hot cognition.

Doubt as Emotional Incoherence

I think that Peirce's account of doubt captures much more of the nature of real doubt than Salmon's cold account, but Peirce does not offer a general theory of what doubt is. First it is useful to have some concrete examples of what Peirce called "real and living" doubt to make it clear what needs to be explained. I am not proposing a definition of the concept of doubt, since such analyses are rarely successful or fruitful. Rather, my aim is to develop a theory of about the nature and causal origins of the mental state of doubting.

Here are some real philosophical, scientific, and legal examples of doubt:
Philosophy: Many students taking their first course in philosophy of mind are surprised to learn that most work in the field adopts some form of materialism, in contrast to their religious views that assume there is a non-material soul that survives death. The students doubt that mind is just the brain, and feel considerable anxiety at the possible challenge to their religious beliefs.
Science: In 1983, medical researchers heard a young Australian, Barry Marshall, propose that most peptic ulcers are caused by infection by a newly discovered bacterium, now known as Helicobacter pylori. The researchers strongly doubted that Marshall could be right about the causes of ulcers, and were very annoyed that a beginner would propose such a preposterous theory (Thagard, 1999).
Law: In 1995, the jury in the O. J. Simpson trial learned that some of the evidence was sloppily handled and that one of the detectives in the case had a long history of racism. For these and other reasons they doubted that Simpson murdered his ex-wife and quickly and enthusiastically voted to acquit him (Thagard, forthcoming).

In each of these cases, people encountered a proposition or set of propositions that did not fit with what they already believed, and they reacted emotionally as well as cognitively.
These cases fit the following prototype of the mental and social situation in which doubt arises. Note that this prototype is not proposed as a definition of the word "doubt," but as a description of the typical nature and origins of doubt. Typically, people doubt a proposition when:
1. Someone makes a claim about the proposition.
2. People notice that the proposition is incoherent with their beliefs.
3. The people care about the proposition because it is relevant to their goals.
4. The people feel emotions related to the proposition.
5. The emotions are caused by a combination of the claim, the incoherence, and the relevance of the proposition.
Let us examine each of these facets of doubt in more detail.

In all three of the cases I described, doubt arises by virtue of claims made by others: mind is material, ulcers are caused by bacteria, O. J. is guilty. But doubt does not have to arise by virtue of a claim made by someone else. Occasional cases of real doubt are internally engendered: I think that my gloves are in my coat pocket, but then it occurs to me that I might have forgotten to put them there. Hence Peirce exaggerated when he stated that genuine doubt always has an external cause, but he was for the most part right in understanding doubt as externally inspired, in contrast to an internal Cartesian exercise. External causes of doubt are most often the claims of others, as in my prototype above, but can also be interactions with the world, as when scientists collect data that cause them to doubt prevailing theories. In the gloves example, my doubt that my gloves are in my coat pocket may be caused by seeing something that reminds me that I put my gloves elsewhere. The typical external origins of doubt are important for the kinds of emotional states involved in doubt, such as surprise when the world does not turn out to be as it was expected to be, or annoyance that someone is making a claim incoherent with one's own beliefs.

Doubt always involves the incoherence of a proposition with the rest of what one believes. Incoherence is best understood in terms of a theory of coherence as constraint satisfaction that I have developed at length elsewhere (Thagard, 2000). f-On this theory, inference is a matter of accepting and rejecting representations on the basis of their coherence with other representations. Coherence is determined by the constraints between representations, where the kinds of constraint and the kinds of representation are different in six kinds of coherence: explanatory, conceptual, perceptual, deductive, analogical, and deliberative. For example, in explanatory coherence, the representations are propositions and the constraints include positive ones that arise between two propositions when one explains another and negative ones that arise between propositions that are contradictory or in explanatory competition. Competing theories in science, law, and ordinary life can be evaluated by accepting or rejecting propositions based on the extent to which doing so maximizes satisfaction of multiple conflicting constraints. Various algorithms for maximizing coherence are available.

A proposition is incoherent with a person's belief system when the process of coherence maximization does not lead to its acceptance into that belief system. The most obvious source of incoherence is contradiction, when a claim is made that contradicts what one already believes. But incoherence can be looser, when a claim has weaker kinds of negative constraints than contradiction. For example, in the ulcer case, the claim that bacteria cause ulcers did not logically contradict the claim that excess acidity causes ulcers, yet medical researchers saw them as competing hypotheses. Doubt can even arise analogically, when a hypothesis is recognized as analogous to one such as cold fusion that has previously been recognized as dubious. So the incoherence that a doubted claim has with a belief system need not be based on contradiction. In all cases of doubt, a claim is not accepted because doing so would diminish coherence.
Just as Salmon distinguishes between disbelief and suspension of judgment, we can distinguish between strong incoherence, in which a proposition is rejected, and weak incoherence, in which a proposition is neither accepted nor rejected. This can happen with the connectionist (artificial neural network) algorithm for maximizing coherence, in which the activation of an artificial neuron representing a proposition can vary between 1 (acceptance) and ­1 (rejection), with activation close to 0 signifying a state of neither acceptance nor rejection. Doubt requires non-acceptance, but it does not require rejection, for it can involve either strong or weak incoherence.

Doubt does not require the conscious recognition of incoherence: we can feel unease about a proposition without being at all aware of the source of the discomfort. Coherence calculations, like most inferences, are performed by the brain unconsciously, with only some of the results being conveyed to consciousness. Hence noticing that a proposition is incoherent with one's belief system (step 2 in the prototype above), need not involve the conscious thought "I can't believe that because it does not fit with my other beliefs" but merely a negative emotional reaction to the claim.
Step 3 in my doubt prototype posits that people only doubt propositions that they care about, where care is a matter of relevance to their goals, both epistemic and practical. The two main epistemic goals are truth and understanding, where the latter is achieved by unifying explanations. If your goals include the achievement of truth and understanding, then you will be provoked by someone who makes a claim that you are convinced is false. Gastroenterologists were in part annoyed by Barry Marshall because his claims about ulcers seemed to them false and inimical to understanding. But personal, practical goals can also contribute to doubt: if a claim is a potential threat to your well-being or self-esteem, then you may be motivated to look at it more critically. For example, the beginning philosophy students may doubt materialist philosophy more intensely because of its potential threat to the solace and social connections that they derive from their religious beliefs, producing a kind of motivated inference (Kunda 1999). Practical goals need not involve only personal interests, but could also be concerned with the general welfare of people or with questions of fairness. As I will discuss further below in connection with reasonable doubt, inference in science and law are not merely aimed at acquiring truths. Science also often has a practical goal of increasing human welfare through useful technology, for example using antibiotics to cure ulcers. And the law is concerned not only to find out the truth, but also to ensure that the accused gets a fair trial and is presumed to be innocent until proven otherwise. Epistemic and practical goals must be relevant to a claim, for there is no point in wasting your time doubting (or even entertaining) a claim that you do not care about.

There are a wide variety of emotions involved with the feeling of doubt, most of them negative. The mildest negative emotions associated with doubt include Peirce's irritation and the unease and discomfort that I mentioned. These emotions can be sufficiently vague and ill-defined that it is not even obvious what their objects are, for example whether you are irritated by the claim that aroused doubt or by its proponent. If a claim is not strongly incoherent with your belief system, so that rejection is not obviously called for, the tension between accepting and rejecting the proposition may cause anxiety, especially if it is highly relevant to your personal goals.

Intense negative emotions can also be associated with doubt. If someone makes a claim that is both strongly incoherent with your belief system and highly relevant to your epistemic and practical goals, then doubting the claim can involve emotions such as annoyance, outrage, and even anger. Believing that the proposed claim is to be rejected is tied in not only with disliking the claim but also with disliking the proponent of the claim. For example, the medical researchers who challenged Barry Marshall called him crazy and irresponsible, and were angry that he kept defending claims that they thought were absurd. According to the seventeenth-century philosopher John Wilkins (1969), doubt is a kind of fear. This claim is not generally true, but there are cases where fear may be part of doubt, as when a scientist fears that new data may show a favored theory to be false.

There are also unusual cases in which doubt is associated with positive emotions. Suppose you are told by a doctor that you need open heart surgery, but you read on the Internet that your condition might be treated less invasively by a new drug. Then you doubt that you should have the surgery, and are happy at the prospect of avoiding a risky procedure. In this case, you are happy to doubt that you need surgery. However, if you are unsure of which treatment to pursue, you may feel strong negative emotions such as anxiety because you have doubts about not getting surgery as well as about getting surgery.

We now have the ingredients of the causal network that produces the emotions associated with doubt. Because someone makes a claim that is incoherent with what you believe and that is relevant to your goals, you respond emotionally to the claim and sometimes also to the claimant. Prototypically, doubt is emotional incoherence.

Reasonable Doubt

If doubt is a cognitive/emotional state caused by the incoherence of a claim relevant to a person's goals, then what is reasonable doubt? This question is of philosophical, legal, and scientific importance. In philosophy, we can ask whether the doubts raised by Descartes, Hume and other skeptics, in ethics as well as epistemology, are reasonable. Is it reasonable to doubt whether there is an external world, whether the future will be like the past, and whether there is an objective difference between right and wrong? In the law, the issue of what constitutes reasonable doubt has been vexing, for practical as well as theoretical reasons. For example, the Supreme Court of Canada recently overturned a number of convictions on the grounds that the judges in the original trial had given an incorrect instruction to the jury concerning the nature of reasonable doubt. Psychological experiments have found that whether mock jurors decide to convict an accused can be influenced by what they are told about the nature of reasonable doubt (Koch and Devine 1999). In science, there are not only epistemic issues about whether scientists are reasonable in doubting a newly proposed theory, but also practical issues about when it is reasonable to doubt the desirability of technological applications of science. For example, were gastroenterologists in 1983 reasonable in doubting the truth of the bacteria theory of ulcers and the efficacy of treatment of ulcers by antibiotics? I will propose a general account of reasonable doubt as legitimate emotional incoherence, and then discuss its application to philosophy, law, and science and technology.

On my view, the reasonableness of doubt is both an epistemic and a practical matter, involving epistemic standards concerning truth and understanding and also practical standards concerning welfare and fairness. In keeping with the prototype of doubt that I advanced in the last section, I will specify that doubt in a proposition is reasonable when:

1. A claim about the proposition has been made.
2. The noticed incoherence of the proposition with other beliefs is based on a legitimate assessment of coherence.

First, the aptness of doubt requires that a claim about a proposition has been made, normally by someone other than the person who doubts it. This rules out the fanciful, imaginary cases of doubt that Peirce rightly derided. The second condition is much more demanding, requiring that, when people come to doubt something because it is incoherent with their beliefs, they have performed a legitimate calculation of coherence.

Legitimacy depends on the kind of coherence involved. For explanatory coherence, which is the kind most relevant to factual claims in metaphysics, law, and science, the requirements of legitimacy include:
1. The available relevant evidence has all been taken into account.
2. The available alternative hypotheses have all been taken into account.
3. The available explanatory relations have all been used to establish constraints among the hypotheses and evidence.
4. Constraint maximization has been performed, consciously or unconsciously, producing a coherence judgment about what propositions to accept or reject.

Doubt can fail to be reasonable according to these legitimacy conditions when people make their judgments of incoherence without taking into account all the available relevant information.
This discussion has been rather abstract, so let me now relate it to philosophical, legal and scientific cases of reasonable and unreasonable doubt. The philosophy students' initial doubts about materialist theories of mind strike me as reasonable, at least initially. They encounter the claim that there is no soul in lectures or reading, and the claim is indeed incoherent with their religious and metaphysical beliefs. Because they care for both theoretical and personal reasons whether there is a soul, they feel negative emotions such as discomfort arising from the materialist claim. Of course, the doubt will remain reasonable only if, as they learn more about the evidence for materialism and against mind-body dualism, they continue to perform a legitimate coherence calculation. My own view is that, once all the available evidence and explanations are taken into account, materialism has more explanatory coherence than dualism (Thagard, 2000). But students initially do not have all this information available to them, so their doubt is reasonable. In contrast, Cartesian doubt about whether one exists is not reasonable: no one claims non-existence and the hypothesis is not incoherent with other beliefs. The same is true for Humean doubt about whether the future will be like the past. There are no negative emotions involved in these philosophical exercises; if there were any people seriously worried about whether they exist, we would judge them to be mentally ill.

In legal trials, the reasonableness of doubt depends on the kind of legal investigation. It is of crucial importance that the standard of "beyond reasonable doubt" that applies in criminal trials is not used in civil trials, where jurors' conclusions need only be based on a preponderance of evidence. A crucial aspect of criminal trials in the English tradition is that there is a presumption of innocence. This is clearly not related to the epistemic goal of truth: there no reason to believe that the priory probability of innocence is greater than that of guilt, and in fact the conditional probability of guilt given arrest is usually much higher than the conditional probability of innocence given arrest. Rather, the presumption of innocence is maintained in order to ensure that trials are fair, not just in the sense that the accused and prosecution are treated equally, as the plaintiff and defendant are supposed to be in civil trials, but in the stronger sense that we place a high moral value on not convicting the innocent. Because fairness is a goal of criminal trials in addition to truth, negative emotions concerning claims about the guilt of the accused can arise that are more intense than would be inspired by explanatory coherence alone. Convicting the innocent is a moral as well as an epistemic mistake, and appropriately provokes outrage.

Finally, consider the reasonableness of doubt in scientific and technological contexts. It might be assumed that scientific doubt is a purely epistemic matter, but Richard Rudner (1961, pp. 32-33) has convincingly argued otherwise:

Since no scientific hypothesis is ever completely verified, in accepting a hypothesis on the basis of evidence, the scientist must make the decision that the evidence is sufficiently strong or that the probability is sufficiently high to warrant the acceptance of the hypothesis. Obviously, our decision with regard to the evidence and how strong is "strong enough" is going to be a function of the importance, in the typically ethical sense, of making a mistake in accepting or rejecting the hypothesis. Thus, to take a crude but easily manageable example, if the hypothesis under consideration stated that a toxic ingredient of a drug was not present in lethal quantity, then we would require a relatively high degree of confirmation or confidence before accepting the hypothesis-for the consequences of making a mistake here are exceedingly grave by our moral standards. In contrast, if our hypothesis stated that, on the basis of some sample, a certain lot of machine-stamped belt buckles was not defective, the degree of confidence we would require would be relatively lower. How sure we must be before we accept a hypothesis depends on how serious a mistake would be.

Thus doubt in science is in part a function of our practical goal of avoiding harm that might result from premature acceptance of a hypothesis. In theoretical astrophysics, the risk of harm is trivial, so doubt can be based largely on epistemic goals, but doubts can have a partially practical basis in areas like medicine (relevant to treating the sick) and nuclear physics (relevant to the construction of power plants and bombs). Just as the concern to acquit the innocent can intensify doubts in legal contexts, so the concern to avoid technological harm can intensify doubts in scientific contexts.
Medical doubts can be reasonable for both epistemic and practical reasons. When gastroenterologists first encountered the bacterial theory of ulcers, they had strong negative emotional reactions in part because it was incoherent with their beliefs about the causes of ulcers and the absence of bacteria in the stomach, but also because of their concern about people being treated inappropriately. Their doubts about Barry Marshall's views were reasonable in 1983, because there was little evidence then that bacteria cause ulcers and none that killing the bacteria could cure ulcers. By 1994, however, the situation had changed dramatically as the result of carefully designed studies that showed that many people's ulcers had been cured by the right combination of antibiotics. At this point, coherence with the relevant medical information required acceptance of the bacterial theory of ulcers, so doubt was unreasonable.

Many epistemologists think that rational belief fixation is a probabilistic rather than a coherence-based process, so that reasonable doubt depends on the probability of a claim. For example, Davidson and Pargetter (1987) give three requirements for a guilty verdict:
(a) the probability of guilt given the evidence is very high,
(b) the evidence on which the probability is based is very reliable, and
(c) the probability of guilt is highly resilient relative to any possible evidence.
But there are powerful reasons why probability theory is not the appropriate tool for understanding reasonable doubt.

First, the interpretation of probability is problematic in legal, scientific, and philosophical contexts. It is obvious that the probability of guilt given the evidence is not the objective, statistical sense of probability as a frequency in a population: we have no data that allow us to say in a particular trial that the accused would be guilty in a specifiable proportion of such trials. So probability must be some kind of logical relation that has never been clearly defined, or a subjective degree of belief.
Second, there is considerable psychological evidence that people's degrees of belief do not obey the rules of the probability calculus (Kahneman, Slovic, and Tversky 1982; Tversky and Koehler 1994). Many psychological experiments have shown that the degrees of confidence that people place in propositions are often not in keeping with the rules of probability theory. Probability theory is a relatively recent invention, having been developed only in the seventeenth century (Hacking 1975). Yet people have been making judgments of uncertainty for thousands of years, without the aid of probability theory. Coherence provides a much more plausible descriptive and normative account of non-statistical human inference than does probability theory.
Third, probability theory is often orthogonal to the aims and practice of law. Cohen and Bersten (1990) argue that high probability is not even a necessary condition of finding someone guilty, which requires satisfying a number of legal rules that must be followed in order to ensure that the accused is given the benefit of the presumption of innocence. Allen (1991, 1994) has described numerous ways in which deliberation in legal trials much better fits a coherence account than a probabilistic one.

Fourth, there are technical reasons why probabilities are difficult to compute in real-life cases in law and other areas. A full probability calculation is impossible in cases involving more than the handful of propositions, because the size of a full joint distribution increases exponentially with the number of propositions. Powerful computational tools have been developed for calculation of probabilities in Bayesian networks, but they require more conditional probabilities than are usually available and strong assumptions of independence that are rarely satisfiable. Computing probabilities in legal and similar cases is much more difficult than coherence computations based on maximization of constraint satisfaction. Hence incoherence is a more plausible basis for reasonable doubt than low probability.

Finally, probability does not provide the basis for understanding reasonable doubt because it is not directly tied in with emotion. I have argued that doubt is a mental state that usually involves negative emotions such as discomfort and fear, whereas probability judgments are purely cognitive. In contrast, coherence judgments routinely give rise to positive emotions such as feelings of satisfaction and even beauty, whereas incoherence judgments give rise to negative emotions such as anxiety (self-reference omitted). If doubt is emotional incoherence, then there must be more to reasonable doubt than just a probability calculation.


This paper has advanced and defended several novel claims about the nature of doubt and reasonable doubt. First, doubt is not just a cold cognitive matter of belief and disbelief, but also involves a hot, emotional reaction to a claim that has been made. Second, doubt is not based on the low probability of a claim, but on its incoherence with a thinker's beliefs and goals, where coherence can be computed in a psychologically realistic manner by parallel satisfaction of multiple constraints. Third, what makes a doubt reasonable is not a probability calculation, but a coherence computation that takes into account constraints based on the full available range of evidence, hypotheses, and explanatory and other relations. Reasonable doubt is legitimate emotional incoherence.

Acknowledgments: I am grateful to Christine Freeman for research assistance, and to her, Jing Zhu, Marcia Sokolowski, and Tim Kenyon for helpful suggestions.

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