Delusions

Abstract

A delusion is a behavioral symptom in the sense MeSH indexes it: a fixed false belief, held with firm conviction, not amenable to contrary evidence and out of keeping with the person’s culture. Cognitive psychology treats it not as a meaningless by-product of illness but as a belief formed by ordinary belief-forming machinery pushed to an extreme. This article develops the two competing traditions: the one-factor view that a delusion is a rational response to an anomalous experience, and the two-factor view that a second impairment of belief evaluation is also required. It covers the reasoning biases measured in delusion-prone people, above all a tendency to gather less evidence before deciding, and the predictive-coding account that unifies experience and belief. A worked example derives the Bayesian posterior behind the beads task, and three interactive demonstrations make the ideas concrete.

Keywords: delusions, belief, two-factor theory, jumping to conclusions, predictive coding

The puzzle a delusion poses is why a belief should survive its own refutation. A person with a persecutory delusion continues to believe they are being hunted though no evidence of a hunter ever materializes; a person with Capgras delusion maintains that a spouse has been replaced by an impostor despite the impostor being identical in every verifiable respect. The clinical definition captures the surface — fixity, falsity, imperviousness to counter-argument (Coltheart et al., 2011) — but cognitive psychology asks the harder question: by what process does a mind arrive at such a belief and then defend it, and is that process continuous with normal believing or a break from it?

The answer that has organized the modern field is that delusions are built by the same belief-forming system that serves everyone, operating on unusual inputs or with one of its checks disabled. This is the program of cognitive neuropsychiatry: to explain a delusion by identifying which component of normal belief formation has been disrupted and how (Coltheart, 2007). On this view the delusion is not alien to cognition; it is cognition under specifiable abnormal conditions, which is what makes it a tractable object of study rather than mere noise.

What Delusions Are

A delusion is defined by three features taken together: the belief is held with full conviction, it is false or at least unwarranted, and it resists the evidence and argument that would ordinarily revise it (Coltheart et al., 2011). None of these alone marks a belief as delusional — ordinary people hold false beliefs firmly and revise slowly — but their conjunction, together with the belief being out of keeping with the person’s culture, is what the clinical concept picks out. Delusions appear across many conditions, most characteristically in the psychoses, and they vary not in their formal structure but in their content, which clinicians group into recurring themes.

The themes matter to cognitive psychology because they constrain any theory of mechanism: a satisfactory account must explain both why delusions take the particular forms they do and why those forms recur across individuals and cultures. Persecutory and referential themes are by far the most common, a fact any mechanistic theory must accommodate (Freeman, 2007). Table 1 sets out the principal themes and the belief that characterizes each.

The recurring structure across these themes is that a delusion is an explanation. It accounts for something — a feeling of significance, a loss of familiarity, an experience of being acted upon — and the content of the delusion is, in each case, a candidate reason for the experience. That observation is the point of departure for the two theories that have dominated the field.

Anomalous Experience and Explanation

The oldest cognitive theory of delusions is the one-factor view, associated with Brendan Maher, which holds that a delusion is a reasonable belief arrived at by normal reasoning applied to an abnormal experience (Maher, 1974). On this account the person with a delusion is not reasoning badly; they have undergone a genuinely strange experience — a feeling that ordinary objects are charged with meaning, or that a familiar face no longer feels familiar — and the delusion is the explanation a normal mind would construct to account for it. The theory’s strength is that it takes the delusion seriously as an attempt to make sense of something real to the person, and it predicts the content of certain delusions well.

Capgras delusion is the sharpest test case. Ellis and Young proposed that it follows from damage to the pathway carrying the automatic affective response to a familiar face: the patient sees a face they recognize as their spouse, yet the usual jolt of familiarity is absent, and the impostor belief is the explanation that resolves the contradiction between recognition and the missing feeling (Ellis & Young, 1990). Here the one-factor logic is compelling — the anomalous experience is specific and the delusion is its natural reading.

But the one-factor theory faces a decisive objection, and it is the objection that motivates the two-factor theory (Langdon & Coltheart, 2000). Patients with the same affective disconnection from faces, caused by the same kind of damage, do not all become delusional; some report the strange feeling and seek an explanation without ever adopting the impostor belief, and crucially, no normal person presented with the anomalous experience would hold to the impostor hypothesis in the face of its overwhelming implausibility. So an anomalous experience cannot be the whole story. A second factor is required: an impairment in the system that evaluates candidate beliefs and rejects the implausible ones. The delusion arises only when both are present — the experience that supplies the content, and the evaluative deficit that lets an implausible explanation be accepted and then protected from revision (Coltheart et al., 2011). The demonstration below lets the reader combine the presence or absence of each factor and see which combination yields a delusion.

A third tradition, developed chiefly for persecutory delusions, places less weight on a discrete anomalous experience and more on the motivational and emotional context in which a belief about threat is built. On this view persecutory delusions are threat beliefs that draw on pre-existing anxiety, negative beliefs about the self, and reasoning biases, and are maintained because the person does not gather the disconfirming evidence that would undermine them (Freeman, 2007; Bentall et al., 2001). The motivational and the deficit traditions are not mutually exclusive, and later work has sought to integrate them (McKay et al., 2007).

Reasoning Biases and Data-Gathering

Whatever supplies a delusion’s content, its formation and persistence implicate how the person handles evidence. The most robust finding in this area is a bias in data-gathering: people with delusions, and people high in delusional ideation, tend to request less evidence before committing to a conclusion. The bias is measured with the beads task, in which a participant watches beads drawn from one of two jars of known but opposite colour composition and decides, after as many draws as they wish, which jar is the source. People prone to delusions characteristically decide after very few draws — often after a single bead — a pattern labelled jumping to conclusions (Garety et al., 2001).

A meta-analysis of the beads-task literature confirmed that the effect is real and reasonably general: delusional ideation is reliably associated with gathering less data before a decision, though the association with the strength of a specific current delusion is weaker and the mechanism remains debated (Ross et al., 2015). The data-gathering bias matters for theory because it offers a candidate for the second factor: a mind that decides on thin evidence will both adopt a delusional hypothesis too readily and fail to accumulate the counter-evidence that would overturn it. The demonstration below runs the beads task and reports how the Bayesian probability of each jar evolves with each draw, letting the reader see how much certainty a given number of draws actually warrants.

The reasoning story is not that delusional thinking is illogical in a formal sense. Given the strong evidence the standard beads task provides, even a single draw is quite diagnostic, so an early decision is not grossly irrational. The bias is subtler and quantitative: a readiness to treat weak evidence as sufficient, which the worked example below makes precise.

The Predictive-Coding Account

The most influential recent framework treats the brain as a prediction machine that continually generates expectations about its sensory input and updates them in proportion to prediction error — the mismatch between what was expected and what arrived. On this predictive-coding view, perception and belief are two levels of a single hierarchy that works to minimize prediction error, and the weight given to any prediction error is set by its estimated precision, or reliability (Fletcher & Frith, 2009).

Delusions, on this account, arise from aberrant prediction-error signalling: prediction errors are generated or weighted inappropriately, so that events carrying no real significance are flagged as surprising and demanding of explanation (Corlett et al., 2010). The idea traces to Kapur’s proposal that psychosis is a state of aberrant salience, in which a dysregulated dopamine system assigns inappropriate significance to neutral stimuli and the delusion is the patient’s own cognitive effort to make sense of that misplaced salience (Kapur, 2003). This aberrant salience is the computational translation of Maher’s anomalous experience — the feeling that something ordinary is charged with meaning is what an unwarranted, high-precision prediction error feels like from the inside. A delusion then forms as a new, higher-level belief recruited to explain away the persistent error, and because that belief comes to dominate the precision-weighting of subsequent evidence, it becomes self-reinforcing and resistant to correction (Sterzer et al., 2018). The framework has been extended to hallucinations, understood as perception dominated by strong priors in the same precision-weighting scheme, unifying the two cardinal psychotic symptoms within one mechanism (Corlett et al., 2019). The demonstration below lets the reader adjust the precision assigned to prior expectations and to sensory prediction error and watch where the balance tips toward an aberrant, delusion-prone inference.

The predictive-coding account is attractive because it closes the gap between the two factors: the aberrant prediction error is the anomalous experience, and the same miscalibration of precision that produces it also distorts how later evidence is weighed, giving a single mechanism for both the content and the imperviousness of the belief (Fletcher & Frith, 2009).

Worked Example

How much certainty does a decision in the beads task actually warrant, and what does an early decision cost in accuracy? Take the standard setup: one jar holds 85 green beads and 15 red, the other holds 85 red and 15 green, and before any draw each jar is equally likely to be the source. A bead is drawn, shown, and replaced, so successive draws are independent.

The belief about which jar is the source is updated by Bayes’ rule. After drawing a single green bead, the posterior probability that the source is the green-majority jar is the likelihood of a green from that jar times its prior, divided by the total probability of a green:

0.85 × 0.5 / (0.85 × 0.5 + 0.15 × 0.5) = 0.425 / 0.5 = 0.85.

So one green bead raises the probability of the green jar from 0.50 to 0.85. A person who decides here is correct 85% of the time — but accepts a 15% chance of being wrong, the quantitative signature of deciding on thin evidence. Drawing a second green bead multiplies the likelihoods: the green jar now has weight 0.85 × 0.85 = 0.7225 and the red jar 0.15 × 0.15 = 0.0225, giving a posterior of

0.7225 / (0.7225 + 0.0225) = 0.7225 / 0.745 ≈ 0.970.

Two draws take the probability from 0.85 to about 0.97, cutting the error rate from 15% to 3%. The lesson is the one the reasoning literature draws: a decision after one bead is not irrational — 85% is a strong majority — but it leaves roughly five times the error of a decision after two, and the delusion-prone tendency to stop at the first draw is therefore best described not as illogic but as a systematic willingness to act on less evidence than the task affords (Garety et al., 2001; Ross et al., 2015). The same willingness, applied to beliefs about threat or meaning, both forms a delusion quickly and starves it of the disconfirmation that would end it.

Discussion

The study of delusions has moved from treating them as empty symptoms to treating them as beliefs with a traceable cognitive history. The one-factor theory established the essential insight that a delusion can be an intelligible response to a real experience, and it remains the best account of why particular delusions take the content they do (Maher, 1974; Ellis & Young, 1990). The two-factor theory added what the one-factor theory could not supply: an explanation of why only some people with the anomalous experience become deluded, and why the belief, once formed, is not given up (Langdon & Coltheart, 2000; Coltheart et al., 2011). The reasoning literature made the second factor measurable, and the predictive-coding framework offered a mechanism that could, in principle, generate both factors from a single miscalibration (Fletcher & Frith, 2009; Corlett et al., 2010).

The open questions are about identity and specificity. It is not settled whether the data-gathering bias is a cause of delusions, a consequence, or a correlate of a third variable, nor how tightly it tracks the presence of an active delusion as opposed to a general liability (Ross et al., 2015). Nor is it clear that a single second factor underlies the heterogeneous delusions seen in practice, or whether different routes converge on the common surface of a fixed false belief. What is now widely accepted is the continuity claim — that delusions sit at the far end of a distribution of belief that runs through ordinary conviction and subclinical ideation — which reframes the question from how a pathological faculty works to how a normal one fails (Freeman, 2007).

Current Directions

Recent work has pressed the predictive-coding account from a metaphor toward a testable computational model. The predictive-coding account of psychosis has been laid out as a hierarchical scheme in which the same disturbance of precision-weighting generates both the aberrant percept and the aberrant belief, with specific predictions for perceptual and learning tasks that can be checked against patient data (Sterzer et al., 2018). The extension to hallucinations, framed as perception dominated by overly strong priors, has been supported by experiments showing that conditioned expectations can induce hallucination-like percepts in proportion to a person’s psychotic tendencies, giving the strong-priors hypothesis direct empirical traction (Corlett et al., 2019).

A second direction has reconsidered whether delusions are best understood as a failure of reasoning at all. One line of argument holds that delusions should be derationalized — treated less as broken inferences and more as the output of altered experience, motivation, and coding operating through otherwise intact belief formation, which would realign the cognitive account with the one-factor intuition while keeping the mechanistic detail of the predictive-coding era (Bell et al., 2021). In parallel, the persecutory-delusion research program has turned its cognitive model into targeted treatment, isolating single causal factors such as worry, reasoning, and sleep and intervening on them one at a time to test whether changing a factor changes the delusion (Freeman, 2016).

Common Misconceptions

A delusion is just any strongly held false belief.

Falsity and conviction are not sufficient. A delusion is distinguished by its imperviousness to counter-evidence and its being out of keeping with the person’s culture and education; ordinary false beliefs are revisable and often widely shared (Coltheart et al., 2011).

People with delusions reason illogically.

The characteristic bias is in how much evidence is gathered, not in the logic applied to it. Given the strong evidence of the beads task, an early decision is close to rational; the difference is a readiness to decide on less data (Garety et al., 2001; Ross et al., 2015).

A delusion is meaningless, a mere symptom of a broken brain.

Delusions have a traceable content and function: they typically explain an anomalous experience. The one-factor and predictive-coding accounts both treat the delusion as an attempt, however mistaken, to make sense of something real to the person (Maher, 1974; Corlett et al., 2010).

Delusions are categorically separate from normal belief.

The evidence supports a continuum: delusional ideation can be measured in the general population, and clinical delusions sit at its extreme rather than in a separate kind (Freeman, 2007).

Glossary

Aberrant salience.

The inappropriate assignment of significance to neutral events, held in the predictive-coding account to arise from miscalibrated prediction-error signalling and to constitute the anomalous experience behind a delusion.

Anomalous experience.

A genuinely unusual perceptual or affective event — a missing feeling of familiarity, a sense of charged meaning — that a delusion is formed to explain; the first factor in the two-factor theory.

Bayes’ rule.

The rule for updating the probability of a hypothesis in light of new evidence by combining the prior probability with the likelihood of the evidence; the normative standard against which data-gathering is measured.

Beads task.

A probabilistic reasoning task in which a participant sees beads drawn from one of two jars of opposite composition and decides, after as many draws as wished, which jar is the source; the standard measure of the data-gathering bias.

Capgras delusion.

The belief that a familiar person has been replaced by an identical impostor; the paradigm test case for a one-factor explanation grounded in a specific anomalous experience.

Delusion.

A fixed false or unwarranted belief held with firm conviction, resistant to contrary evidence, and out of keeping with the person’s culture and education.

Delusional ideation.

Delusion-like thinking measured as a continuous trait in the general population, supporting the view that clinical delusions lie at the extreme of a normal distribution of belief.

Jumping to conclusions.

The tendency, heightened in delusion-prone people, to reach a decision after gathering little evidence; the most replicated reasoning finding in the delusions literature.

One-factor theory.

The view that a delusion is a reasonable belief reached by normal reasoning applied to an abnormal experience, requiring no further cognitive deficit.

Persecutory delusion.

The belief that one is being watched, harmed, or conspired against; the most common delusional theme and the focus of the motivational-cognitive tradition.

Precision.

In predictive coding, the estimated reliability of a signal, which sets how much weight a prediction error or a prior receives; its miscalibration is the proposed root of delusional inference.

Prediction error.

The mismatch between a predicted and an actual signal; the quantity the predictive brain works to minimize, and whose aberrant signalling is held to generate aberrant salience.

Predictive coding.

A framework in which the brain continuously predicts its sensory input and updates its models in proportion to precision-weighted prediction error, unifying perception and belief in one hierarchy.

Prior.

A pre-existing expectation or belief that, in Bayesian and predictive-coding accounts, is combined with new evidence; an overly strong prior is proposed to underlie hallucination.

Two-factor theory.

The view that a delusion requires both an anomalous experience (Factor 1) that supplies its content and a deficit in belief evaluation (Factor 2) that lets the implausible explanation be adopted and never revised.

Key Researchers

Richard Bentall

(University of Sheffield). Clinical psychologist who advanced a symptom-focused psychology of psychosis and an attributional account of persecutory delusions, arguing that delusions are best explained at the level of individual symptoms rather than broad syndromes. ORCID - Google Scholar - University of Sheffield - Wikipedia - Wikidata

Max Coltheart

(Macquarie University). Cognitive neuropsychologist and principal architect of the two-factor theory of delusional belief, which holds that an anomalous experience and a separate deficit in belief evaluation are jointly necessary for a delusion to form and persist. ORCID - Google Scholar - Macquarie University - Wikipedia - Wikidata

Philip R. Corlett

(Yale University). Psychiatrist and cognitive neuroscientist who developed the prediction-error and predictive-coding account of delusion formation and showed experimentally that conditioned expectations can induce hallucination-like percepts. ORCID - Google Scholar - Yale University - Wikidata

Daniel Freeman

(University of Oxford). Clinical psychologist whose cognitive model of persecutory delusions, and the Feeling Safe treatment program built from it, isolate and target single causal factors such as worry, reasoning, and sleep. ORCID - Google Scholar - University of Oxford - Wikipedia - Wikidata

Philippa Garety

(King’s College London). Clinical psychologist whose cognitive model of the positive symptoms of psychosis and work on the jumping-to-conclusions reasoning bias made the second factor empirically measurable and clinically actionable. ORCID - King’s College London - Wikipedia - Wikidata

Robyn Langdon

(Macquarie University). Cognitive scientist who, with Coltheart, developed the two-factor account of monothematic delusions and has investigated the theory-of-mind and reasoning impairments that bear on the second factor. Google Scholar

Brendan A. Maher

(1924–2009). Harvard psychologist who originated the one-factor, rational-response account of delusions, arguing that a delusion is a normal explanation of an abnormal experience; his framing set the terms of cognitive theorizing about delusions for decades. Wikipedia - Wikidata

Ryan McKay

(Royal Holloway, University of London). Psychologist whose work integrates motivational and deficit theories of misbelief and examines when a departure from accurate belief can be adaptive, bearing directly on how delusional beliefs are formed and defended. ORCID - Google Scholar - Royal Holloway

Frequently Asked Questions

What is a delusion?

A delusion is a fixed false or unwarranted belief held with firm conviction, resistant to the evidence and argument that would ordinarily revise it, and out of keeping with the person’s culture and education (Coltheart et al., 2011).

What is the difference between the one-factor and two-factor theories?

The one-factor theory holds that a delusion is a normal explanation of an abnormal experience and needs no further deficit. The two-factor theory holds that an anomalous experience supplies the content but a second impairment, in the evaluation of beliefs, is required to explain why the implausible explanation is adopted and never revised (Maher, 1974; Langdon & Coltheart, 2000).

What is the jumping-to-conclusions bias?

It is the tendency, heightened in delusion-prone people, to decide after gathering little evidence. It is measured with the beads task, and a meta-analysis confirms that delusional ideation is reliably associated with requesting fewer draws before a decision (Garety et al., 2001; Ross et al., 2015).

Does jumping to conclusions mean people with delusions are illogical?

No. Given the strong evidence the beads task provides, an early decision is close to rational; the bias is a readiness to treat weaker evidence as sufficient rather than a failure of logic (Ross et al., 2015).

What does the predictive-coding account say about delusions?

It holds that delusions arise from aberrant, miscalibrated prediction-error signalling that flags insignificant events as meaningful, with the delusion forming as a belief recruited to explain the persistent error and then dominating how later evidence is weighed (Fletcher & Frith, 2009; Corlett et al., 2010).

How are delusions and hallucinations related?

The predictive-coding framework treats both as failures of precision-weighting: hallucinations as perception dominated by overly strong priors, delusions as belief dominated by aberrant prediction error, unifying the two within one mechanism (Corlett et al., 2019).

Is Capgras delusion explained by a single factor?

The anomalous experience in Capgras — a face recognized but not felt as familiar — is specific and well characterized, but a single factor does not suffice, because people with the same affective disconnection do not all become delusional; a second, evaluative deficit is needed (Ellis & Young, 1990; Coltheart et al., 2011).

Are delusions completely separate from ordinary beliefs?

No. The evidence supports a continuum on which delusional ideation can be measured in the general population and clinical delusions occupy the extreme, which reframes the question as how a normal belief-forming system fails (Freeman, 2007).

References