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Delusions in individuals with schizophrenia are personal-level phenomena and no accounto delusion could be complete unless it included a rich phenomenological description oindividuals experience o their delusions (Sass and Pienkos, Chapter 39, this volume).Cognitive approaches aim to contribute to our understanding o delusions by providing anexplanatory ramework that extends beyond the personal level to the subpersonal level oinormation-processing systems (Cratsley and Samuels, Chapter 27, this volume). At othersubpersonal levels, contributions are also offered by neurobiological, neurocomputational,and psychopharmacological approaches.1

Tere are questions to be asked about the relationships between these different subper-sonal levels (or example, about the relationship between the level o cognitive psychologyand the level o neurobiology; Gold and Stoljar 1999). Tere are also questions about therelationship between the personal level, where description extends to phenomenology andnormativity and where there are distinctive practices o rationalizing explanation, and sub-

personal levels o mechanistic description and explanation. According to one extreme viewo this relationship, all that is literally true at the personal level can be recast in the termsavored by the sciences o the mind. According to the opposite extreme, what is distinctive

Te distinction between personal and subpersonal levels o description was introduced by Dennett(). Te personal level o description is the olk psychological level at which we describe people asexperiencing, thinking subjects and agents. It includes descriptions o conscious mental states as suchand descriptions o normative requirements o rationality, or example. Personal-level descriptionsgure in explanations in which actions are rationalized in terms o mental states such as belies anddesires. Subpersonal levels, in contrast, are suited to the mechanistic descriptions and explanations othe objective sciences o the mind, such as inormation-processing psychology and neurobiology.

(For discussion, see Davies ; Shea, Chapter , this volume.)

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and important at the personal level is independent rom the sciences o the mind. But inter-mediate options, between reduction and independence, are available (interlevel interaction

without reduction; Davies 2000). It is a amiliar point that there seems to be an explana-tory gap between the objective sciences o the mind and the subjective character o con-scious experience (Levine 1983; Nagel 1974). But it would be an overreaction to this pointto maintain that the science o color vision, or example, could contribute nothing at all toour understanding o the normal or impaired experiencethe what it is likeo seeingcolors. In a similar way, we can agree that phenomenological description is essential whilemaintaining that cognitive psychology and cognitive neuroscience can contribute to ourunderstanding o personal-level phenomena, including personal-level pathologies (such asaddiction or hearing voices; Shea, Chapter 62, this volume).

Cognitive approaches to understanding delusions have ocused rst, not on the elabo-rated polythematic delusional systems or worlds o some individuals with schizophrenia,

but on monothematic delusionsislands o delusion in a sea o apparent normalityandparticularly, on monothematic delusions o neuropsychological origin. A starting point orunderstanding monothematic delusions is provided by Mahers (1974, 1988, 1992) anoma-lous experience hypothesis: a delusion arises as a normal response to an anomalous experi-ence. Te methodology o cognitive approaches has been that o cognitive neuropsychiatry(David 1993; Halligan and David 2001); that is, the application o the methods o cognitiveneuropsychology to psychiatric disorders. Tus, it has been assumed that the anomalousexperience that gures in Mahers proposed etiology o delusions is the product o a neuro-psychological decit (Coltheart 2007, p. 1047):

Te patient has a neuropsychological decit o a kind that could plausibly be related to the

content o the patients particular delusionthat is, a decit that could plausibly be viewed ashaving prompted the initial thought that turned into a delusional belie.

Maher himsel shares the assumption that [t]he origins o anomalous experience lie in abroad band o neuropsychological anomalies (1999, p. 551) but, as we see in the quota-tion rom Coltheart, cognitive approaches allow that Mahers anomalous conscious expe-rience might not always be essential. In some cases, the route rom neuropsychologicaldecit to delusional belie might be wholly hidden rom consciousness so that the delu-sional belie is the rst delusion-relevant event o which the patient is aware (Coltheartet al. 2010, p. 264).

Because the neuropsychological decit is supposed to be related to the content o the

delusion in some plausible way, the type o decit (and anomalous experience, i any) willvary rom delusion to delusion. Te type o decit may also vary between individuals withthe same delusion i different decits can prompt the same initial thought. Tus, cogni-tive approaches need to document types o neuropsychological decit (and perhaps alsotypes o experience) that could plausibly give rise to each o a variety o monothematicdelusions, such as: Capgras delusionTis [the subjects wie] is not my wie. My wie hasbeen replaced by an impostor (Capgras and Reboul-Lachaux 1923; Edelstyn and Oyebode1999), Cotard delusionI am dead (Cotard 1882; Young and Leafead 1996), FregolidelusionI am being ollowed around by people who are known to me but who are unrec-ognizable because they are in disguise (Courbon and Fail 1927; de Pauw et al. 1987; Elliset al. 1994), mirrored-sel misidenticationTe person I see in the mirror is not really

me (Breen et al. 2000a, 2001a), somatoparaphreniaTis [the subjects le arm] is not




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my arm (Bottini et al. 2002; Halligan et al. 1995), and the delusion o alien controlOtherpeople can control the movements o my body (Frith 1992; Frith and Done 1989).

Candidate neuropsychological decits have been proposed as actors in the etiology o eacho these delusions and others. But, in each case, there are examples o individuals who havethe proposed decit but not the delusion. Te conclusion that is drawn rom this dissocia-tion is that there must be some additional actor or actors implicated in the etiology o delu-sions. In this chapter, we shall be concerned with the two-factorcognitive neuropsychologicalapproach to understanding delusions (or early expositions, see e.g., Davies and Coltheart2000; Davies et al. 2001; Langdon and Coltheart 2000; or recent reviews, see e.g., AimolaDavies and Davies 2009; Coltheart 2007, 2010; Coltheart et al. 2011; McKay 2012).

Beore moving on, we shall illustrate the proposal o a neuropsychological decit as a rstactor, and the dissociation argument or a second actor, in the widely discussed case oCapgras delusion. We shall draw on important early work in cognitive neuropsychiatry (Ellis

and Young 1990), which in turn built on a well-supported model o normal ace processing(Bruce and Young 1986). In the Bruce and Young model, inormation about known acesis stored in ace recognition units (FRUs), one or each known ace. When a known aceis seen, one FRU will be activated to a high level and biographical inormation stored ina corresponding personal identity node (PIN)such as inormation about the personsoccupationwill be accessed, as will the persons name. An important unctional differencebetween FRUs and PINs is that only a seen ace will activate an FRU, whereas a PIN can beaccessed rom the persons seen ace or heard voice, or in other ways.

In some individuals with severely impaired ace recognition (prosopagnosia), skin con-ductance responses continue to discriminate between amiliar and unamiliar acesthereis covert recognition (ranel and Damasio 1985, 1988; see also Bauer 1984). So, althoughthe primary ace-recognition system is damaged in these individuals, there must be a pre-served connection between an early stage o ace processing (the FRUs) and the autonomicnervous system. Ellis and Young (1990) proposed that the neuropsychological decit inCapgras delusion is the mirror image o the decit in prosopagnosia with covert recogni-tion. In Capgras delusion, the primary ace-recognition system is intact but the connectionbetween the FRUs and the autonomic nervous system is damaged. Normally, the seen aceo a loved one, such as the spouse, causes activity in the autonomic nervous system and theexperience o the loved ones ace has a strong affective component. But now, with the con-nection between the ace-recognition system and the autonomic nervous system disrupted,this component o the experience is missing.

Ellis and Youngs proposal about the neuropsychological decit and anomalous expe-rience in Capgras delusion made a clear empirical prediction that the skin conductanceresponses o individuals with Capgras delusion would not discriminate between amiliarand unamiliar aces. Tis prediction was subsequently conrmed in our studies using pho-tographs o amiliar (amous or amily) aces and unamiliar aces (Brighetti et al. 2007; Elliset al. 1997, 2000; Hirstein and Ramachandran 1997)an exemplary vindication o the newdiscipline o cognitive neuropsychiatry (Ellis 1998). Tus, it is plausible that a neuropsycho-logical decit, disconnection o the primary ace-recognition system rom the autonomicnervous system, is a actor in the etiology o Capgras delusion. But there is a dissociationbetween this decit and the delusion. Tere are individuals (patients with damage to ventro-medial regions o rontal cortex; ranel et al. 1995) whose skin conductance responses

do not discriminate between amiliar and unamiliar aces, but who do not have Capgras




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delusion (or any other delusion). Tere is also a report o an individual who (ollowing tem-poral lobe surgery or relie o epilepsy) had an anomalous Capgras-like experience o her

mothershe was different, something was different about her . . . you can look differentby, you know, doing your hair or whatever, but it wasnt different in that way . . . it didnt eellike her (urner and Coltheart 2010, pp. 371372)but did not have the Capgras delu-sion.2Tus there must be a second actor in the etiology o Capgras delusionpresumably,in cases o neuropsychological origin, a second decit.

T T-F F

E D

Coltheart (2007 p. 1044) has proposed that, in order to explain any delusion, we need toanswer two questions. First, where did the delusion come rom? Second, why does thepatient not reject the belie? Te leading idea o the two-actor ramework or explainingdelusions (Coltheart 2007, 2010; Coltheart et al. 2011) is that the two actors will provideanswers to these two questions.

Te rst question is always: where did the delusion come from?that is, what is responsible orthe contento the delusional belie? Te second question is always: why does the patient notreject the belief? . . . that is, what is responsible or thepersistenceo the belie? (Coltheart p. )

Factor is what is responsible or the belie having occurred to the person in the rstplace . . . : this actor determines the contento the delusional belie. Factor is responsibleor the ailure to reject the hypothesis despite the presence o (oen overwhelming)evidence against it . . . this actor determines the persistence o the delusional belie.(Coltheart , p. )

Te rst question is, what brought the delusional idea to mind in the rst place? Te secondquestion is, why is this idea accepted as true and adopted as a belie when the belie is typicallybizarre and when so much evidence against its truth is available to the patient? (Coltheart et al., p. )

Te two-actor ramework has provided explanations (at least in outline) o a range odelusions including those that we have already mentioned and also anosognosia or motor

impairments (Aimola Davies and Davies 2009; Aimola Davies et al. 2009; Davies et al. 2005).It has been proposed that the second actor is the same in all cases o delusion (or at least inall cases o delusion o neuropsychological origin) and that it consists in an impairment onormal processes o belie evaluation, associated with pathology o right lateral prerontalcortex (e.g., Coltheart et al. 2011, p. 285). Te nature o the putative task o belie evaluationsuggests that the second actor could be an impairment o executive unction or workingmemory (or both), consistent with its proposed neural basis (Aimola Davies and Davies2009). But the cognitive nature and neural basis o the second actor have not been speciedas precisely as the nature and basis o putative rst actors.

Tis patient was studied by Nora Breen and Mike Salzberg.




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Adoption and persistence: Two options for the

two-factor framework

It is important to notice that the three quotations listed earlier leave open two possible inter-pretations o the second question (that is, the question to which the second actor is sup-posed to provide an answer). In the third quotation, the second question is about adoptiono the delusional belie. But it is possible initially to adopt a belie and then, on reection,to reject it. Sometimes we initially believe what we see and then realize that we are subjectto an illusion or we initially believe what we are told and then realize that our inormant isunreliable. In the case o a delusional belie we can ask why the belie, once adopted, is notsubsequently rejected. Why is it rmly sustained (American Psychiatric Association 2000,p. 821), why does itpersist? Tis is more like the version o the second question that is posed

in the rst two quotations.Explaining a delusion requires answers to both the adoption question and the persist-

ence question. In principle, it might turn out that two actors (two pathologies or depar-tures rom normality) are needed to answer the adoption question and that a third actoris needed to answer the persistence question. Tat would, o course, be incompatible withthe two-actor ramework, but compatible with a less specic multi-actor ramework. Anexactly-two-actor account must say either:

(A) that no pathology or departure rom normality beyond the irst actor is neededto answer the adoption question and the second actor answers the persistencequestion;

or else:

(B) that two actors are needed to answer the adoption question and no additionalpathology or departure rom normality is needed to answer the persistencequestion.

(In principle, it might be that option (A) is correct or some delusions and option (B) orothers.)

According to option (A), we should expect each dissociation o the rst decit without

delusion orm (e.g., ventromedial rontal damage without Capgras delusion; ranel et al.1995) to be a case in which the delusional belie is initially adopted, but does not persist.According to option (B), we should expect each dissociation to be a case in which the rstdecit is present, but the delusional belie is not even initially adopted. Tis presents a poten-tial problem or option (A) because there is no evidence that patients with ventromedialrontal damage, or example, initially adopt the Capgras delusion but subsequently reject it(nor is there evidence that this is not the case; see Coltheart et al. 2010, p. 281 and McKay2012, pp. 341342, or discussion).

On the other hand, there are reports o individuals who, aer recovering rom a delusion,still eel the attraction o the belie that they now reject. For example, a patient (HS) who hadrecovered rom anosognosia reported that the idea that he could move his paralyzed limbs




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still seemed credible even though he was able to reject it (Chatterjee and Mennemeier 1996,p. 227):

E: What was the consequence o the stroke?HS: Te le hand here is dead and the le leg was pretty much.HS: (later): I still eel as i when I am in a room and I have to get up and go walking . . . I just eel

like I should be able to.E: You have a belie that you could actually do that?HS: I do not have a belie, just the exact opposite. I just have the eeling that sometimes

I eel like I can get up and do something and I have to tell mysel no I cant.

urner and Coltheart describe a patient in the early stages o recovery rom Capgras delu-sion (2010, p. 371):

Ive started going through it, and seeing what could possibly happen and what couldnthappen. Tat was wrong, that couldnt happen. Even though it has happened it couldnt. Marycouldnt suddenly disappear rom the room, so there must be an explanation or it. . . . Andthen I worked it out and Ive wondered i its Mary all the time. Its nobody else.

In summary, the standard examples o decit without delusion, which gure in the dis-sociation argument or a second actor, are potentially problematic or option (A) and toption (B) better. But the examples o recovery rom delusion t option (A) well, on theassumption that the recovery resulted rom remission o the second actor. Tus, not onlythe cognitive nature and neural basis o the second actor, but alsoand even more impor-tantlyits role in the etiology o delusions, requires urther specication.3

Bayesian approaches

One o the aims o cognitive neuropsychology is to understand disorders o cognition interms o theories or models o normal cognition. Cognitive impairments are understoodin terms o damage to one or more components o the normal cognitive system. When themethods o cognitive neuropsychology are applied to delusionspathologies o beliewhat is required is an inormation-processing model o the normal ormation, evaluation,and revision o belies. Tus, one o the problems aced by cognitive neuropsychiatryincomparison with the cognitive neuropsychology o ace recognition, or exampleis that

we do not have an articulated, still less a computationally implemented, model o normalbelieving. Indeed, there may be reasons o principle why it is diffi cult to understand believ-ing in terms o the computational theory o mind (Fodor 1983, 2000; see Cratsley andSamuels, Chapter 27, this volume, on Fodorian pessimism).

More than twenty-ve years ago, Hemsley and Garety suggested a strategy or makingprogress in the absence o a model o normal believing (1986, p. 52): A normative theory

In this chapter, we shall be deending a version o option (A), but we do not offer a resolution o thepotential problem associated with option (A). In the specic case o the ventromedial rontal patients,it might be suggested that they do not initially adopt the Cagras delusion because they do not, in act,have exactly the same neuropsychological decit as Capgras patients (see Ellis and Lewis ). Tatsuggestion provides a response to the potential problem or option (A) but at the price o removing the

standard dissociation argument or a second actor.




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o how people shouldevaluate evidence relevant to their belies can provide a conceptualramework or a consideration o how they do in factevaluate it. Teir specic proposal

was to begin rom a probabilistic analysis o hypothesis evaluation and then to investigatewhether individuals with delusions deviate rom the normative Bayesian model. In pursuingthis strategy and interpreting its results, it is important to distinguish the normative romthe normal; it is important not to orget that, as Hemsley and Garety put it, there is normaldeviation rom the prescriptive model (p. 55).

Recently, the Bayesian approach has been married with the neuropsychological decitapproach in continuing development o the two-actor ramework or explaining monothe-matic delusions (Coltheart et al. 2010; McKay 2012). A second body o work has adopted aBayesian approachand, specically, the theoretical ramework o predictive coding andprediction error signals, in which neural processing aims to minimize prediction error orree energy (Friston 2005, 2009, 2010; Friston and Stephan 2007)to delusions in schizo-

phrenia (Corlett et al. 2009; Fletcher and Frith 2009).4In this chapter, we shall ocus on theBayesian two-actor approach to explaining monothematic delusions and on the idea thatdelusions arise through a process o Bayesian inerence or updating.

Bayesian inference

On a Bayesian approach, probabilities are updated on the basis o evidence, E, so that thenew orposteriorprobability o a hypothesis, H, is equal to the old orpriorconditional proba-bility o H given E. Tis updating procedure is known as simple conditionalization. By Bayestheorem, the conditional probability, P(H|E), can be urther unpacked to give:

Simple conditionalization:

P (H) = P(H|E) = P(H) P(E|H)/P(E).

(Here, P is the new distribution o probabilities.) Te notions o prior and posterior prob-abilities are relative. Te prior probability o H is prior only to the evidence E; it alreadytakes account o antecedently available evidencetodays priors are yesterdays posteriors.In simple conditionalization, the evidence is treated as certain: P (E) = 1. A more generalupdating procedure, Jeffrey conditionalization (Jeffrey 1965/1983), allows that the evidencemay be less than certain, so that P (E) < 1.5

Te posterior probability o a hypothesis, H, updated on the basis o evidence E by simpleconditionalization, is proportional to the prior probability o H, P(H), and to the probabil-ity o E given H, P(E|H), also known as the likelihoodo H on E. Te likelihood provides ameasure o how well H predicts E. In this chapter, we shall usually be more interested inthe balance o probabilities between two competing hypotheses than in the precise prob-ability o each hypothesis. I we are considering two hypotheses, H1and H2, then the ratio

See Frith (, chapters and ) or an accessible introduction to the predictive coding approachand Corlett et al. (, ) or prediction error and delusion. See also Shea (Chapter , this volume)or discussion o prediction error signals.

In Jeffrey conditionalization, the probability o H is updated to:

P (H) = P(H|E) P (E) + P(H|not-E) P (not-E).




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o posterior probabilities (the posterior odds) is the product o two other ratios, the ratio oprior probabilities (the prior odds) and the likelihood ratio:

Bayes ratio ormula:

P (H) =P(H|E) =

P(H) P(E|H)

P (H) P(H|E) P(H) P(E|H)

Tus, on a Bayesian approach, the balance o probabilities between two candidate hypo-theses, updated on the basis o evidence E, depends on (a) how probable each hypothesis isin the light o available evidence other than Egiven by the prior probability P(Hi)and(b) how well each hypothesis predicts the evidencegiven by the likelihood P(E|Hi).

In the next two sections, we shall review two versions o the Bayesian two-actor approach(Coltheart et al. 2010; McKay 2012) in some detail. One section is about the initial adoption

o a delusional belie and the other is about the persistence o the belie. Beore moving on,however, we note that there are complex and diffi cult issues surrounding the relationshipbetween, on the one hand, Bayesian inerence or updating and, on the other hand, abductiveinerence or inerence to the best explanation (Lipton 2004).

Coltheart et al. (2010) sketch two models o abductive inerence, the logical empiricistmodel based on an understanding o explanation as logical implication and the Bayesianmodel based on a probabilistic account o explanation (p. 271): the hypothesis H explainsobservations O to the degree xjust in case the probability o O given H is x. Tey adopt aBayesian model o abduction, but we are not committed to the view that Bayesian inerenceis a model o inerence to the best explanation. One reason is that the likelihood, P(E|H), isnot in general a good measure o how well a hypothesis H explains evidence E. A hypothesisabout barometer readings (e.g., the barometer is alling) does not explain weather patterns(e.g., a storm is coming), however high the likelihood (that is, the probability o the weatherpatterns given the barometer readings) may be. Rather, causation and explanation run in theopposite direction, rom weather patterns to barometer readings (van Fraassen 1980, p. 104).

More generally, Liptons account o inerence to the best explanation takes account, notonly o whether a candidate explanatory hypothesis is the most probable given the avail-able evidence, but also o whether it exhibits explanatory virtues such as parsimony, scope,depth, uniying disparate phenomena, and making new predictions. Te question thenarises whether it could ever be rational to accept an explanation because o its virtues, ian alternative explanation was more probable (van Fraassen 1989). Lipton (2004) aims to

neutralize this concern about the relationship between inerence to the best explanation andBayesianism by suggesting that explanatory virtues are a guide to probability, but we take nostand on that issue.

In our discussion o delusions and Bayesian inerence, it will be the standard Bayesianapparatus o probability assignments, likelihoods, and updating that bears the theoreticalload. Te notion o explanatory virtue will play only a peripheral role, in that it may inuencethe psychological accessibility o hypotheses. It is true that some o the literature that we shallengage with is couched in terms o inerence to the best explanation. But this seems to belargely inessential and, because o the issues that we have just mentioned, potentially distract-ing. Most or all o the theoretical work in explaining the adoption and persistence o delu-sional belies in terms o Bayesian abductiveinerence could be done just as well by talking

about Bayesian inerence simpliciter, thereby sidestepping those complex and diffi cult issues.




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B T-F F:

A D B

Coltheart and colleagues (2010) propose that the answer, in outline, to the question where adelusion came rom is that it arose through a process o Bayesian inerence. In principle, thismight be a process o inerence carried out consciously by the person with the delusion, butColtheart and colleagues ocus on the case o unconscious inerential processes. o illustratetheir approach, Coltheart and colleagues provide a worked example o how Bayesian iner-ence could lead rom a neuropsychological decit to the initial onset o Capgras delusion.

From decit to delusional belief: Capgras delusion

Suppose that, as the result o a stroke, a patient suffers disconnection o the primary aceprocessing system rom the autonomic nervous system (while the two disconnected systemsthemselves remain intact). Beore the patient suffered the stroke, the appearance o his wiecaused activation o the ace recognition unit or the wie (FRUW), which normally led toactivation, not only o the corresponding personal identity node (PINW), but also o theautonomic nervous system. As a result o the learned association between the appearanceo the patients wie and activation o his autonomic nervous system, the appearance o hiswie generated an unconscious prediction o activity in the autonomic nervous system, andthis prediction was reliably ullled. Following the stroke, some things remain the same andsome things are different. When the patient sees his wie, the ace recognition unit FRUWand the personal identity node PINWare still activated, and activity in the autonomic nerv-ous system is still predicted. But, because o the disconnection, the prediction is not ullled.Te abnormal absence o the predicted autonomic activity, resulting rom the neuropsycho-logical decit (disconnection), stands in need o explanation.

Te aim o the Bayesian approach is to show that a delusional hypothesis may be initiallyadopted as a belie as a result o Bayesian inerence or updating on the basis o abnormaldata, D (in this case, the absence o activity in the autonomic nervous system). Consequently,the next stage o Coltheart and colleagues (2010) worked example involves two competing

hypotheses. One is the true hypothesis, HW, that the woman that the patient sees in ronto him, who looks like the patients wie and says that she is the patients wie is, indeed, hiswie. Te other is the delusional hypothesis, HS, that the woman is not the patients wie buta stranger.6

What needs to be shown is that the ratio o posterior probabilities, P(HS|D)/P(HW|D),could avor the stranger hypothesis, HS, over the wie hypothesis, HW. Te Bayes ratio or-mula tells us that this ratio is equal to the product o the ratio o prior probabilities and the

Coltheart et al. () do not consider hypotheses that are incompatible with both HWand HS,such as the hypothesis HA, that the person that the patient sees in ront o him is aunt Agatha, or thehypothesis HB, that the person that the patient sees in ront o him is Bob the bank teller. As a result o

this simplication, HSis treated as the negation o HW.




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likelihood ratio. So, how might the balance between those two ratios avor H Sover HW? Teprior probabilities, P(HW) and P(HS), are prior only to the to-be-explained abnormal data D.

Tey take account o antecedently available evidence including, in particular, the evidencethat the woman that the patient sees in ront o him looks just like his wie and says that sheis his wie. Consequently, the probability that the woman is the patients wie is much higherthan the probability that she is a stranger and the ratio P(HS)/P(HW) is correspondingly low.In contrast, Coltheart and colleagues say, the likelihood ratio, P(D|HS)/P(D|HW) is high: Itwould be highly improbable or the subject to have the low autonomic response [D] i the per-son really was his wie, but very probable indeed i the person were a stranger (2010, p. 277).

According to the worked example, then, the ratio o prior probabilities avors the wiehypothesis, HW, but the likelihood ratio avors the stranger hypothesis, HS. Whether theratio o posterior probabilities avors HWor HSdepends on the relative values o these ratiosand, specically, on whether the likelihood ratio is suffi cient to outweigh the ratio o prior

probabilities. Suppose, or example, that the prior probabilities avored HWin the ratio 100:1but the likelihoods avored HSin the ratio 1000:1. Ten the posterior probabilities wouldavor HSin the ratio 10:1. I these were the only two hypotheses to consider, their probabili-ties would be P(HS) = 0.91 and P(HW) = 0.09. Tus, Bayesian inerence might lead rom theabnormal data D to the assignment o a high probability to the hypothesis that the womanwho looks just like the patients wie and also claims to be the patients wie is not his wiebut a stranger, and so an impostor. Equally, i the prior probabilities avored HWin the ratio100:1 but the likelihoods avored HSonly in the ratio 10:1, then the posterior probabilitieswould be reversed: P(HS) = 0.09 and P(HW) = 0.91.

Coltheart et al. suggest that the likelihood ratio does outweigh the ratio o prior probabili-ties (2010, p. 278):

Te delusional hypothesis provides a much more convincing explanation o the highly unusualdata than the nondelusional hypothesis; and this act swamps the general implausibility o thedelusional hypothesis. So i the subject with Capgras delusion unconsciously reasons in thisway, he has up to this point committed no mistake o rationality on the Bayesian model.

One diffi culty in evaluating this suggestion about Bayesian inerence is that it is somewhatunclear which probabilities are to gure in the worked example. Are they supposed to be, orexample, realistic probabilities or the patients subjective probabilities (credences)? As weshall see later (in the Bayesian inerence in a perceptual module section), there are prob-lems with each o these options. But the main point here is that i Coltheart and colleagues

suggestion is correct then the disconnection o the patients ace processing system rom theautonomic nervous system is the only pathology or departure rom normality that need beimplicated in the processes leading up to the initial onset o Capgras delusion. Consequently,the role or a second actor in the etiology o the delusion must lie beyond that point, in animpairment o post-onset belie evaluation that explains the persistence o the delusion. Tisis option (A) (see Adoption and persistence section).

Coltheart and colleagues move rom the act that the delusional hypothesis, HS, provides a muchmore convincing explanation o the data than the wie hypothesis, HW, does to the claim that thelikelihood ratio strongly avors HS. It is worth noting, however, that explanatoriness is not always a goodindicator o likelihood. From the act that a hypothesis, H, utterly ails to explain evidence, E, it does not

ollow that the likelihood, P(E|H), is close to zero.




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Biased Bayesian inference

McKay (2012) challenges Coltheart and colleagues (2010) description o the unconsciousinerential processes that lead up to the initial onset o the delusional belie. Te generalpoint that Coltheart and colleagues make is that the superior explanatory (better: predic-tive) potential o the stranger hypothesis can outweigh the prior odds in avor o the wiehypothesis. McKay objects that the prior probability o the stranger hypothesis in theirworked example (P(HS) = 0.01) is unrealistically high (2012, p. 339). A more realistic esti-mate would give a ratio o prior probabilities that would much more strongly avor the wiehypothesis and would be much more diffi cult or the likelihood ratio to outweigh.8

Te exact value o P(HS) is, o course, a point o detail. But the moral that McKay (p. 340)draws is that, with a realistic distribution o prior probabilities, unbiased Bayesian iner-ence would not lead rom abnormal data to the onset o delusional belie. Specically, the

likelihood ratio in Coltheart and colleagues worked example (999:1 in avor o HS) wouldbe insuffi cient to outweigh a realistic ratio o prior probabilities avoring HW. Unbiasedupdating o probabilities gives weight to both the prior probabilities and the likelihoods ocompeting hypotheses. Actual updating departs rom the normative Bayesian model i itdiscounts either o these components in the Bayes ratio ormula. McKay proposes that, iupdating is to lead to the onset o Capgras delusion, there must be a departure rom the nor-mative Bayesian model. I posterior probabilities are to avor HSover HWthen prior prob-abilities must be discounted to increase the relative weight given to likelihoods.9

Once again, it is diffi cult to evaluate this proposal because it is unclear how we are tounderstand the probabilities that are supposed to gure in the worked examples. But weset aside issues o interpretation or the time being (see Bayesian inerence in a percep-tual module section) in order to highlight a clear and important point o contrast betweenMcKay (2012) and Coltheart et al. (2010). According to McKay, the disconnection o thepatients ace processing system rom the autonomic nervous system is notthe only pathol-ogy or departure rom normality that is implicated in the processes leading up to the onset oCapgras delusion (McKay 2012, p. 345): the second actor in delusion ormation comprisesa bias towards explanatory adequacy. Here, we should recall that a bias or other deviationrom the normative Bayesian model might be normal (Hemsley and Garety 1986). But iMcKays proposed updating bias does amount to a departure rom normality then, in orderor his account to remain within the exactly-two-actor ramework, no additional pathology

McKay points out, in effect, that i Coltheart et al.s () proposed prior probability,P(HS) = .,were correct then one should expect that one time in a hundred, an encounter with a person who looked

just like ones spouse and claimed to be ones spouse would be an encounter with a stranger (impostor).He suggests that a more realistic prior probability or HSwould be two orders o magnitude lower; that is,o the order o .. (McKays proposal is P(HS) = ..)

In a case o comparison between two hypotheses, i the ratio o prior probabilities were : then theratio o posterior probabilities would be equal to the likelihood ratio. So an updating bias in avor olikelihoods can be implemented by treating the ratio o prior probabilities as being closer to : than itreally is. Tis could be achieved by treating the absolute magnitude o the logarithm o the prior odds asbeing closer to zero than it really is (by subtraction, so that the logarithm would approach zero linearly,or by division, so that the logarithm would approach zero asymptotically). Conversely, a reduction in theabsolute magnitude o the logarithm o the likelihood ratio would implement an updating bias in avor oprior probabilities. See McKay (, pp. ) or a different, and more general, way o implementing

these biases.




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should be needed to answer the persistence question. Tis is option (B) (see Adoption andpersistence section).

B T-F F:

P D B

Te Capgras patient believes that the woman who looks like his wie and says that she is hiswie is really a stranger; his wie has been replaced by an impostor.10We have been consider-ing two Bayesian answers to the question how this belie came to be adopted. Now we turnto the question why, given that this belie has been initially adopted, it is not subsequently

rejected when evidence and implausibility count against it. One possible orm o answer tothis question is that there is a separate impairment o post-adoption belie evaluationas inoption (A). Te other is that no additional pathology or departure rom normality is neededto explain the delusional belie s persistence once it has been adoptedas in option (B).

Two accounts of persistence

Coltheart and colleagues (2010) envisage that, aer adopting the delusional belie, thepatient will be presented with new evidence, N, that is better explained (predicted) by thewie hypothesis than by the stranger hypothesis. Friends and relatives assure the patient thatthe woman he believes to be an impostor is really his wie, the woman knows many thingsabout the patients lie, and she arrives home rom his wies place o employment, drivinghis wies car, wearing his wies clothes, and carrying his wies briecase with his wies ini-tials in gold lettering.

So there should be a new round o Bayesian updating o probabilities. Te new prior prob-abilities are P (HS) = P(HS|D), and P (HW) = P(HW|D) and, because the delusional beliehas been adopted, the ratio o new prior probabilities avors HS(perhaps in the ratio 10:1).In contrast, the likelihood ratio, P (N|HS)/P (N|HW), avors HW. For example, riends andrelatives would be more likely to give such assurances i the woman were the patients wiethan i she were a stranger. I the likelihood ratio is suffi cient to outweigh the ratio o prior

probabilities then, according to the normative model, the ratio o posterior probabilities,P (HS|N)/P (HW|N), should avor HWover HSand the delusional belie should be rejectedon the basis o the new evidence N. However, the delusion persists. According to Coltheartand colleagues (2010), this persistence is to be explained by the second actor, which is somekind o impairmentto be speciedin the evaluation o already adopted belies in thelight o new evidence.

Te proposition, HS, that the woman that the patient sees in ront o him is a stranger is strictlyspeaking distinct rom the proposition that the woman is an impostorthat is, a stranger who lookslike the patients wie and says that she is the patients wie. But since probabilities have already beenupdated to take into account the evidence that the woman that the patient sees in ront o him looks likehis wie and says that she is his wie, the stranger hypothesis and the impostor hypothesis have the same

probability and we can elide the distinction between them.




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:

It is crucial to this account o persistence as being explained by a second actor that,according to the normative Bayesian model, the delusional belie, HS, shouldbe rejected on

the basis o the new evidence N. Tis, in turn, depends on the claim that the likelihood ratio,P (N|HS)/P (N|HW), avors HWstrongly enough to outweigh the ratio o prior probabili-ties, which avors o HS. Tere is a potential problem or the account here. An estimate o thelikelihood ratio, and particularly an estimate o P (N|HS), depends on what exactly the newevidence N is taken to be.

On a Bayesian approach, evidencesuch as the new evidence, Nis a proposition.Suppose, or example, that a trusted riend o the patient asserts that the woman who looksjust like the patients wie isthe patients wie. Is the evidence, N, the proposition that thewoman is the patients wife(essentially, the proposition HW) or the proposition that the trustedfriend asserted that the woman is the patients wife? On the rst (more committed) interpre-tation, the likelihood, P (N|HS), is low; in act it is zero (or very close to zero). But on the

second (more cautious) interpretation, P (N|HS) might be quite high and almost as high asP (N|HW): even a trusted riend may be taken in by a very good impostor.

11Te potentialproblem or Coltheart and colleagues explanation o persistence is that, on the more cau-tious interpretation o what the evidence is, the likelihood ratio might not avor HWstronglyenough to outweigh the ratio o prior probabilities. (We shall consider the more committedinterpretation shortly; see Rejecting evidence section.) I the ratio o posterior probabilitiesstill avors HSrather than HWthen, o course, there is no need or a second actor (a pathol-ogy or departure rom normality) to explain the persistence o the delusional belie.

On McKays (2012) account, in contrast to that o Coltheart et al. (2010), there are alreadytwo actors involved in the answer to the question how the delusional belie came to be ini-tially adopted (the neuropsychological decit and the updating bias in avor o likelihoods).But we still need an answer to the question why the belie is not subsequently rejected whenthere is so much evidence against it. Is a thirdactor needed in order to explain the persist-ence o the delusion?

Our discussion (two paragraphs back) o Coltheart and colleagues (2010) account sug-gests that there may be no need or an additional actor to explain persistence and this is,indeed, McKays (2012) view. He agrees that, aer the initial adoption o the delusionalbelie, there will be new evidence that counts in avor o the wie hypothesis and against thestranger hypothesis. But he points out that much o this new evidence (e.g., trusted riendssay that the woman is the patients wie) is similar in kind to evidence that was taken intoaccount in the previous prior probabilities o the competing hypotheses (e.g., the woman

hersel says that she is the patients wie). Te patients evidential situation remains verysimilar to the situation that led to the initial adoption o the delusional belie and so thesame processes o updating (processes biased in avor o likelihoodsMcKays secondactor) will lead to similar posterior probabilities. Tus, McKay says (2012, p. 343): i the

For some other pieces o new evidence, there will be similar, though less dramatic, differences inlikelihood estimates depending on what exactly the evidence is taken to be. Suppose, or example, thatthe woman is carrying what is in act the wies briecase. Is the evidence, N, the proposition that thewoman is carrying the wifes briefcaseor the proposition that the woman is carrying a briefcase that looksjust like the wifes? However, the distinction between more committed and more cautious interpretationso what the evidence is might not extend smoothly to all pieces o new evidence (e.g., the act that thewoman is able to give correct accounts o many past events involving the patient and his wie). Different

kinds o new evidence require more discussion than they can receive here.




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neuropsychological data that stimulate the stranger hypothesis are so salient that they cancompensate or the low prior probability o that hypothesis, then supplementary testimony

rom riends and clinicians will be powerless to overwhelm those data.

Diagnostic evidence, similar evidence, and unfalsiability

Consider just a subset o the evidence against the Capgras patients delusional belie: theevidence that the woman that the patient sees in ront o him looks just like his wie and saysthat she is his wie. Tis evidence is predicted by the patients impostor hypothesis no lessthan by the true hypothesis, HW. Te evidence is not diagnosticbetween the two hypothe-sesit cannot shi the prior balance o probabilities toward HW, because the likelihood ratiois 1:1. In this limited way, the Capgras patients hypothesis is similar to skeptical hypotheses

(such as Descartess evil demon hypothesis) in being unalsiable. Te evil demon hypo-thesis, or the brain in a vat hypothesis, is not alsied by the evidence o my senses, Hereis one hand, and here is another (Moore 1939), because a perceptual experience as o handsis predicted by the skeptical hypothesis no less than by the external world hypothesis. (It isimportant to note that, on a Bayesian approach, this unalsiability depends on the evidencebeing the cautious proposition that I am having a perceptual experience as of hands ratherthan the committed proposition that I have hands.)

It is only a small set o evidence (only the evidence that the woman looks just like thepatients wie and says that she is his wie) that is utterly unable to shi the balance oprobabilities toward HW. But, as we have just seen, the value o a larger set o evidence isdiminished because accepted evidence makes other similar evidence more probable. It isimprobable that a trusted riend should assert, concerning a stranger, that she is the patientswie. But it is not so improbable that a trusted riend should assert, concerning a strangerwho looks just like the patients wie and says that she is his wie (an impostor, and a goodimpostor at that), that she is the patients wie. So, although the evidence o the trustedriends testimony is somewhat better predicted by the wie hypothesis, HW, it does not avorHWvery stronglyarguably not strongly enough to outweigh the ratio o prior probabilitiesin avor o HS. It is or this reason that McKays (2012) account and, equally, our reservationsabout Coltheart et al.s (2010) account, seem plausible. It is diffi cult to identiy a role or apathology or departure rom normality that would distinctively explain the persistence o adelusional belie aer its initial adoption had been accounted orthat is, a role or a second

actor according to option (A).Coltheart and colleagues view is, o course, that they have identied such a role. So let us

consider their example (2010, p. 279) again.12

Coltheart and colleagues say (, p. ): subjects are impaired at revising preexisting belieson the basis o new evidence relevant to any particular belie. McKay interprets this as a Bayesianproposal that the second actor is an updating bias in which likelihoods are discounted to increase therelative weight given to prior probabilities. Against the proposal, he objects that it is hard to see how thedelusional belie would ever have been adopted i a bias in avor o prior probabilities were in place. Withsuch a bias, the patient would have updated his credences much more conservatively on the basis o theunexpected absence o activity in the autonomic nervous system (McKay , section .). Tis is aninteresting objection, but we set it aside here and consider a strand in Coltheart et al.s () account o

the second actor that is rather different rom the idea o a general bias in avor o prior probabilities.




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Rejecting evidence

Te patient has adopted the delusional belie and the ratio o new prior probabilities,P (HS)/P (HW), avors HS. But now, new evidence N is presented, and the likelihood ratio,P (N|HS)/P (N|HW), avors HW. I the likelihood ratio is suffi cient to outweigh the ratio oprior probabilities then the delusional belie should be rejectedbut it persists. We pointed toa potential problem or Coltheart and colleagues explanation o persistence in terms o a sec-ond actor. On the more cautious interpretation o which proposition the evidence is, the likeli-hood ratio might not avor HWstrongly enough to outweigh the ratio o prior probabilities. Inact, we suggested that the likelihood P (N|HS) might be only slightly lower than P (N|HW).

Coltheart and colleagues (2010) go on to say that, beore the new evidence is actually pre-sented, the patient should attach a low credence to the evidence proposition. In the norma-tive model, the prior probability o N is given by:

P (N) = P (N|HS) P (HS) +P (N|HW) P (HW).

I, as Coltheart et al. say, P (N|HS) and P (HW) are both low, then P (N) is also low: the patientshould not expect N to be true. We suggested, however, that P (N|HS) is not low and that theprior probability o N might be quite high. (Tis is what diminishes Ns evidential value.)

Te potential problem that we saw or Coltheart and colleagues explanation o persistencedisappears i we read them as adopting the more committed interpretation o the evidence(e.g., taking N to be the proposition that the woman is the patients wiferather than the proposi-tion that the trusted friend asserted that the woman is the patients wife). On that interpretation (asthe more committed terminology suggests), the prior probability, P (N), and the likelihood,P (N|HS), are loweras Coltheart et al.s account requires. Consequently, it is more plausiblethat the likelihood ratio outweighs the ratio o prior probabilities so that the ratio o posteriorprobabilities avors HWover HS. It is also more plausible that, normatively, the delusional belieshould be rejected on the basis o the new evidence, N. Why, then, does the delusional beliepersist? Coltheart and colleagues answer this question as ollows (2010, pp. 279280):

What the deluded Capgras subject seems to be doing here is ignoring or disregarding any newevidence that cannot be explained by the stranger hypothesis. It is as though he is so convincedo the truth o the stranger hypothesis by its explanatory power that his conviction makeshim either disregard or reject all evidence that is inconsistent with that hypothesis, or at leastcannot be explained by the hypothesis. . . . it seems as i the new inormation does not even

enter the deluded subjects belie system as data that need to be explained.

It is striking that there is nothing evidently Bayesian about this answer to the persistencequestion.14

Tis is an instance o the total probability theorem. We ollow Coltheart et al. (, p. ) inassuming (or simplicity) that hypotheses inconsistent with both HSand HW, such as the aunt Agathahypothesis and the Bob the bank teller hypothesis, have probability zero (equivalently, that HWis thenegation o HS).

Tere are two other notable eatures o this quotation. First, the answer that it gives to thepersistence question seems to be completely different rom the answer quoted in ootnote (Coltheartet al. , p. ; also quoted by McKay , p. ). Second, it does not seem to describe any

impairment o inormation processing.




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One important idea behind Coltheart and colleagues account o how the Capgras patientgoes wrong is that, it is reasonable in suitable circumstances to accept the evidence o ones

senses and the testimony o others (2010, p. 281; see also p. 275). It is clear that, on theirview, it would be reasonable or the Capgras patient to accept as evidence, and update hiscredences on the basis o, not just the cautious proposition that the trusted friend assertedthat the woman is the patients wifebut also the committed proposition that the woman isthe patients wife. But Coltheart and colleagues also accept that it is sometimes reasonableto reject inormation that cannot be explained by the hypothesis that one is committed to(p. 280). For example, i a trusted riend and distinguished scientist tells you that, in a tun-nel under Switzerland and Italy, particles travel aster than the speed o light, it might bereasonable not to accept the proposition that particles travel aster than the speed o light asevidencenot to update all your credences on that proposition. So when is it reasonable toaccept and when is it reasonable to reject, the evidence o perception and testimony?

As we noted earlier, Coltheart and colleagues draw attention to the act that, in the case othe Capgras patient, the prior probability o the new evidence in avor o the wie hypothesisis low (on the more committed interpretation o which proposition the evidence is). But lowprior probability is not supposed to be suffi cient to make rejection reasonable (2010, p. 281;emphasis added):

Capgras subjects are so much in the grip of the stranger hypothesisthat they reuse to accept theevidence o their senses and the testimony o others. Tey ail to incorporate the new data intotheir belie systems when it is reasonable to do so.

No explicit account is offered o what conditions, in addition to low prior probability, needto be met i rejection o evidence is to be reasonable. Furthermore, there seems to be a sug-gestiondepending on what being in the grip o a hypothesis amounts tothat the realproblem is the patients initial adoption o (assignment o a high credence to) the impostorhypothesis. But, i persistence ows rom adoption without additional pathology or depar-ture rom normality, then there is no need or a second actor.

Even i we step back rom any suggestion that there is no need or a second actor, itremains the case that Coltheart and colleagues have provided no distinctively Bayesiananswer to the persistence question.15

Tere is, in act, a airly natural Bayesian answer to the specic question about the conditions

under which acceptance or rejection o evidence (that is, evidence on the committed interpretation)is reasonable. Acceptance o (assignment o a high credence to) a committed evidence proposition, E+(e.g., that the woman is the patients wife), is reasonable i the probability o E+given E, P (E+|E), is high,where Eis the corresponding cautious evidence proposition (e.g., that a trusted friend asserted that thewoman is the patients wife). Similarly, rejection o (assignment o a low credence to) E+is reasonable iP (E+|E), is low. Tis will be so i there is a proposition, E*, inconsistent with E+, such that P (E*|E) >P (E+|E)that is, i a proposition that is inconsistent with E+has a higher probability than E+given E.

Evidently, however, that Bayesian proposal would take us back to the earlier potential problem orColtheart and colleagues () account. Rejection o the committed evidence proposition, E+(e.g., that the woman is the patients wife), wouldbe reasonable because there is a proposition, HS,inconsistent with E+(= HW), such that P (HS|E

) > P (E+|E), where Eis the corresponding cautiousevidence proposition (e.g., that a trusted friend asserted that the woman is the patients wife). Te reasonor this is that the prior probability o HS(P (HS)) is substantially higher than the prior probability o

E+(= P (HW)), while the likelihood P (E|HS) is only slightly lower than P (E|E+) (= P (E|HW).




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Interim summary

We have considered two recent Bayesian developments o the two-actor ramework orexplaining delusions. Tere is a airly clear disagreement between the two accounts overwhether, in addition to the rst neuropsychological decit, a second pathology or depar-ture rom normality gures in the explanation o the initial adoption o the delusionalbelie. Coltheart et al. (2010) say that unbiased Bayesian inerence could lead to the onseto Capgras delusion, whereas McKay (2012) says that a bias in avor o likelihoods at theexpense o prior probabilities would be required. But we have not been able to identiy a roleor a urther actor (a second actor in Coltheart et al.s account, a third actor in McKays)that would explain the persistence o the belie, once it had been adopted. When we adopt aBayesian approach to the adoption question, persistence o the newly adopted belie appearsto be the normal caseand even the normatively correct case.

Te lesson that we draw rom this is not that there is something wrong with the two-actorramework or explaining delusions, nor that there is something wrong, specically, with theproposal that the second actor answers the persistence questionoption (A). Our view isthat the Bayesian approach does not reveal how post-adoption belie evaluation goes wrongin individuals with delusions because it provides no account at all o evaluation o belies,once they have been adopted and beore new evidence becomes available, even in healthyindividuals. In the next section, we argue that the problem lies, not with the Bayesianapproach as such, but with a standard idealizing assumption.

B E F M

I we conceive o believing as a binary (on/off) matter, so that each proposition is eitherbelieved or not believed, then the normative ideal or an individuals system o belies seemsto require a single consistent set o belies (propositions or which believing is on) that guideaction in all contexts. I we adopt a Bayesian approach and conceive o believing as a gradedmatter, so that each proposition is assigned a credence (subjective probability), then theideal or a system o belies seems to require a single coherent distribution o credences that

guide action in all contexts.Notoriously, we all short o these supposed ideals. Actual belie systems are ragmented

or compartmentalized. Individual ragments are consistent and coherent but ragments arenot consistent or coherent with each other and different ragments guide action in differentcontexts. We hold inconsistent belies and act in some contexts on the basis o the belie thatP and in other contexts on the basis o the belie that not-P. Frequently we ail to put thingstogether or to join up the dots. It can happen that some actions are guided by a belie that Pand other actions are guided by a belie that i P then Q, but no actions are guided by a beliethat Q because the belie that P and the belie that i P then Q are in separate ragments. Forexample, some people are described as having their philosophical belies and their religiousbelies in separate compartments. David Lewis describes himsel as having once had rag-

mented belies about the geography o Princeton. According to one ragment, Nassau Street




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ran north-south and was parallel to the railway track; according to another ragment, therailway track ran east-west and was parallel to Nassau Street (Lewis 1982, p. 436).

It is natural to assume that ragmentation is a consequence o our limitedinormation-processing resources and that consistency and coherence across a single web obelie, though practically unattainable, is indeed the ideal. Fragmentation allows inconsist-ency and it allows ailure to believe the consequences o our belies. But ragmentation alsobrings a benet: it allows us to undertake reective, critical evaluation o our own beliesaer their initial adoption.

Limits on belief evaluation imposed by consistency

and coherence

It is a datum that sometimes we initially adopt a belie (assign a high credence to a proposi-tion), subsequently reect on the matter and, on the basis o other things that we alreadyknow and believe, without any new evidence, reject the belie (assign a lower credence tothe proposition). As we shall now explain, this kind o critical reection involves a departurerom the supposed norm o a single consistent and coherent web o belie (Egan 2008).

Te limits that are imposed on belie evaluation by the supposed normative ideals areparticularly clear in the case o binary (on/off) belie. No consistent system o belie includesboth Pand not-P, or all or P, Q, and at least one of P and Q is false . No consistent systemincludes all o P, my belief that P was formed by method M, and every belief formed by methodM is false. And no consistent system includes belies, P, Q, R, . . . ormed on the basis o per-ception, those are all the beliefs that I have formed on the basis of perception, and at least one ofthe beliefs that I have formed on the basis of perception is false. Obviously, i you are a consist-ent binary believer then you will never be in a position to reject an already adopted belie onthe grounds that it is inconsistent with other things that you believe. Tus, the ideal o a sin-gle consistent system o binary belie excludes rejection o a belie on the basis o evaluation(without new evidence) aer the belie has been adopted. Te ideal requires that evaluationo a hypothesis should always precede adoption o the hypothesis as a belie.

In the case o graded belie, similar limits are imposed by the supposed ideal o a sin-gle coherent assignment o credences. No coherent assignment o credences includes bothPand not-P amongst the propositions assigned a credence greater than 0.5. No coherentassignment includes Pand Q amongst the propositions assigned a credence greater than

0.9 and assigns a credence greater than 0.2 to at least one of P and Q is false. And no coher-ent assignment includes P, Q, R, . . . amongst the propositions assigned a credence greaterthan 0.9 and assigns a credence greater than 0.2 to at least half of the those propositions, P,Q, R, . . . , are false. I you are a coherent graded believer and you assign a credence greaterthan 0.9 to some propositions then, provided that you are well inormed about your owncredences, you cannot assign a credence greater than 0.2 to half of the propositions to which Iassign a credence greater than 0.9 are false.16

Te general situation is that, i you are a coherent graded believer then you will neverbe in a position to reject an already adopted belie (reduce the high credence that you haveassigned to a proposition) on the grounds that it is not coherent with other things that you

For the general theorem, see Egan and Elga ().




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believe (the assignment o high credences to other propositions). I you have assigned ahigh credence to P, and Qis evidence against P(the conditional probability o Pgiven Q

is low) then, because your assignment o credences is coherent, you will not have assigneda high credence to Q. On a Bayesian approach, there is no place or post-adoption (that is,post-updating) belie evaluation, without new evidence.

Compartmentalization and Spinozan belief formation

A ragmented belie system and, specically, a belie system in which newly adopted belieswere compartmentalized, would escape the limits imposed by the ideal o a single consist-ent and coherent system. Assignments o credences that were not coherent with each othercould be separated and, specically, a new assignment o a high credence to a proposition

could be separated rom a prior assignment o credences with which it was not coherent.By retaining the prior credences, such compartmentalization would allow the possibilityo post-adoption belie evaluation, even without new evidence. It might be suggested that,although our belie systems are in act ragmented in various ways, earlier evaluation o can-didates or belie is always preerable to the post-adoption evaluation that compartmentali-zation allows. But, as we explain in the next ew paragraphs, deault or prepotent doxasticresponses to incoming inormation, particularly rom perception, may leave little, i any,opportunity or early evaluation o candidates or belie.

In a series o papers, Gilbert and colleagues (Gilbert 1991; Gilbert et al. 1990, 1993) havecontrasted Cartesian and Spinozan views o belie and have presented experimental resultsin support o the Spinozan view.17Each view o belie can be summarized in terms o twostages, a representation stage and an assessment stage. On the Cartesian view, the repre-sentation stage involves comprehension. A hypothesis is rst grasped and then, in a separateassessment stage, the hypothesis is either acceptedas true and adopted as a belie, or elserejectedas alse. On the Spinozan view, in contrast, the representation stage involves bothcomprehension and acceptance(Gilbert 1991, p. 107): People believe in the ideas they com-prehend, as quickly and automatically as they believe in the objects they see. Ten, in theseparate assessment stage, the already adopted belie is either certiedor else unaccepted.

Consider, or example, a case o belie based on perception, such as my belie that there isa pencil on the desk in ront o me. Te Cartesian view is that the representational content omy perceptual experience as ofthere being a pencil on the desk is rst grasped as a hypoth-

esis, which is then assessed. Such an assessment might consider the explanatory potential othe hypothesiswhether the hypothesis that there is a pencil on the desk explains my hav-ing an experience as o there being a pencil on the deskand how probable the hypothesisis in the light o other available evidence. Whatever the exact nature o the assessment, itsoutcome is that the hypothesis is either acceptedI adopt the belie that there is a pencil onthe deskor else rejectedI do not believe my eyes. Te Spinozan view, in contrast, is thatcomprehension and acceptance are inseparable. Tere is no gap between grasping how theexperience represents the world to be and believing that the world is that way. On the basiso the perceptual experience, I automatically adopt the belie that there is a pencil on the

We shall not discuss the relationship between the two views that Gilbert describes and the historical

philosophers or whom they are named.




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desk. Assessment is still separate rom comprehension and so it ollows this initial accept-ance. Te outcome o the assessment is that the already adopted belie is either certied and

retained or else unaccepted in a deliberate revision o belie (1991, p. 108).Gilbert assumes that assessment, whether Cartesian or Spinozan, is demanding o cogni-tive resources and that i resources are depleted or in use elsewhere then the pre-assessmentstate o the system will be revealed. He nds the Spinozan view to be supported by a rangeo empirical ndings (see Gilbert 1991, or a review) including results rom his ownexperiments (Gilbert et al. 1990, 1993). As Gilbert explains the logic o these experiments,resource-depleted Cartesians should be uncertain, uncommitted, but not persuaded,whereas the results indicate that resource depletion acilitate[s] believing (1991, p. 111).Belie based on perception seems to be the most promising case or the Spinozan view butGilberts results also suggest that the view may be correct or belie based on heard testi-mony and read text, even when individuals are orewarned that some o what they hear or

read is not true.Spinozan belie ormation, by denition, excludes assessment or evaluation o hypotheses

beore they are adopted as belies. I belie systems were required to be consistent and coher-ent, then Spinozan belie ormation would also exclude post-adoption belie evaluationwithout new evidenceacceptance would preclude assessment. Te reason is that automaticadoption o an antecedently implausible belie would, given consistency and coherence,eliminate the very considerations in the light o which the belie was implausible. So therewould be no basis or reective, critical evaluation o the newly adopted belie. Spinozanbelie ormation would be consistent with post-adoption belie evaluation, however, i newlyadopted belies were to be compartmentalized, at least until evaluation (Gilberts assess-ment) had been undertaken. We assume that these compartmentalized belies would guideaction in some, but not all, contexts.

Prepotent doxastic responses, compartmentalization,

and belief evaluation

We have said that it is a datum that belies are sometimes evaluated aer they have been ini-tially adopted and we have shown that a ragmented belie system in which newly adoptedbelies were compartmentalized would allow post-adoption belie evaluation, even withoutnew evidence. As we have just seen, this is important or the Spinozan view o belie orma-

tion, which places evaluation (assessment) aer adoption (acceptance). Te claim that belieis the deault or prepotent doxastic response to perceptual experience (Davies et al. 2001,p. 153) allows that the prepotent response might sometimes be inhibited; so it is not quiteas strong as the claim that belie ormation based on perception is Spinozan.18Nevertheless,on this near-Spinozan view the deault case will be that there is no assessment beore accept-ance; reective evaluation will have to ollow initial adoption o the belie. Evidently, ibelies that are newly adopted on the basis o perceptual experience are compartmental-ized then the near-Spinozan view is consistent with post-adoption belie evaluation. o the

Hasson et al. () argue that the relationship between comprehension and acceptance is more

complex than the Spinozan view allows.




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extent that belie is also the prepotent doxastic response to heard testimony or read text, asimilar argument will apply.

On a Bayesian approach, the near-Spinozan view is that, in the deault case, a high cre-dence is automatically assigned to a proposition that species how a perceptual experiencepresents or represents the world as being (e.g., the proposition that there is a pencil on thedesk in front of me). Te ideal o a single coherent distribution o credences would requirethat all other credences should be automatically updated (presumably by simple condition-alization or Jeffrey conditionalization). Compartmentalization separates the assignmento a high credence to the perception-based proposition rom the prior assignment o cre-dences and the two assignments coexistpro tem. Tus the prior credences remain availableto gure in subsequent evaluation o the high credence that was initially assigned to theperception-based proposition.

With some understanding o howthanks to compartmentalizationthere could be

post-adoption belie evaluation in healthy individuals, we can return to the explanation odelusions. Te two-actor ramework or explaining delusions is also a three-stage rame-work (Aimola Davies and Davies 2009; Aimola Davies et al. 2009). At the rst stage there isa neuropsychological decit, the rst actor, which is supposed to be related to the content othe delusional belie in some plausible way. Tere is then a second stage that leads rom theneuropsychological decit to the initial adoption o the delusional belie. Finally, there is thethird, post-adoption, stage o persistence rather than rejection o the delusional belie.

H D P C

A B

Colthearts rst question is, Where did the delusion come rom? (2007, p. 1044). One kindo answer to this question simply cites the rst actor; the answer species the neuropsycho-logical decit rom which the delusions content is supposed to have arisen in some plausibleway. In the case o Capgras delusion, the decit is disconnection o the primary ace process-ing system rom the autonomic nervous system. But a neuropsychological decit is not abelie and an answer to the adoption question must speciy, not only the neuropsychologicaldecit, but also the route rom the decit to initial adoption o the delusional beliethe

second stage in the two-actor/three-stage ramework.

Abnormal data and anomalous experience

Te ramework allows or considerable variation in the second stage. For example, thisstage might be hidden rom consciousness to a greater or a lesser extent. As we have alreadyseen, Coltheart and colleagues commend the view that the processing that leads up toonset o the delusion is wholly unconscious, so that the delusional belie itsel is the rstdelusion-relevant event o which the patient is aware (2010, p. 264).

On a Bayesian account o the kind that we have been considering, there must be, near

the beginning o the second stage, evidence or data rom which Bayesian inerence leads to




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initial adoption o the delusional belie. On Coltheart and colleagues account, the startingpoint or Bayesian inerence leading to the Capgras delusion is abnormal data; namely, the

absence o activity in the patients autonomic nervous system. Importantly, this absence oautonomic activity is assumed notto be available to consciousness (2010, p. 264): people arenot conscious o the activities o their autonomic nervous systems, and so a man would notbe conscious o a ailure o his autonomic nervous system to respond when he encounteredhis wie. Tere is a good theoretical reason behind this assumption (Coltheart 2005). I theautonomic activity that is normally produced in response to a amiliar ace were availableto consciousness then patients suffering rom prosopagnosia, but with covert recognition,should be able to use their experience o autonomic activity to discriminate amiliar romunamiliar aces. But such patients are unable to do this (ranel and Damasio 1985, 1988).19

We assume, with Coltheart and colleagues (2010), that neither autonomic activity pro-duced by amiliar aces, nor the absence o autonomic activity, is available as such to con-

sciousness. But this does not rule out the possibility that the abnormal absence o autonomicactivityitsel unavailable to consciousnessshould lead to an anomalous experience thatwould be causally antecedent to the adoption o the delusional belie. Indeed, Coltheart sug-gests just such a possibility, beginning rom an important idea about inormation processing(2005, p. 155): It is a general principle o cognitive lie that we are continually making pre-dictions, on the basis o what we currently know about the world, concerning what will hap-pen to us next. Sometimes we engage in the conscious mental activity o making predictionsand then learning whether our predictions are ullled. But prediction and the comparisono predictions with actual outcomes are also ubiquitous eatures o unconscious inorma-tion processing. Coltheart says (2005, p. 155): Only when a prediction ails does conscious-ness get involved; the unconscious system makes some kind o report to consciousness to

Garry Young has suggested that the results o a study by Greve and Bauer () lend support to theview that autonomic activity does pervade consciousness in the orm o a sense o preerence (Young, p. ; see also ). Greve and Bauer presented a prosopagnosic patient with pairs o unamiliaraces. One ace in each pair had previously been exposed ve times (or msec each time), ollowingtrials o a task in which verbal personality descriptors were presented. When asked to select the ace thathe liked best, the patient chose the previously exposed ace rom % o the pairs. Tis is certainly aninteresting nding and Youngs proposal that there was something-it-was-like . . . or [the patient] topreer one ace over the other (, p. ) is plausible. But the nding does not support the proposalthat this sense o preerence was underpinned by activity in the patients autonomic nervous system.Greve and Bauer () report no data on skin conductance responses and they explicitly attribute

the patients preerence responses, not to autonomic activity, but to perceptual uency (Mandler ;Whittlesea ). Tey also tentatively suggest that the patient may have a decit in orming new FRUsand that the more uent processing o the briey exposed ace stimuli may have been independent otheir status as aces.

Although Greve and Bauers () results do not support Youngs claim that autonomic activity isavailable to consciousness as a sense o preerence, we speculate that the results may indirectly raisea question about Colthearts () argument that autonomic nervous system responses to aces arenotavailable to consciousness. It is plausible that, when a previously exposed ace was presented to thepatient in Greve and Bauers study, inormation about perceptual uency was, in some way, availableto consciousness (e.g., as a sense o preerence) although the patient was not able to make use oinormation about uency to identiy the ace as previously exposed. By analogy, it might be suggested,the act that prosopagnosic patients are not able to use inormation about autonomic activity todiscriminate amiliar rom unamiliar aces does not absolutely exclude the possibility that inormation

about autonomic activity is, in some way, available to consciousness.




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instigate some intelligent conscious problem-solving behavior that will discover whatswrong. Tus, in the case o the Capgras patient, what happens is (2005, p. 155): the uncon-

scious system predicting that when the wie is next seen a high autonomic response willoccur, detecting that this does not occur, and reporting to consciousness, Teres somethingodd about this woman.

Maher makes a very similar suggestion about the consequences or conscious experienceo the unconscious operation o prediction and comparison systems (1999, p. 558):

Survival requires the existence o a detector o changes in the normally regular patterns oenvironmental stimuli, namely those that are typically dealt with automatically. Te detectorunctions as a general non-specic alarm, a signicance generator, which then alerts theindividual to scan the environment to nd out what has changed.

Mahers (1999) and Colthearts (2005) suggestions converge on the idea that, as the result

o a neuropsychological decit and the subsequent operation o a comparator system, theCapgras patients experience o his wie is anomalous, characterized by a sense o signi-cance and change.

In summary: From a starting point o abnormal data, the processing that leads tothe initial adoption o the delusional belie might be wholly hidden rom consciousness.Alternatively, unconscious processes might lead to an anomalous experience that is causallyantecedent to the delusional belie.

Explanation or endorsement

Tere are two importantly different ways in which an anomalous experience might gure inthe etiology o a delusion (Davies et al. 2001). On the rst (explanation) option, the contento the delusion is not encoded in the anomalous experience. For example, the content o theexperience might be: Tis woman looks just like my wie but there is something different orodd about her. Te content o the delusion itsel arises rst as the content o an explanatoryhypothesis that is then adopted as a belie. Tis is the account given by Maher (1974, p. 103):

[]he explanations (i.e. the delusions) o the patient are derived by cognitive activity that isessentially indistinguishable rom that employed by non-patients, by scientists, and by peoplegenerally. . . . [A] delusion is a hypothesis designed to explain unusual perceptual phenomena.

It is clear that, on the explanation option as Maher conceives it, the project o explaining theanomalous experience is a project o the person. I explanation proceeds by Bayesian iner-ence, then this is personal-level inerence. We shall understand the explanation option inMahers way.

On the second (endorsement)20 option, the content o the delusion is encoded in theanomalous experience. Tus, a state in which the content o the delusion is present is therst delusion-relevant event o which the patient is aware. Te anomalous experience is

Te terminology o endorsement comes rom Bayne and Pacherie (). Descriptions othe explanation versusendorsement options, with varying terminology, are also given by Davies andColtheart (), Fine et al. (), Aimola Davies and Davies (), Langdon and Bayne (), and

urner and Coltheart ().




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not the delusional belie itsel, but the belie would arise as the prepotent doxastic responseto the experience (or, on the Spinozan view, would be adopted automatically on the basis

o the experience). Although the endorsement option is distinct rom Coltheart and col-leagues (2010) view that the delusional belie itselfis the rst conscious delusion-relevantevent, both agree that no conscious personal-level reasoning is involved in the stage leadingto onset o the delusion (see urner and Coltheart 2010, p. 368).

Te explanation and endorsement options are distinct. But it is important to observe thatthe distinction between them is notthat one allows, while the other excludes, the possi-bility that Bayesian inerence gures in the etiology o the delusion. It is entirely consist-ent with the endorsement option that the anomalous experience encoding the content othe delusion is the product o perceptual processes that are well described as unconscioussubpersonal-level Bayesian inerence.

Bayesian inference in a perceptual module

In our earlier discussion o the processes leading up to initial adoption o the delusionalbelie (see Bayes in the two-actor ramework: Adoption o the delusional belie sec-tion), we noted that it is somewhat unclear which probabilities are supposed to gure inthe worked examples o Coltheart and colleagues (2010) and McKay (2012). Are theysupposed to be realistic probabilities or the patients credences, or example? McKaychallenges Coltheart et al.s account on the grounds that their proposed prior prob-ability or the stranger hypothesis, P(HS) = 0.01, is unrealistically high (2012, p. 339)and offers a much lower estimate. But he accepts their estimate o the likelihood ratioas avoring HSin the ratio 999:1. Tis acceptance is puzzling because it seems clear thatrealistic values or the likelihoods, P(D|HS) and P(D|HW), would be identical. Te seenace o a woman who looked just like the patients wie would activate FRUWin the sameway as the seen ace o the patients wie would; and it would cause the same activityin the autonomic nervous system. So a realistic likelihood ratio would be 1:1 and noamount o discounting prior probabilities (which avor HW) would produce posteriorprobabilities avoring HS.

It may seem more natural to interpret the probabilities in the worked examples as thepatients own credences but this, too, is problematic. First, the worked examples (so inter-preted) are ar rom intuitive i, as Coltheart and colleagues explicitly maintain, activity

in the patients autonomic nervous system is not available to the patients consciousness.How are we to understand a credence such as P(D|HW) i the patient knows nothing oautonomic activity as such and does not even experience autonomic activity? Second,waiving this rst concern, suppose that the patient assigns a low conditional credence tothere being no activity in his autonomic nervous system given that the woman he sees inront o him is his wie and a high conditional credence to there being no activity in hisautonomic nervous system given that the woman is not his wie but looks just like his wie.Te only way or the patients credences P(D|HW) and P(D|HS) coherently to come apartin the way described is or the patient to assign high credences to hypotheses accordingto which the autonomic nervous system is not just responsive to qualitative inputs romvisual perception via the FRUs, but also directly sensitive to acts about the identity o the

person perceived.




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Our suggestion is that the probabilities in Bayesian inerence that starts rom theabnormal data, D (the absence o activity in the patients autonomic nervous system),

should be conceived as probabilities assigned by a subpersonal-level unconsciousinormation-processing system or perceptual module.21Te modules probabilities may notbe realistic, because a module has only limited inormation about how the world (includ-ing the module itsel) really works. And the modules probabilities may not be coherentwith personal-level credences because modules are, at least to some extent, inormation-ally encapsulated (Fodor 1983). Processes in a module do not draw on all that the personknows or believes and so we sometimes experience what we, at the personal level, know tobe perceptual illusions. It is also because o this relative independence o the probabilitydistributions o perceptual systems rom a persons credences that we can learn rom expe-rience (Fodor 1989).

Let us return to Coltheart and colleagues (2010) and McKays (2012) worked examples,

now conceived as examples o Bayesian inerence within a perceptual module. Fodor saysthat the unction o modules is to so represent the world as to make

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