Logical deductions about events that cannot be observed directly are referred to as

Reasoning styles

Before discussing positivism and inteipretivism, it is necessary to examine two styles of reasoning, with which the approaches are associated: ‘deductive’ and ‘inductive’ reasoning styles. Deductive reasoning is mainly associated with the scientific (or positivist) approach to research. Interpretivist approaches are associated with inductive reasoning. These differences will be described further below in relation to the discussions of the two schools.

Deduction

Deductive reasoning, which is defined as reasoning from general principles to particular cases (as in deducing from the principles that ‘All men are mortal’ and ‘Socrates is a man’ the consequence that ‘Socrates is mortal’), is in general not creative. On the other hand, viewed in a certain way, all of mathematics is logical deduction: there are theorems for which it is difficult or impossible to see intuitively whether or not they are true, let alone prove they are true by showing the steps through which they can be deduced from general principles. Hence not all deductions are trivial; some may well require formidable creativity to accomplish. In general, it is the size of the deductive gap between the principles and their consequences that determines whether or not deduction requires creativity: ‘Socrates is mortal’ does not; Fermat's last theorem does.

Deductive Reasoning

Deductive reasoning, also known as top-down logic, is defined as the ability to make inferences about the veracity of a conclusion based on several, often competing, hypotheses. In the most comprehensive meta-analysis of deductive reasoning in neuroimaging studies to date, it was determined that this ability was not unitary and that the brain contains three subsystems for understanding deductive reasoning – categorical, relational and propositional – and different varieties of problems require different mental representations, potentially due to some tasks requiring greater use of visuospatial mechanisms and others requiring greater use of rule-based mechanisms (Prado et al., 2011). Categorical reasoning was theorized by Piaget to develop during the concrete operational stage from 7- to 11-years-old (Inhelder and Piaget, 1964), and empirical studies have found subsequently found that this is indeed a key period for improving at these categorical tasks (Markovits and Thompson, 2008) rather than during adolescence. Based on the research literature, it appears that for relational and propositional problems, pre-adolescents can understand the most basic versions of these tasks, but that more advanced versions are typically mastered only by adolescents and adults. This development could be due to a number of reasons, but is likely due to the concurrent development of related subdomains such as abstract thinking and hypothetical thought.

Abstract thought is the ability to generate and manipulate thoughts that are not specifically related to the immediate environment. Hypothetical thought is the capacity to consider multiple alternatives as being true and then to make inferences about them (Amsel, 2011). Hypothetical thought relies upon abstract thought in that it requires the ability to think about things that have not necessarily happened. Although Piaget often overestimated the abilities of adolescents and adults to think hypothetically (Boden, 1980), there is some evidence he underestimated the ability of pre-adolescents to think abstractly. Evidence suggests that while 6- to 7-year-olds cannot use false premises to think logically, 9- to 11-year-olds can do so (Markovits and Lottie-Forgues, 2011). Furthermore, in an intervention design, practice reasoning with false premises facilitated the ability of 12- to 15-year-olds to reason abstractly (Markovits and Lottie-Forgues, 2011). The ability to think abstractly and thus hypothetically also allows for a variety of other psychological phenomena such as ‘reasoned anticipation’ (Larson, 2011) and regret (Rafetseder and Perner, 2012). By being able to generate abstract thoughts, adolescents can make judgments on hypotheticals and be able to make deductive inferences on which of two hypotheticals is more likely to be true than the another.

In order to determine the exact point when advanced deductive thought matures in individuals, researchers have frequently used the methodology of comparing adolescents' reasoning to that of younger children. Relational reasoning is the ability to “reason about abstract relationships among items in our environment” (Krawczyk et al., 2011, p588). For example, Crone et al. (2009) used the Raven's Progressive Matrices test to compare pre-adolescents and early adolescents with adults and found that although 8- to 12-year-olds can consistently solve simple 0- and 1-dimensional relational problems, they struggle with working with 2 dimensions compared to 18- to 25-year-olds. The intermediate performance of 12- to 18-year-olds suggests that this cognitive growth is gradual rather than tightly scaled, which conforms to a number of studies in related tasks (Keating, 2011). Propositional reasoning is the ability to understand ‘if … then’ statements. With a similar purpose, Gauffroy and Barrouilet (2011) hypothesized that determining what possibilities can be true based on a given sentence is easier (‘reasoning about possibilities’) then determining the falsity of a sentence based on known possibilities (‘reasoning about truth-values’). Accordingly, they found that there was a three-year lag between the former type of reasoning and the latter; sixth graders showed relative mastery of reasoning about possibilities but not the veracity of sentences, in comparison to ninth graders. While pre-adolescents show some competence at relational and propositional reasoning tasks, adolescents show a much greater age-related competence.

Although the evidence suggests that cognitively, there is a distinction to be made between pre-adolescents and adolescents, is there a clear difference between adolescents and adults? Moshman (2011a, 2011b) has argued that from the age of 12, adolescents should not be considered cognitively distinct from adults. That is not to say that he believes that adolescents are fully cognitively developed, rather that the development from this point forward shows substantial inter-individual differences, and does not follow a universal trajectory (2011a, 2011b). The argument being made here is not that there are no substantial differences between groups of adolescents and adults, but rather that other contextual factors, such as education, are a better explanation of the difference, instead of merely age. As evidence of this, in a study that compared adolescents with adults on deductive reasoning tasks, it was found that whether adults outperformed adolescents depended on the level of education the adults had (Demetriou and Bakracevic, 2009). College-educated young adults outperformed adolescents in spatial, propositional and social reasoning; non-college-educated young adults, however, performed worse than adolescents in two of these three domains, social reasoning being the exception. The neurocognitive evidence on average differences in impulse control is reviewed in the next section and suggests that adolescents and adults might have similar capabilities but differ in their context-dependent performance. In any case, the evidence seems consistent that from adolescence onwards, deductive reasoning shows inter-individual differences that are greater than the mean difference between adolescents and adults.

In summary, deductive reasoning consists of multiple subcomponents that show substantial development during adolescence. This advancement in deductive thought is likely the result of the ability to think hypothetically, which itself is the result of greater abstract thought. The ability to think logically also appears likely to be significantly affected by one's context. These separate but related abilities that make up the global domain of deductive reasoning do not develop at the same rate and all show substantial inter-individual differences, which are likely due to differences arising from genetics, the environment, and their interaction.

Deduction

Deductive reasoning, strictly speaking, involves arguments whereby, if the premises are true, then the conclusions must also be true. In a deductive argument, the conclusions flow directly from the premises given (Walton, 1989, p. 110). Or, as Lee et al. (1983, p. 2) describe it,

In deductive logic, a conclusion follows inescapably from one or more of the premises. If the premises are true, then the conclusion drawn is valid.

Burch (2003, p. 6) reminds us:

When the arguer claims that it is impossible for the conclusion to be false given that the premises are true, then the argument is best considered a deductive argument. When the arguer merely claims that it is best considered improbable that the conclusion be false given that the premises are true, then the argument is best considered an inductive argument.

A deductive argument is structured so that the conclusion is implicitly contained within the premise; unless the reasoning is invalid (as in a false deduction or a non sequitur), the conclusion follows as a matter of course. It is designed so that it takes us from truth to truth. That is, a deductive argument is valid if (Alexandra, Matthews, and Miller, 2002, p. 65)

- It is not logically possible for its conclusion to be false if its premises are true.

- Its conclusions must be true, if its premises are true.

- It would be contradictory to assert its premises yet deny its conclusions.

For these reasons, it is incumbent on the criminal profiler to establish the veracity and validity of every premise before attempting to draw conclusions from them. Inferences without this level of care are not deductive.

A criminal profile that results from a deductive argument is by no means static. Like any forensic report, its conclusions should be re-examined when new facts and information become available. However, a criminal profile that results from this process is by no means static and may be updated in light of new information. Further evidentiary considerations, such as new physical evidence, may be incorporated into the decision process to update the conclusion. Also, new advances in science and understanding may challenge long-held assumptions and question the current hypothesis. This is not a problem with the process, because a deduction can only operate within the realm of established laws and principles. Farber (1942, p. 48) makes clear this tenet of argumentation:

Every “logical system” is governed by principles of structure and meaning. A system that claims to be a “logic,” i.e., which operates formally with one of the various definitions of implication, possibility, etc., is subject to the laws of construction of ordered thought, namely, to the fundamental principles of logic. This requirement imposed on all systems cannot amount to a law that there shall be law. The specific application is provided by the rules in each system.

When the laws or principles of a logical system, such as a crime scene, change because of new knowledge from further testing or observation, so too must the nature of the deductions made.11

IV.B Imagery and Spatial Representations

Does deductive reasoning rely on visual imagery? Behavioral studies have produced little evidence to suggest this is the case. Readers might suppose that this lack of evidence counts against the model theory. This view, however, confuses models with images. The model theory distinguishes between the two: Mental models are structural analogs of the world, whereas visual images are the perceptual correlates of certain sorts of model from a particular point of view. Indeed, many mental models are incapable of supporting visual images because they represent properties or relations that are not visualizable, such as ownership, obligation, and possibility. Recent studies have sharpened the need to distinguish between the degree to which relations evoke spatial models as opposed to visual images. The studies examined three sorts of materials, as rated by an independent panel of judges:

Relations that are easy to envisage spatially and easy to visualize, such as above, below, in front of, and in back of

Relations that are not easy to envisage spatially but are easy to visualize, such as cleaner, dirtier, fatter, and thinner

Control relations that are neither easy to envisage spatially nor easy to visualize, such as better, worse, smarter, and dumber

The studies examined both conditional inferences and inferences about simple relations among entities. They showed that inferences were faster with contents that were easier to envisage spatially than with the control contents, which in turn were faster than contents that were easy to visualize but difficult to envisage spatially. It seems that a relation such as “dirtier”, elicits a visual image, but one that is irrelevant to the construction of a mental model that allows reasoners to make the required inference. In contrast, a relation, such as “in front of” elicits a spatial model that helps individuals to draw the inference. An fMRI study has also examined spatial reasoning. Given spatial problems, such as

The red rectangle is in front of the green rectangle.

The green rectangle is in front of the blue rectangle.

Does it follow that the red rectangle is in front of the blue rectangle?

significant activation occurred in regions of parietal cortex that are known to represent and to process spatial information. Moreover, there was no reliable difference in the degree of activation between the right and the left hemispheres. Clinical studies of how brain damage affects the use of imagery in reasoning have produced mixed results, perhaps because they have not separated the two sorts of contents—spatial and non-spatial—that are both easy to visualize.

In summary, clinical and imaging studies of the brain have yet to establish how reasoners make deductions. There is evidence for separate systems mediating logical inferences with neutral content and personal inferences with a content that engages knowledge and beliefs. Future studies may determine whether separate brain mechanisms underlie the control of different deductive strategies, the use of diagrams as opposed to verbal premises, and the construction and evaluation of multiple models.

6 Reasoning and Analogies

While deductive reasoning, in logic, refers to the necessary outcomes of a set of conditions, inductive reasoning is concerned with determining the likelihood of an outcome. Only possible conclusions can be drawn, since not all of the conditions influencing or determining the outcome of a given situation are known. Analogical reasoning has a different character; it is basically a more precise form of conjecture. It is based on the mapping of structures or relations valid in one domain of knowledge onto another—less familiar or unknown—domain. The structures to be mapped are selected on the grounds of the similarity between the novel problem and the familiar one. The novel area is defined as the target domain of analogy construction, the familiar area as the source domain. With respect to the truth values of the conclusion, analogical reasoning spans all variants—from the absolute certainty of the modus ponens to a posteriori probabilities according to Bayes' Theorem, some of which are very weak. Suppose, for example, a second pair of terms is sought for a pair of numbers such as 3:6. Pairs such as 8:16 and 64:128 among many other combinations meet the requirements of the analogy.

As shown in Fig. 1, analogy construction can also be applied to geometric figures. It may be, but does not have to be the same factor of horizontal stretch which is mapped to produce a rectangle from a square or an oval from a circle. The boundaries within which geometric analogies are accepted are fuzzy, but when these boundaries are overstepped, the analogies are rejected. The same holds for meaningful words in natural languages. Let us imagine that analogous pairs with the same relational correspondence are to be generated for the following pairs of words: (a) collie: dog, (b) walk: run, (c) oak: birch. A good number of satisfactory analogies can be found, for example: (a) rose: flower, (b) speak: shout, (c) carp: trout. In each pair, the first term has all the relevant properties of the second (animal, voice, plant), as well as some of its own. The first pair is characterized by a sub-super-concept relation, the second by the intensity of the characteristic feature (the semantic relation of the comparative). The third pair shares a super-concept with common properties, but each term has specific properties of its own (the semantic relation of coordination). Pairs of terms such as dress and bullet or flea and fog do not allow analogies to be drawn on the basis of common properties, as these are non-existent. Clearly, similarity between the terms is an integral element in the construction of analogies. This similarity is not necessarily rooted in common properties, however. For us pairs of terms such as (a) ship and ocean, (b) hunter and deer, and (c) surgeon and scalpel, for example, do not share common properties. Nevertheless, the relational connections between the concepts are comparable with those found in other pairs of terms. In example (a) the shared relational connection is the location (as in flower and garden), in (b) it is the object of the action (as in butcher and cow), and in (c) the instrument (as in farmer and scythe). More complex relations can also be involved, as in ‘learn: know’ paired with ‘fight:win.’ Here, the common semantic relation is the objective or purpose. Such relational connections are the basis for analogy construction: ‘The shark is the wolf of the ocean,’ for example, or ‘May is the Mozart of the calendar’ (Erich Kästner). Many such examples are to be found in the Bible, particularly in the parables of the New Testament.

Effects of Knowledge on Inductive Reasoning

Unlike deductive reasoning, where it should be possible to determine just from the form of an argument whether the conclusion must necessarily follow, inductive reasoning is uncertain by nature. Hence it should be rational to go beyond the information given, seeking other knowledge that could reduce this uncertainty and make inductive inferences more accurate. Indeed, all of the examples of inductive reasoning in this section rely on some use of world knowledge that is not explicitly stated in the inductive arguments, such as that cows and horses are more similar than are cows and ferrets. However, in other ways researchers have aimed to study the “essence” of inductive reasoning by discouraging the use of outside knowledge. For example, Rips [1975] used fictional diseases that people would not have strong prior beliefs about and Osherson et al. [1990] used “blank” properties such as “has sesamoid bones” which sounded somewhat biological but were fairly unfamiliar. These decisions by these researchers were helpful indeed in uncovering the various empirical regularities such as similarity, typicality, and diversity effects.

Still, other researchers have studied the role of knowledge in induction more directly. For example, Medin et al. [1997] looked at inductive reasoning about categories of plants, by various kinds of tree experts, such as taxonomists and tree maintenance workers. Here the main interest was effects of similarity, for groups that differed in their notions of similarity. For example, in a sorting task, maintenance workers tended to organize tree species in terms of their shape or purpose for various landscaping tasks. Medin et al. devised questions on a test of inductive reasoning that pitted scientific matches against alternative, functional category structures. For example, two tree species might be distant in terms of the scientific taxonomy but they could both be useful for providing shade. It was found that taxonomists (not surprisingly) sorted trees on the basis of scientific taxonomy and likewise favored inductive arguments between categories that were close in the scientific taxonomy. Maintenance workers seemed to favor a more functional category organization for both sorting and reasoning. In sum, the groups of experts generally showed the similarity effects that had been documented in other studies of induction, but their knowledge about trees mediated these similarity effects.

Other evidence for knowledge effects has highlighted the effects of the property that is being inferred. The Nisbett et al. [1983] study is a good illustration of how knowledge about the scope of a property affects inductive inference. As already reviewed, seeing that just one member of the Barratos group is obese does not seem to promote the inference that other people in this group will be obese. Obesity seems to be more of an individual characteristic rather than a group characteristic. On the other hand, Nisbett et al. found that people make stronger inferences for the same category but another property, skin color. Here, seeing the skin color of just one Barratos promotes inferences about other members of this group, on the assumption that members of the same ethnic group will likely have some shared physical characteristics. (See [Goodman, 1955] for further discussion of how properties differ in their tendency to promote induction.)

Although it might seem from the previous section that some properties have a wider scope for inference than others, the picture is actually more complicated. Depending on the categories in an inductive argument, a particular property may lead to strong inferences or weak inferences or something in between. Consider the following example, from [Heit and Rubinstein, 1994]. For an anatomical property, such as “has a liver with two chambers,” people will make stronger inferences from chickens to hawks than from tigers to hawks. Because chickens and hawks are from the same biological category, and share many internal properties, people are quite willing to project a novel anatomical property from one bird to another. But since tigers and hawks differ in terms of many known internal biological properties, it seems less likely that a novel anatomical property will project from one to the other. However, now consider the behavioral property “prefers to feed at night.” Heit and Rubinstein [1994] found that inferences for behavioral properties concerning feeding and predation were weaker between the categories chicken and hawk than between the categories tiger and hawk — the opposite of the result for anatomical properties. Here, it seems that despite the major biological differences between tigers and hawks, people were influenced by the known similarities between these two animals in terms of predatory behavior, thus making strong inferences about a novel behavioral property

Logical (Deductive) Reasoning

Logical or deductive reasoning involves using a given set of facts or data to deduce other facts by reasoning logically. It involves drawing specific conclusions based on premises. Transitive inference, or linear syllogistic reasoning, is one of the simplest forms of logical reasoning, and involves combining two premises R(a,b) and R(b,c) to draw the conclusion that R(a,c). Transitive inference is often used to examine young children's abilities to use previous knowledge and basic logic to determine a missing piece of information. Transitive inference is evident if a child can infer that if John is taller than Mary, and Mary is taller than Sue, then John is taller than Sue, even if information about the relative height of Sue and John is not available.

Preschoolers engage in transitive inference, as evident in Bryant and Trabasso's study (1971) that showed that children as young as 4 years of age could solve transitive tasks with minimal memory demands. Similarly, Halford (1993) showed that reducing the information processing load by utilizing tasks in everyday contexts and with familiar objects, and by reducing the relational complexity of the tasks (e.g., requiring 1 instead of 2 premise relations), facilitated young children's transitive inference. These findings confirmed that information processing load is a factor that influences young children's deductive reasoning. Studies have also demonstrated the role of mapping between relations in preschoolers' transitive inference. Four- and 5-year-olds exhibited the capacity to make transitive reasoning when inferences were made by mapping relations between analogous tasks (blocks and sticks). The role of analogy in logical reasoning was further examined in a study by Goswami (1995). Preschoolers were found to be capable of solving a transitive inference task by analogizing from the story of Goldilocks and the Three Bears. The findings that exposure to analogical tasks improved young children's ability to make transitive inferences further demonstrated that the core deductive reasoning competence is in place in early life. These researchers further confirmed that young children engage in analogical mapping in order to solve various problems.

A recent study (Gazes et al., 2015), used visual scenarios with puppet characters and a looking-time method to create events that were either consistent with or violated the expected transitive-inference relationship. Ten- and 13-month-olds saw a video with two dominance interactions between three puppets (bear > elephant; hippo > bear) in a social hierarchy: first the elephant was seen holding a toy, the bear reached over and forcibly took the toy from the elephant, and then the hippopotamus took the toy from the bear. The infants were then presented with different scenarios that either violated the expected transitive-inference relationship (e.g., the elephant took the toy from the hippo), or that were not inconsistent with the transitive inference. Infants looked longer at displays that violated the transitive inference than at other scenarios. The researchers interpreted the pattern of looking longer to suggest that 1-year-olds were engaging in transitive inference when they viewed scenarios of unexpected behavior by the puppets, compared to other displays. Infants as young as 10 months of age, therefore, showed the rudimentary ability to make transitive inferences about which character should dominate another character, even when their interaction was not directly observed.

Another form of logical reasoning involves conditional reasoning, which involves drawing a conclusion based on a conditional, or “if … then,” proposition. This has been tested in studies of young children's logical inference. Harris and Núñez (1996), for example, examined young children's ability to engage in conditional reasoning by presenting a simplified, child-appropriate version of the four-card selection task. The child was given a conditional sentence such as “If Julie goes out (p), she should put her coat on” (q),” and was shown four pictures: “a child in a house not wearing a coat (not-p, not-q),” “a child in a house wearing a coat (not-p, q),” “a child outside a house not wearing a coat (p, not-q)” and “a child outside a house wearing a coat (p, q)”. The child was then asked to select the picture that violated the conditional sentence (p, not-q) from these cards. Three- and 4-year-olds were capable of identifying the protagonist as being naughty in the picture that showed the condition not being met and displayed an understanding of actions that would breach a permission or set of rules.

Children's logical thinking continues to develop through elementary school. Pillow et al. (2000) examined preschool and elementary school children's ability to identify deductive inference or guessing as a source of a belief. Children were presented with an event that involved a puppet and two different-colored objects. The objects were then hidden in two separate boxes. The child and the puppet could not see the objects. The puppet then made a statement about the color of one of the hidden objects after looking directly at the object (the direct looking condition), looking at the other object (the inference condition), or looking at neither object (the guessing condition). Four- and 5-year-olds failed to distinguish inference from guessing, while 8- and 9-year-olds referred to the premises of deductive inference in their explanations of the puppet's knowledge. These findings showed the continued progress of children's explicit deductive reasoning ability from infancy and toddlerhood to preschool and elementary school ages, in response to increasingly complex reasoning tasks.

5.3 The absence of reasoning deficits

If delusions involve violations of the norms of epistemic rationality, then one would expect the reasoning patterns of delusional individuals to show systematic departures from the norms of epistemic rationality. However, there is rather little evidence that this is the case.

Let us begin with deductive reasoning. Anecdotally, many delusional individuals appear to retain the capacity to follow deductive arguments. Consider, the following interview with a patient suffering from somatoparaphrenia, who denied ownership of his left hand. The examining physician placed the patient’s left hand between his own hands and asked, “Whose hands are these?”

Patient: Your hands.

Examiner: How many of them?

Patient: Three

Examiner: Ever seen a man with three hands?

Patient: A hand is the extremity of an arm. Since you have three arms, it follows that you must have three hands. (Bisiach, 1988, p. 469)

Such anecdotal reports are reinforced by the failure to find any general deficit in the capacity of delusional individuals to reason deductively (Cutting, 1997; Maher, 1992). Indeed, studies have found that when common sense and deductive validity come into conflict, schizophrenic individuals are more influenced by validity than nondelusional controls are (Owen, Cutting, & David, 2007).

Of course, deduction is only one aspect of everyday reasoning, and it is arguably a rather marginal element of it at that. To the extent that delusions involve departures from the norms of epistemic rationality it is likely that those departures concern inference to the best explanation or abduction (Lipton, 2004). In abductive reasoning, one proposition recommends itself as belief-worthy (or at least, as more worthy of belief than a competing proposition) in virtue of its capacity to explain a particular datum. For example, one might conclude that it rained last night on the grounds that there is water in the street. Here, the hypothesis that it rained is justified on the grounds that it accounts for the datum (water in the streets) better than competing hypotheses (eg, that a water pipe burst) do.

Might delusional individuals fail to reason in accord with the norms of abduction? In an important study, Huq, Garety, & Hemsley (1988) discovered an association between delusions and what has become known as a jumping to conclusions (JTC) reasoning bias (Garety & Hemsley, 1994; Garety et al., 2005; see also Dudley & Over, 2003; Fear & Healy, 1997; Fine, Gardner, Craigie, & Gold, 2007). A JTC reasoning bias is paradigmatically tested with the beads task, in which participants are presented with a series of beads that they have been told are drawn from only one of two jars. The jars contain beads of two colours in complementary ratios, for example, 85:15 red to green and 85:15 green to red. Participants are required to guess which of the two jars the beads are being drawn from. Individuals who guess more quickly—or with more certainty—than is typical are said to have a JTC reasoning bias.

Although it is intriguing, the finding that delusional individuals appear to exhibit a JTC bias provides little justification for the epistemic approach. For one thing, the relationship between a JTC bias and the presence of delusions is far from straightforward. A JTC bias has been found in nondelusional schizophrenic individuals (Moritz & Woodward, 2005), in patients whose delusions had remitted (Peters & Garety, 2006), and in the nondelusional relatives of individuals with delusions (Van Dael et al., 2006). More importantly, those who display a JTC bias need not be violating the norms of epistemic rationality. Consider a subject who is disposed to make a judgment about which urn the beads are being drawn from on the basis of a single draw. Such judgments will be correct 85% of the time, and that does not seem to be an unreasonable basis on which to form a belief.5

Of course, the beads task taps only one form of abductive reasoning, and it is entirely possible that delusions are associated with systematic deficits or biases in other forms of abductive reasoning. But even if that were the case, it would be a further question whether those biases involve violations of the norms of epistemic rationality. Discussion of this issue is problematized by the fact that the evaluation of abductive inferences is far from straightforward. The beads task lends itself to a straightforward Bayesian solution, for its structure supports precise probability assignments. But few domains share the formal features exhibited by the beads case, and questions about whether a particular abductive inference is legitimate will often be contested.6

Although the considerations just adduced put some pressure on the epistemic conception, they are obviously not decisive, and the advocate of the view could argue that delusional individuals have systematic reasoning deficits that simply have not been identified. However, any such response needs to be accompanied by an account of why these deficits might have escaped detection. One possibility is that they are relatively subtle. However, they cannot be too subtle given our capacity to distinguish delusional irrationality from everyday irrationality. Another possibility is that they have escaped detection because they are domain specific. But here too the advocate of the epistemic approach must tread carefully, for the domains in terms of which reasoning is structured are unlikely to be as specific as those that characterize (monothematic) delusions. (It is unlikely that there is a module dedicated to reasoning about the identity of close family members.) There is clearly a great deal more to be said on these issues, but the considerations presented here suggest that the epistemic approach faces something of a challenge in explaining away the lack of general reasoning deficits in individuals with (monothematic) delusion.

Deductive Reasoning

The brain systems that implement deductive reasoning depend on whether the reasoning problem consists of familiar versus unfamiliar semantic content. When reasoning about familiar semantic content (e.g., All dogs are pets / All poodles are dogs / Therefore, all poodles are pets), a left frontotemporal system is engaged, including left inferior frontal cortex (BA 47), left middle/superior temporal cortex (BA 21/22), and left temporal pole (BA 21/38). Previous research has implicated this system, not only in deductive reasoning, but also in memory and language tasks that employ familiar semantic content. In general, linguistic processing appears central to all these tasks.

In contrast, reasoning about unfamiliar semantic content (e.g., All P are B / All C are P / Therefore all C are B) activates a bilateral frontoparietal system, including bilateral dorsal (BA 6) and inferior (BA 44) frontal lobes, bilateral superior and inferior parietal lobes (BA 7), and bilateral occipital lobes (BA 19). This pattern of activation is also found during the processing of spatial information, and is similar to the neural activity observed while people make transitive inferences about geometrical shapes.

Thus, deductive reasoning recruits left and right prefrontal cortex asymmetrically as a function of familiarity. Across both familiar and unfamiliar deduction problems, left prefrontal cortex is generally active, suggesting that this region is necessary for deductive inference. Conversely, right prefrontal cortex is engaged only when a problem involves unfamiliar semantic content or a conclusion that conflicts with prior beliefs (e.g., No harmful substances are natural / All poisons are natural / Therefore, no poisons are harmful). Whereas language may often dominate familiar reasoning, language and spatial/visual processing may often be central for unfamiliar reasoning.

The brain systems that implement deductive reasoning also depend on whether a reasoning problem produces correct versus incorrect conclusions. Research on this issue has used inhibitory belief problems, namely, problems whereby individuals must inhibit a highly accessible belief that could interfere with correct reasoning (e.g., No addictive things are inexpensive / Some cigarettes are expensive / Therefore, some cigarettes are not addictive). Drawing a correct conclusion on these problems requires that individuals (1) detect the conflict between their prior beliefs and the logical inference, (2) inhibit the prepotent response associated with their belief bias, and (3) engage the appropriate reasoning mechanisms. In contrast, drawing an incorrect conclusion on these problems results from failing to detect the conflict between beliefs and logical inference, and/or failing to inhibit the prepotent response associated with a belief bias.

When people draw correct conclusions on inhibitory belief problems, right inferior prefrontal cortex becomes active. When they draw incorrect conclusions, ventromedial prefrontal cortex is active instead. Activation in right inferior prefrontal cortex when drawing correct conclusions appears to reflect the detection and/or resolution of the conflict between belief and logic. Conversely, activation in ventromedial prefrontal cortex when drawing incorrect conclusions appears to reflect the role of nonlogical mechanisms, perhaps associated with greater affective processing.

In summary, the neural systems that underlie deduction vary considerably, depending on task factors and cognitive demand. Consistent with the task specificity hypothesis, the areas that support deduction vary with the familiarity of the materials, and with whether belief violations occur and are detected. Consistent with the cognitive demand hypothesis, more neural areas are recruited for difficult unfamiliar problems than for easier familiar ones. Consistent with the modularity view, left prefrontal cortex generally appears active across most deduction paradigms, suggesting that it is essential for deductive inference.