9 Intuition, reasoning and development: a fuzzy-trace theory approach – The Development of Thinking and Reasoning

Intuition, reasoning and development

A fuzzy-trace theory approach

Valerie F. Reyna


Intuition is unconscious

In this chapter, I discuss a framework for reasoning and rationality that contrasts with traditional approaches, such as Piagetian logicism – reasoning as logic – and information-processing formalism – reasoning as computation. This framework is called “intuitionism” because reasoning is conceived of as intuition, as defined in fuzzy-trace theory (Reyna & Brainerd, 2011). By “intuition,” I mean fuzzy, impressionistic thinking using vague gist representations that capture essential meaning. As in traditional approaches, intuition in fuzzy-trace theory tends to influence cognition unconsciously. People can consciously report what they think the gist of information is, a boon to measuring gist, but they cannot introspect reliably regarding the influence of gist on their reasoning and remembering.

The unconscious influence of gist explains why people can report “false” memories of events that never occurred with great confidence as though they were true memories (Brainerd & Reyna, 2005; Robinson & Roediger, 1997). The memories are false in the sense that the events never actually occurred, but they are typically derived from memories for the gist of events that did occur, which wend their way from the unconscious to become consciously experienced as real. This issue of consciousness has a checkered past in psychology, but the claims about consciousness made in fuzzy-trace theory are grounded in tests of mathematical models that must incorporate this assumption in order to fit real data (e.g., Brainerd, Reyna, & Mojardin, 1999). As elaborated below, the effort after meaning shapes the gist memory representations that reasoning operates on (Reyna, 2011a).

Origins of the verbatim-gist distinction in psycholinguistics

In the 1970s, psycholinguists were convinced, based on good evidence at the time, that people extracted gist information from verbatim surface form (Clark & Clark, 1977). That is, they cracked the kernel of meaning at clause boundaries and extracted the substance from a sentence’s words, throwing away the husk of the surface form (i.e., the verbatim words). In this view, long-term memory for verbal information was schematic, stripped of precise wording or detail that had been jettisoned in the act of comprehension. The influential ideas of the day, redolent of the epic battle between Noam Chomsky and B. F. Skinner, pitted the deep structure versus surface structure ideas of transformational grammar against the mindless memorization of Skinnerian associationism (Gallo, 2006). These conflicts are echoed in the contrast between gist (deeper meaning) versus verbatim representation (surface form) in fuzzy-trace theory.

Later research showed that the verbatim-to-gist model was mistaken (Singer & Remillard, 2008). Instead of a serial process in which gist was extracted from verbatim words (and the exact words vanished from information processing), subsequent research demonstrated that people extract separate mental representations of information roughly in parallel: a verbatim representation and sometimes multiple gist representations (Reyna, 2011b; Reyna & Brainerd, 1995). The verbatim representations become inaccessible much more rapidly than the gist, they disintegrate over time as forgetting came to be characterized, but the verbatim and gist representations lead separate lives. As I review below, these verbatim and gist mental representations also support qualitatively different kinds of reasoning, the gist-based intuition noted above that is fuzzy and impressionistic and verbatim-based analysis that is precise and computational.

Intuition is reasoning

In his best-selling book entitled Thinking, Fast and Slow, Nobel Prize winner Daniel Kahneman distinguishes System 1 which is fast, intuitive and emotional from System 2 which is slower, more deliberative, and more logical (Kahneman, 2011; see also Stanovich & West, 2000). Similarly, echoing the Chomsky–Skinner debate, Sloman (1996) described low-level (System 1) thinking as associative and high-level (System 2) thinking as deliberative. Although intuition can produce right answers and it even has its “marvels” on occasion, in traditional approaches, the crux of the matter is that intuition is an evolutionarily primitive process from which biases and logical fallacies emerge. Animals and children think intuitively, an idea that would be familiar to Piaget, Freud, or Descartes (Reyna & Brainerd, 2008, 2011). In general, intuition ought to be tamed or censored, in favor of logic or deliberation, as the rider should control the horse, not vice versa (Kahneman, 2003). The horse might wander onto a right path that the rider is unaware of; emotion, spontaneity, and “unbridled passion” also have their appeal (as dramatized in Peter Shaffer’s 1973 play Equus, among many other works of fiction). Nonetheless, from this traditional perspective, the horse is not considered smarter or more rational than the rider. Indeed, the word “reasoning” is often reserved in traditional approaches only for those cases in which logic and deliberation are used, in contrast to intuition.

In fuzzy-trace theory, reasoning encompasses intuition (Reyna & Brainerd, 1992). In fact, gist-based intuition is not only an admissible form of reasoning, but is also considered the default mode of adult reasoning that generally determines judgments and decisions. Unlike some traditional approaches that assume intuition operates alone until censored, both verbatim and gist processing are assumed to occur simultaneously, but task demands constrain which representation (and its associated processing) trumps the other (Reyna & Brainerd, 1995, 2011). These assumptions have been tested in myriad experiments. For example, when task instructions stress word-for-word recognition, verbatim processes are used to reject answers that are gist-consistent but not exact matches (Brainerd, Reyna, Wright, & Mojardin, 2003); when task instructions stress meaning-based recognition, verbatim processes no longer trump gist (Garcia-Marques, Ferriera, Nunes, Garrido, & Garcia-Margques, 2010; Reyna & Kiernan, 1994).

Intuition is not impulsivity: executive processes of monitoring and inhibition

Fuzzy-trace theory distinguishes insightful intuition that reflects understanding from mindless impulsive reaction. Such claims are based on research comparing reasoning by children and adolescents to that of adults, and reasoning of adult novices to that of experts. In addition to verbatim and gist processes, a generalized executive process of cognitive control develops from childhood to adulthood (Casey, Getz, & Galvan, 2008; Reyna, 1995; Reyna & Mills, 2007b; Steinberg et al., 2008). As a result, impulsivity – or disinhibition – decreases (e.g., Levin & Hart, 2003; Reyna & Mills, 2007b). However, the ability to remember verbatim information, and use it to reject gist-consistent answers when appropriate, differs from this generalized ability to control oneself (e.g., to withhold responses, or set a strict response criterion; Reyna & Brainerd, 1998; Reyna & Mills, 2007b). In this respect, fuzzy-trace theory differs from such social-affective theories as imbalance theory (Steinberg, 2008) and such cognitive theories as activation/monitoring theory (Roediger, Watson, McDermott, & Gallo, 2001) and its antecedent source-monitoring theory (Johnson, Hashtroudi, & Lindsay, 1993), which combine cognition (e.g., verbatim memory) and cognitive control into a global “monitoring” ability.

Rather than conflate verbatim memory with monitoring (cognitive control), fuzzy-trace theory distinguishes the fast, impulsive responses of young children; the fast, insightful responses of advanced reasoners (based on rapid retrieval and processing of gist); and the relatively slow retrieval and processing of verbatim details (Brainerd, Payne, Wright & Reyna, 2003; Dodson & Hege, 2005). Thus, there are two kinds of fast and simple ways of thinking: a stupid kind that represents a primitive form of thinking (lack of cognitive control or impulsivity) and a smart kind that represents a highly developed form of thinking (insightful intuition). Impulsivity decreases as children mature, whereas insightful intuition increases as life experience and greater expertise transform the random dots of reality into recognizable gestalts (e.g., Reyna & Ellis, 1994; Reyna & Farley, 2006; Reyna & Lloyd, 2006). In the foundations of mathematics, intuition has similarly been promulgated as an advanced form of thinking (Brouwer, 1927).

What special populations reveal about reasoning: autism, Asperger’s syndrome, traumatic brain injury, and attention-deficit disorder

This developmental trajectory of increasing reliance on gist-based intuition is not universal. Developmental disorders, such as autism and Asperger’s syndrome, are characterized by a cognitive style that has been called “weak central coherence,” a focus on literal details at the expense of global coherence (Frith, 1989). For example, comprehension of metaphors is often limited in this population (metaphors are interpreted literally, even among autistic adults), whereas metaphors are ordinarily interpreted using gist among normally developing older children and adults (Reyna, 1996b; Reyna & Kiernan, 1995). Autism spectrum disorders have recently been analyzed not as a lack of intelligence or reasoning ability, but as a verbatim-based analytical information-processing style, which predicts worse performance when accurate reasoning requires non-literal gist thinking and better performance when non-literal gist thinking is the source of reasoning biases and fallacies (Reyna & Brainerd, 2011). As examples, people with Asperger’s syndrome show less bias due to framing equivalent outcomes as gains versus losses and they show fewer conjunction fallacies (De Martino, Harrison, Knafo, Bird, & Dolan, 2008; Morsanyi, Handley, & Evans, 2010).1

Although attention-deficit disorder is quite different from Asperger’s or autism, a smaller window of attention seems to impair the semantic integration of information that is essential for gist extraction. Thus, individuals with attention-deficit disorder show comparable verbatim “fact learning,” but reduced gist-based reasoning, compared to typically developing youth (Gamino, Chapman, Cook, Burkhalter, & Vanegas, 2008; Gamino, Chapman, & Cook, 2009; Gamino, Chapman, Hull, Vanegas, & Cook, 2009). Again, despite very different etiologies, patients with traumatic brain injuries show a similar profile; they eventually close the gap with comparable controls on verbatim fact-learning tasks, but the ability to extract gist does not recover spontaneously (Chapman et al., 2006; Gamino, Chapman, & Cook, 2009; Gamino, Chapman, Hart, & Vanegas, 2009). In a randomized control trial, programs that specifically targeted gist-extraction skills significantly improved reasoning performance for those with attention-deficit disorder, beyond interventions that trained attention (Gamino, Chapman, Hart, & Vanegas, 2009). Such interventions, which did not teach content, also improved performance on standardized achievement tests among academically under-performing students (Chapman, Gamino, & Mudar, 2012; Gamino, Chapman, Hull, & Lyon, 2010). By supplying the “active ingredient” (i.e., the ability to extract gist) for superior reasoning to students who were lacking that ingredient, these students were able to improve their reasoning performance on a wide range of tests. These results are impressive not only because they test the mechanisms postulated in fuzzy-trace theory, but also because they demonstrate that research on causal mechanisms has practical implications for reducing underachievement in education (Reyna, Chapman, Dougherty, & Confrey, 2012).

Summary: comparisons with different theories and implications

The fuzzy-trace framework builds on a treasure trove of evidence accrued from the theoretical approaches that preceded it (e.g., see Bjorklund, 1989; Siegler, 1991). Centrally, fuzzy-trace theory draws on evidence for independent gist and verbatim-memory representations of information. In that regard, it is a dual-process theory (Reyna, 2004). Like logicist and formalist approaches, fuzzy-trace theory assumes a growing ability to perform computations during childhood because of schooling (Barrouillet, 2011; Klaczynski, 2001). Like the heuristics and biases approach, the theory draws on Gestalt theory, particularly the distinction between non-productive thought (rote associations, akin to verbatim-based analysis) and productive thought (conceptual understanding that supports transfer, akin to gist-based intuition) (Wertheimer, 1959; Wolfe & Reyna, 2010). (Transfer is the ability to apply prior learning to novel situations.) Non-productive thought focuses on the isolated dots of experience, without being biased by context or prior experience, but productive thought uses context to connect the dots and make meaningful inferences that go beyond surface information, integrating current and prior experience (Asch, 1946; Lloyd & Reyna, 2009; Reyna & Brainerd, 1995).

Fuzzy-trace theory does not make the same predictions, however, as traditional approaches. Unlike traditional approaches, advanced processing, such as the reasoning of experts in their domain of knowledge, often occurs unconsciously rather than through conscious processing (Reyna & Lloyd, 2006). It is not just that experts have practiced reasoning until it has become automatic and, therefore, unconscious (cf. Evans, 2003; Sloman, 1996; Stanovich & West, 2000). Clearly, the automatic processing of experts and the automatic (unthinking) responding of impulsive children are not the same thing, and should not both be assimilated to System 1 processing. Reasoners can provide conscious reports, such as verbal explanations, of their reasoning, but these reports can be epiphenomenal (i.e., they can be incidental to the underlying cognitive processes responsible for performance). For example, children typically are able to engage in accurate reasoning several years before they can verbally articulate that understanding; despite their impoverished verbal protocols, they are capable of far transfer to novel instances of a concept, which demonstrates conceptual understanding (e.g., Brainerd, 1973; Jacobs & Potenza, 1991).

Further, the theory differs from other dual-process models in emphasizing that there are degrees of rationality and that intuition is an advanced form of reasoning. The degrees of rationality reflect different sources of errors in reasoning, from less to more fundamental, at different points in processing (Reyna, Lloyd, & Brainerd, 2003). Some errors involve verbatim (literal) thinking; some involve processing gist, but the wrong gist for the task at hand; still other errors involve mental bookkeeping lapses in which people lose track of denominators (e.g., denominators of fractions; Reyna & Brainerd, 2008). Literal thinking is a more fundamental error in thinking, and occurs earlier in development, compared to denominator neglect, which still occurs in adult reasoning about ratios. Denominator neglect is a less fundamental error (compared to literal thinking, which represents a lack of understanding) because adults understand ratios; they lose track of denominators because they are confused by overlapping and nested sets (Acredolo, O’Connor, Banks, & Horobin, 1989; Brainerd & Reyna, 1993; Reyna & Brainerd, 2008).

The theory predicts parallel development of verbatim-based analysis and gist-based intuition, which produces developmental reversals (e.g., children outperform adults) under specific circumstances (e.g., Reyna & Ellis, 1994). As an example, despite increasing competence in reasoning, some biases in judgment and decision making grow with age, producing more “irrational” violations of coherence among adults than among adolescents and younger children (De Neys & Vanderputte, 2011). The latter phenomena are linked to developmental increases in gist processing with age (Reyna & Farley, 2006).

Finally, these developmental predictions have implications for health and economic well-being, including saving and spending decisions (e.g., Rémy Martin costs more than Courvoisier, and Courvoisier costs more than Hennessy; which cognac costs the most?); disease-prevention decisions (deciding to get a mammogram or to avoid transfats); and medical and surgical decisions (e.g. survival rates are equal for Treatment A and for Treatment B; Treatment A has more side effects; which treatment is best?), especially decisions that involve risk and probability (Reyna, Wilhelms, Brust, Sui, & Pardo, 2011). As reliance on gist-based intuition increases, the theory predicts that people become better able to understand the nature of catastrophic risks, the qualitative gist of possibility (as opposed to probability), and the qualitative gist of good or bad consequences. This type of gist-based reasoning has been associated empirically with better health and well-being (e.g., Mills, Reyna, & Estrada, 2008; Reyna, Estrada et al., 2011; Reyna & Farley, 2006). As I now discuss, both laboratory and consequential real-life reasoning often involve integrating representations of information about risk, probability, and consequences.

Content and cognitive options

Content matters in reasoning and gist represents meaningful content

As the examples above suggest, everyday life requires reasoning, including logical deductions, pragmatic inferences, and probability judgments (e.g., judgments about disjunctions of events; what is the probability A or B will happen?). Thus, reasoning includes such cognitive activities as deducing conclusions in transitive reasoning (also called linear syllogisms). For example, Paris Hilton is richer than Kim Kardashian; Kim Kardashian is richer than Donald Trump. Who is richer: Paris or Donald? These famous names can be replaced with symbols such as A, B, and C, respectively, and the logical conclusion still holds: based on these premises, A (Paris) is richer than C (Donald). Some scholars have therefore concluded that logical reasoning is about abstract – content-free – structures.

These kinds of deductive inferences are said to be independent of content for the reasons noted above – symbols can be substituted and deductions remain valid. However, as Johnson-Laird (e.g., 2010) and others have argued, this reasoning is not entirely content-free: if people are seated around a circular table, inferences about “to the left of” eventually come full circle – if Paris is to the left of Kim and Kim is to the left of Donald, is Paris to the left of Donald? The inference about “to the left of” follows if the situation referred to is, in fact, linear (Paris, Kim and Donald are arranged roughly in a line), but it fails at some point if they are seated around a circular table. At some point, someone is “to the right of” another person.

Pragmatic inferences rely even more heavily on content. For example, world knowledge about spatial relations supplies the key content to enable inferences such as the diamond is in the box, the box is under the table – is the diamond under the table? That is, there is no abstract structure that applies to all uses of “under” or “to the left of” to produce valid inferences. As in mental models approaches, fuzzy-trace theory captures this reality about reasoning – that there is always some content that has to be interpreted to enable valid inferences – by assuming that the content has both a verbatim (literal) and gist representation (again, often more than one gist representation). The gist representation depends, in turn, on knowledge and experience (Reyna, 1996a).

How the content stored in memories provides options for reasoning

Although there are similarities to the fruitful mental-models approach, fuzzy-trace theory differs in several ways from classic mental-models approaches to reasoning. Significantly, the core mechanism for predictions in these approaches is limited working memory; more complex reasoners’ models require more memory (and produce more errors) (Barrouillet, Gauffroy, & Lecas, 2008; Johnson-Laird, 2010). However, scores of experiments have shown that reasoning quality is independent of working memory for problem information in adults (for reviews, see Reyna, 1995; Reyna & Mills, 2007b).

This necessity argument – that memory for problem information is necessary for reasoning about that information – must be distinguished from individual differences in memory and reasoning, which are correlated rather than independent (i.e., people who reason better in one task tend to remember more, in both related and unrelated tasks, due to general intelligence and other general cognitive abilities; Cokely & Kelley, 2009; Liberali, Reyna, Furlan, Stein, & Pardo, 2011). The necessity argument is false because reasoning generally does not depend on working memory for problem information. People tend to answer memory questions about exact details using verbatim memory, whereas they tend to answer reasoning questions using vague gist memory. Because verbatim memory and gist memory are independent, ergo memory and reasoning are often independent.

Independence between reasoning and memory characterizes adults under standard conditions: memory is tested after information has been presented (in the same session), but with a short buffer task interpolated between study and test (for an overview, see Reyna & Brainerd, 1995). Older preschoolers and kindergartners, however, have been shown to answer reasoning questions literally, that is, by reporting contents of verbatim memory. For example, told that “the bird is in the cage” and “the cage is under the table” young children reject inferences such as “the bird is under the table” because the experimenter “did not say that” (despite clear instructions and examples; Brainerd & Reyna, 1993). These answers to memory questions (what the experimenter said) and answers to inference questions are dependent in young children because children reject true inferences to the degree that they remember what was said. Rejecting a true inference is called a “verbatim-exit bias” because children exit processing as soon as they retrieve a verbatim memory for what was said. Around the same age, young children also reject abstract metaphorical interpretations in favor of more concrete or literal interpretations of sentences (Gentner, 1988; Reyna & Kiernan, 1995).

The verbatim-exit bias can be increased in young children by increasing their access to verbatim memories (Brainerd & Reyna, 1993; Reyna & Brainerd, 1995). For example, when pictures accompany and illustrate verbal sentences describing spatial relations (e.g., “The bird is in the cage” and “The cage is under the table”), verbatim memory improves. However, this improvement in verbatim memory augments the verbatim-exit bias in young children. In other words, when verbatim memory improves, rejection of true inferences (e.g., “The bird is under the table”) increases – although the task calls for inferences about meaning (and it can be demonstrated that young children have understood those meaning instructions). Increases in verbatim memory produce decreased acceptance of true inferences, which are rejected because they do not match the exact wording of presented sentences.

Interestingly, young children have a “verbatim-exit” bias despite having the competence to draw true inferences, and to distinguish those true inferences from false ones. After several questions (that reduce verbatim memory accessibility), asking the true inference question now elicits acceptance (Brainerd & Reyna, 1993). The same children who rejected true inferences when they could remember what was said, accept true inferences (but reject false statements) after some memory interference because they had the rudimentary competence to reason all along. Analogously, adults show ratio bias (e.g., prefer nine chances to win out of 100 over one chance to win out of ten) despite having the competence to compute ratios correctly; and they show conjunction fallacies despite having the competence to realize that feminist bank tellers are bank tellers (and therefore being a feminist bank teller could not be more likely than being a bank teller) (Reyna & Brainerd, 1994, 2008; Villejoubert, 2009).2

Even adults can reason literally, however, responding with the contents of verbatim memory in an unfamiliar or cognitively challenging domain, such as probability theory. For example, to the question “Imagine that we roll a fair, six-sided die 1000 times. Out of 1000 rolls, how many times do you think the die would come up even (2, 4, or 6)?” fully 9.7% of college students in one sample (N = 259) gave either 2, 4, or 6 as a response (Liberali et al., 2011). Numeracy (the ability to understand and use numbers) is composed of rote memories, such as retrieving memorized facts from multiplication tables, as well as appreciation of concepts such as ordinal magnitude (e.g., that.02%, 1%, and 11% are ordered from low to high) and procedural skills (Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999; Venkatraman, Soon, Chee, & Ansari, 2006). Procedural skills are about “knowing how” rather than “knowing that,” such as how to perform long division (i.e., retrieving a sequence of steps applied to diverse problem content, as opposed to retrieving specific multiplication facts) (Reyna, Nelson, Han, & Dieckmann, 2009; Siegler & Opfer, 2003).

Rote association or meaningful thought: the mind has cognitive options

An implication of this panoramic view of variability in types of processing is not simply that reasoning is variable or that people have different types of reasoning skills. Rather than select from a menu of cognitive options that varies haphazardly, people choose from either verbatim or gist representations, which then influences their information processing to be either rote or conceptual, respectively. The choice to use one type of representation or another is predictable, and derives from mechanisms tested using fuzzy-trace theory as a framework. The choice depends on: (a) development (more precisely, knowledge and experience in a domain, which correlates with age); (b) task (people can be instructed to provide verbatim responses or meaning-based responses); (c) materials (some materials are easy to remember verbatim, such as metaphors and pictures, others are hard); (d) delay (short delays between experience and use of information from that experience make verbatim memory an option, but long delays usually foreclose that option); and (e) developmental and individual differences in the ability to monitor cognition and inhibit responses that are inappropriate (e.g., to provide a verbatim response to a verbatim question and a gist response to a gist question; Reyna, 1995; Reyna & Kiernan, 1994).

For example, in developmental studies, children were presented with short sentences that imply inferences, such as “The diamond is in the box” and “The box is on the table,” which together imply that the diamond is on the table (Reyna & Kiernan, 1994). Some sentences implied pragmatic inferences, as in the aforementioned example. Other sentences implied logical inferences (e.g., “The ruby is larger than the emerald” and “The emerald is larger than the diamond” imply “The ruby is larger than the diamond”). In Experiment 1, six- and nine-year-olds were instructed to accept only verbatim sentences that were presented, and were explicitly told to reject true inferences, such as “The diamond is on the table.” (Naturally, instructions were conveyed using child-friendly language with examples.) Although older children were better at rejecting true inferences than younger children were (called “recollection rejection” in the memory literature), both age groups were able to significantly discriminate true presented from true unpresented sentences under verbatim instructions.

In Experiment 2, instructions were changed (Reyna & Kiernan, 1994). Children were told to accept both presented and other true, but unpresented, sentences, that is, to accept meaning-consistent sentences. Instructions to use gist, as opposed to verbatim, memories of sentences changed the pattern of responses on immediate tests, with older children better able to shift responses across experiments. (Subsequent mathematical models took advantage of this ability to shift responses across verbatim and gist instructional conditions; e.g., Brainerd, Reyna, & Estrada, 2006.) After a delay of a week after sentences were presented, responses in both experiments converged, with gist governing responses on both verbatim and gist tests. Thus, responses on “memory” tests reflected reasoning in that true inferences (but not false sentences) were endorsed after a delay almost as often as presented sentences.

These cognitive options of verbatim-based analysis and gist-based intuition blur the boundaries between memory and reasoning (Reyna & Mills, 2007b). Clearly, for young children and for adults under some circumstances, reasoning problems become rote memory problems, as also evidenced in non-productive thought in Gestalt theory (Luchins, 1942). However, when people use their memory for gist, including semantic and pragmatic inferences, to report their veridical experience, memory tests reflect reasoning. Schema theory and constructive memory theory do not adequately describe the gamut of memory performance because people use verbatim memory, too, which can produce opposite results from gist (or schematic) memory. Blanket generalizations that memory is schematic or constructive have been repeatedly falsified; predictions have failed (Alba & Hasher, 1983; Reyna & Kiernan, 1994, 1995). These results cannot be explained away by appealing to retrieval failure for stored memories. Verbatim and gist memories produce crossover interactions and other non-monotonic patterns that could not be produced with a single memory system.

Conversely, blanket generalizations that memory is based on rote associations (the old verbal learning tradition) have also failed repeatedly (e.g., activation-monitoring theory). Association theories (associations activated at study, at test, or both) cannot explain many fundamental findings, which are explained by fuzzy-trace theory’s gist (meaning) concept. To take a few examples, if associative activation were the correct account of memory, false memories would not be remembered over a delay (activated at study, they would fade like true memories); if instead gist were the basis of false memories, it makes sense that they would be retained over a delay. (“False” memories are memories for events that never happened, although they are often consistent with true inferences.) Study after study shows that false memories are retained over a delay (see Gallo, 2006). Further evidence against associative accounts (but favoring fuzzy-trace theory) includes: true and false memory do not correlate positively (which they would if they were both based on activation); testing true items does not increase acceptance of false-memory items (which it would if true and false memories were both based on activation); and sentences and narratives display huge false memory effects (although these sentence effects are clearly not based on word association).

Regarding the latter finding, it should be noted that the same mathematical models, which incorporate parameters for verbatim and gist representations, fit data for both words and sentences, supporting a unified fuzzy-trace theory account of both words and sentences (Brainerd et al., 2006). To be sure, association between words is correlated with meaning because words that are meaning-related tend to occur together in the same contexts, but to be “associated” merely means contiguity – that items occurred together (McEvoy, Nelson, & Komatsu, 1999). Again, rote association cannot account for all of memory and reasoning, despite valiant efforts to the contrary (Anderson, Budiu & Reder, 2001; Howe, 2008; Skinner, 1957). Instead, considering the evidence for and against mindless association, it appears that critics and supporters are both right: the same mind can toggle between verbatim-based analysis (rote association and memorized computations) and gist-based intuition (meaningful thinking that interprets information, and, as much as possible, reduces it to its essence) under theoretically predictable conditions.

Worked examples: reasoning about risks, probabilities, and consequences

Advantages of gist-based intuition: content and context dependence

Given that people enjoy cognitive options, it might seem obvious to some scholars that precise accuracy, as offered by verbatim-based analysis, would be preferable across a range of tasks. Indeed, standard dual-process perspectives place precise reasoning on a pedestal: emotion and other primitive influences are said to flatten out precise numerical distinctions, whereas an emphasis on calculation sharpens up those distinctions (Hsee & Rottenstreich, 2004; Hsee, Rottenstreich, & Xiao, 2005; Rivers, Reyna, & Mills, 2008). Similarly, a lack of precise distinctions among numbers, such as among probabilities or among outcomes (e.g., dollars to be gained), is thought to produce inferior decisions (Peters, Slovic, Vastfjall, & Mertz, 2008).

To other scholars, gist-based intuition seems the preferable choice for reasoning because it captures meaning and understanding. Empirically, as noted above, adults generally have a fuzzy processing preference for reasoning, which means that they rely on the lowest level of gist – the least precise representation – whenever that level can be used to accomplish a task, ratcheting up in precision until the task can be completed. Based on reviews of results from standard reasoning (e.g., Reyna & Brainerd, 1990, 1994, 1995) and judgment-and-decision-making tasks (Reyna & Farley, 2006), gist-based reasoning seems to offer global advantages (with important exceptions) in improving internal coherence and in achieving positive outcomes (e.g., better health outcomes; Reyna, 2008; Reyna & Adam, 2003).

A rose by any other name: when 20% is not 20% and $1 million is not $1 million

To understand how these salutary effects of gist-based intuition might be achieved, let us consider some examples. Suppose there is a 20% probability that an event will happen (strictly speaking, probabilities should be expressed as values from 0 to 1.0, but the % format is often used to better communicate magnitudes). Experts in the legal system and experts who study numeracy have advocated standardized interpretations of probabilities. What could be wrong with having a consistent definition of what 20% probability means? A number such as 20% probability might seem to have a straightforward definition as a “low” probability, well below even a 50% chance of the event happening. This definition would serve for the probability of rain, for example, and meteorologists have worked out such standardized mappings between numerical probabilities and words expressing probabilities.

Now, consider that 20% probability refers to the chance of an imminent heart attack (or myocardial infarction). Clinical practice guidelines in cardiology identify any probability greater than 15% as meriting immediate admission to a hospital, and label a probability of 20% as intermediate or high. A 20% chance of a heart attack is cause for alarm, but a 20% chance of rain would not even cause one to carry an umbrella. It is not just that the consequences differ in severity and, hence, that the decision threshold is lower for heart attacks (Reyna & Lloyd, 2006), but, rather, that the meaning of 20% differs starkly in the two examples: low versus high probability.

To take another example, suppose that the 20% probability referred to a woman’s lifetime risk of invasive breast cancer (the average woman has a risk of just over 12% in the US). Many women would consider a risk of 20% to be high, especially in contrast to 12% (Fagerlin, Zikmund-Fisher, & Ubel, 2005). One could say that this variability in interpretation, including sensitivity to reference points (such as 12% in this example), suggests that 20% has little meaning for people or that people do not really understand such numerical scales (e.g., Windschitl, 2002). In addition, the idea that probabilities are difficult to interpret in the abstract, without their outcomes, has been noted in the literature.

However, I argue a more fundamental point, that the essential meaning of 20% is not the same across content and context – and should not be interpreted as similar (Reyna, 2008). An effort to make the interpretation of 20% uniform misses the point. Even the most highly numerate person does not understand a number if he or she does not know whether that number is low or high in the gist sense (Hans & Reyna, 2011; Reyna & Hamilton, 2001). Informed consent is not informed if the patient can regurgitate probabilities, but fails to grasp their meaning. In other words, patients who do not know whether their risk is low or high cannot give informed consent. As Reyna and Hamilton (2001) pointed out, informed consent hinges on appreciating categorical and ordinal distinctions: between no risk versus some risk or between low risk versus high risk. Numeracy, as it is currently measured, is necessary but not sufficient for understanding the gist of numbers (Reyna et al., 2009). In short, the effects of content and context are not contaminations of true meaning, but, rather, required for true meaning.

Note that the hypotheses described here differ sharply from the arguments put forth by Gigerenzer, Todd and the ABC group (1999). To begin with, fuzzy-trace theory is grounded mainly in experimental tests of predictions as opposed to evolutionary arguments (for reviews, see Reyna, 2008; Reyna & Brainerd, 1995, 2011). In addition, gist is processed when the content of judgments or decisions is familiar and when working memory load is low, in contrast to fast-and-frugal approaches (which assume that fast-and-frugal approaches are triggered when content is unfamiliar, as in the recognition heuristic, or when working memory is taxed). Results demonstrating working memory independence, and subsequent data showing dependence under predictable conditions, contradict the rationale for “fast and frugal” processing. Yet another important difference is that, unlike fast-and-frugal approaches, gist is not simply processing less information. Gist involves meaning – integrating dimensions of information to distill its essence, not just processing fewer dimensions of information that are “good enough.”

Beginning processing with categorical and ordinal gist

Fuzzy-trace theory predicts that decision makers begin with all-or-none categorical distinctions, the simplest gist, and then move on to finer distinctions if categorical distinctions do not get the job done. For probabilities, these are nominal-scale distinctions between no risk and some risk, zero probability and some probability, or certain and uncertain. For outcomes, such as dollars, these distinctions are no money and some money or a little money and a lot of money. Initially, the reasoner decides which probabilities or outcomes are categorically similar or categorically different. (If the quantities are categorically similar, reasoners move on to ordinal distinctions, such as low versus high.) The key feature of the gist representation is that it reflects qualitative differences, as opposed to quantitative differences. At the same time, in parallel, the verbatim-based analysis of the literal numbers is performed, which captures their quantitative nuances. Thus, in fuzzy-trace theory, it is not the case that reasoners do not process quantities such as expected value (e.g., an option that has a 50% probability of winning $2 million has an expected value of $1 million). Verbatim-based analysis and gist-based intuition unfold in parallel (for details about predictions, critical tests, and mathematical models, see Kuhberger & Tanner, 2010; Reyna & Brainerd, 1991, 1995, 2011).

Therefore, faced with two options that are equal in expected value, $1 million for sure versus a 50% probability of winning $2 million (50% chance of winning nothing), decisions pivot on categorical distinctions between some money (sure thing) versus none (gamble) or between a lot of money (sure thing) versus none (gamble). The fact that the gamble can turn out one of two qualitatively different ways is what matters, and one of these categorical possibilities compares unfavorably with the categorical win of “some” money in the sure thing (i.e., winning some money is better than taking a chance on winning none). The other categorical possibility in the gamble – winning something – offers no advantage over the sure thing (which also involves winning something, equivalent from a categorical perspective).

Similar arguments have been made regarding playing Russian roulette for a great deal of money (e.g., Would you play Russian roulette, with one bullet inserted in a six-chambered gun, for $1 million?). The quantities of money or number of chambers in the gun are immaterial, compared to the qualitative possibility of death (Reyna, Adam, Poirier, LeCroy, & Brainerd, 2005; Reyna & Farley, 2006). Another example of the preeminence of qualitative gist involves risking exposure to the human immunodeficiency virus (HIV) – unprotected sex involves a quantitatively tiny probability of contracting HIV in most populations, but this unlikely outcome is a qualitatively life-altering possibility (Reyna, 2004; Reyna & Farley, 2006). In each of these examples, making a good decision involves having insight into the bottom-line gist of the information (just as understanding whether 20% is low or high involves insight), in contrast to mental shortcuts or fast-and-frugal processing.

Now, consider a decision between winning $1 million for sure versus a gamble with an 89% chance of winning $1 million, 10% chance of winning $5 million, and a 1% chance of winning nothing (the Allais paradox; List & Haigh, 2005; Reyna & Brainerd, 2011). Most adults prefer the sure million dollars. However, unlike the decision above about $1 million dollars, this problem does not involve equal expected values. Verbatim-based analysis would divulge that the expected value of the gamble ($1,390,000) is higher than the expected value of the sure thing ($1,000,000). Highly numerate reasoners can calculate these quantities, but even children as young as four and five years old roughly estimate expected value, when clear instructions and external memory stores are provided (Reyna & Ellis, 1994; Schlottmann & Anderson, 1994). Despite being able to compute lower expected value, most adults prefer the quantitatively inferior sure option (inferior as measured by expected value).

When the two options are expressed as gambles, 11% chance of $1 million versus 10% chance of $5 million, most people prefer the gamble with $5 million. So, it is not as though a difference of $390,000 dollars does not matter to them! According to fuzzy-trace theory, people prefer the sure option as opposed to the possibility of nothing, despite the fact that many realize that the probability of nothing is very small and the differences in expected value favor the gamble. However, the qualitative difference between a “whole lot of money” versus nothing cuts through the quantitative details, favoring the sure thing. It seems smart to treat $1 million differently in the two problems, although the exact magnitude – $1 million – is identical. In fact, Frederick (2005) has shown that even people who score higher on the Cognitive Reflection Test make decisions about risk that defy quantitative analysis, but make sense at a qualitative level (e.g., a 75% chance of $200, with an expected value of $150, is frequently rejected in favor of a sure $100).

The tendency to be biased by context and content grows from childhood to adulthood. Hence, children are more likely to treat probabilities – 20% – and outcomes – $1 million – literally (though numbers smaller than $1 million are used in studies with children; Reyna, 1996a, 1996b). For example, young children are not as influenced as adults are by objectively identical framing of information; their preferences do not shift if given four toys from which two toys are then subtracted (treated as a loss by older children and adults) compared to simply being given two toys (a gain) (Reyna & Ellis, 1994; Reyna, Estrada et al., 2011). To take another example, children are less biased than adults are by the context of other, semantically related words on a list; they are less likely to connect the dots among the list words and falsely remember a meaning-related but never-presented word (e.g., Brainerd, Reyna, & Zember, 2011).

Public health decisions and surgical decisions often have content that is similar to the hypothetical risk decisions I have discussed. HIV prevention has already been mentioned; adolescents are more likely to approach unprotected sex and other risks as a numbers game, favoring risk taking because most bad consequences are objectively low in probability (e.g., contracting HIV; Mills et al., 2008; Reyna, Estrada et al., 2011). Indeed, a review of the literature in 2006 showed that, in just about all of the studies measuring perceptions of risks and benefits, these perceptions predicted adolescent risk taking – even though the perceived risks were often overestimates (Reyna & Farley, 2006; see also Reyna & Adam, 2003). Adults, however, were more likely to make all-or-none categorical distinctions about risks, and they engaged in less risk taking. In a recent study comparing adolescents and young adults using a variety of separate measures of verbatim-based analysis and gist-based intuition, Reyna, Estrada et al. (2011) found that gist-based intuition was consistently associated with reductions in unhealthy risk taking (and verbatim-based analysis predicted greater unhealthy risk taking; see also Mills et al., 2008).

Monitoring and inhibition: cognitive control

It is important to acknowledge that impulsivity (or lack of monitoring and inhibition) also accounts for some reasoning errors and for some unhealthy risk taking (Casey et al., 2008; Reyna, Estrada et al., 2011; Steinberg et al., 2008). However, the effects of mental representations and associated processing differ from the effects of impulsivity (Reyna & Rivers, 2008). Impulsivity declines with age, although individual differences remain in adulthood (Eigsti et al., 2006). Cognitive control, which restrains impulsivity, has a narrow and a broad interpretation. Narrowly, cognitive control refers to behavioral inhibition and self-control, sometimes using “cold” cognitive strategies such as distraction (Metcalfe & Mischel, 1999). Broadly, cognitive control refers to self-regulation through reinterpretation of emotional stimuli and other cognitive strategies that create new meanings (Ochsner & Gross, 2005); the latter involves gist-based intuition. In this chapter, I refer mainly to the narrow interpretation of cognitive control, which is distinct from gist-based intuition.

Monitoring and inhibition produce effects that are difficult to understand in a simple dual-process framework; a third monitoring and inhibition process is needed that can act on verbatim or gist representations in order to account for results (Reyna & Brainerd, 1998; Reyna & Rivers, 2008). For example, Stanovich and West (2008) summarized a number of studies on framing effects showing that framing effects were not related to intelligence or cognitive ability (e.g., SAT scores) when superficially different but quantitatively equivalent frames were presented between subjects, but they were related when framing problems were presented within subjects. Using a between-subjects manipulation of framing, Stanovich and West compared choices for the positive (gain) and negative (loss) versions of problems (see note 1). The gain and loss groups chose from among six responses, varying from strongly favoring the sure option to strongly favoring the risky option (the gamble).

Stanovich and West found that both subjects with high SAT scores and those with low SAT scores showed framing effects: the risky option (gamble) was more highly favored in the loss than in the gain condition, but the interaction between gain-loss and high-low SAT scoring groups was not significant. If anything, contrary to traditional theories, high-SAT scorers had a slightly greater framing effect (even greater risk preference for losses). However, when the same subjects receive both gain and loss versions of the framing problem (i.e., within-subjects framing), those with high intelligence (and high need for cognition) notice the relation between the gain and loss versions of the framing problem, and censor their responses to make them more consistent, reducing framing differences (e.g., Frederick, 2005).

According to fuzzy-trace theory, between-subjects framing effects are the result of gist-based intuition when expected values are equal (sure vs. gamble options differ categorically, as described above). Verbatim-based analysis yields indifference (because expected values are equal or close to it), and, thus, categorical gist representations rule preferences (for critical tests of this framing account, as examples, see Kuhberger & Tanner, 2010; Reyna & Brainerd, 1991, 1995). In other words, the account of framing provided earlier, that begins with categorical gist, applies.

In contrast, the within-subjects’ framing effect is related to monitoring and inhibition: results suggest that some subjects monitor the problems, detect that they are versions of the same problem, and inhibit inconsistent answers (Kahneman, 2003; Stanovich & West, 2008). Thus, subjects who show less of a framing effect within subjects due to monitoring and inhibition can still show a framing bias between subjects due to gist-based intuition, especially when expected values are equal (i.e., strong preference for the sure thing in the gain frame and for the gamble in the loss frame). Because within- and between-subject framing effects are governed by different mechanisms, the results are not truly inconsistent with one another. Subjects who monitor and inhibit also seem to be more likely to spontaneously translate positive quantities into equivalent negative ones (and vice versa; translate 20% errors into 80% correct) (Peters et al., 2006). They are also more likely to notice when expected values are unequal and shift to responses with higher expected values (Frederick, 2005; Reyna & Brainerd, 1995). Although these processes, such as analysis, intuition, and monitoring/inhibition, can be distinguished experimentally and in mathematical models, naturally, multiple processes are ordinarily in play during reasoning (Reyna & Brainerd, 2008; Reyna & Mills, 2007a).

Class-inclusion confusion: gist representations and combining judgments about classes

In fuzzy-trace theory, class-inclusion reasoning includes logical reasoning involving quantifiers such as all or some, conjunction and disjunction fallacies in probability judgments, conditional probability judgments (and base-rate neglect which is a special case of such judgments), and the classic Piagetian class-inclusions task (e.g., there are seven cows and three horses; are there more cows or more animals?; Reyna, 1991; Winer, 1980). For example, up to the advanced age of about ten years old, children are likely to respond that there are more cows than animals when presented with the Piagetian class-inclusion task. The task is referred to as “class inclusion” because the class of cows is included in the class of animals (children actually count the ten animals and the seven cows correctly prior to giving the erroneous class-inclusion response that cows are more numerous than animals). Adults monitor and inhibit these classic class-inclusion responses; their response times to provide the correct response are protracted, reflecting inhibition of the wrong answer.

According to fuzzy-trace theory, base-rate neglect is also a “class-inclusion” task, with similar pitfalls involving confusion about overlapping classes, because some conditional probabilities (e.g., the accuracy of a diagnostic test for patients with a disease) are classes of events that are included in the base rate (e.g., the patients with the disease). For example, suppose that the base rate of a disease in the population is 10% and the diagnostic medical test for that disease is 80% accurate (i.e., an 80% chance of a “positive” result if the patient does have the disease; an 80% “negative” result if the patient does not have the disease). If a patient has a positive test result, how likely is it that he or she has the disease; is it closer to 30% or to 70% (Reyna, 2004). Surprisingly, the correct answer is 30%.

The low base rate of 10% is said to be “neglected” because most people choose the higher probability of 70% (conversely, a high base rate tends to be neglected given a negative test result; Reyna & Brainerd, 2008). In the base-rate problem above, the conditional probability of around 30% refers to people with the disease who also have a positive test result, which is included in the class of people with a positive test result. Because only 10% of the population has the disease, even if they are all accurately diagnosed, even more people without the disease receive a positive test result than those with the disease (remember that the test has a 20% error rate). The problem is not lack of medical training or low intelligence: only 31% of doctors (N = 82) selected the correct answer, significantly below chance, despite making these kinds of diagnostic judgments routinely (Reyna & Adam, 2003). Among adolescents (N = 258) with no medical training, 33% chose the correct response. Developmentally, class-inclusion confusion about overlapping classes (e.g., about keeping straight which probabilities refer to which subsets of other probabilities) remains a problem for reasoners into adulthood (Reyna et al., 2003).

Any reasoning about relations between classes is subject to confusion brought on by losing track of reference classes, a problem that is not attributable to working memory limitations or conceptual deficits in logical or probabilistic reasoning (e.g., Reyna & Brainerd, 1994). As noted earlier, class-inclusion reasoning is difficult owing to processing interference – people lose track of the reference class (denominator) as they reason about focal classes (numerators).

For example, the denominator for the probability of A given B is the probability of B, whereas the denominator for the probability of B given A is the probability of A. People confuse the two conditional probabilities with one another, called conversion errors, because they forget that the denominators are not the same, and focus instead on the joint probability (probability of A and B), which is in the numerator of both conditional probabilities. They “forget” or neglect denominators because they become confused by overlapping and nested classes (Reyna, 2004).

People generate estimates of probabilities from two kinds of representations: their experiences with frequencies of events (verbatim memories) and their semantic and pragmatic gist. The gist integrates semantic knowledge, stereotypes, beliefs about causation, and implicit theories of events (building on distinctions between prototype vs. exemplar models and between the intension vs. extension of a set; Reyna & Brainerd, 1991, 1992). Although people have debated whether humans are frequentists (probabilities are derived from experience) or Bayesians (probabilities are derived from beliefs), psychologically, people are both. The rationale for these distinct components of perceived likelihood lies in theoretical distinctions about memory representations.

For example, people estimate their probability of having a sexually transmitted disease by drawing on their memories for their own risky behaviors (e.g., Bruine de Bruin, Downs, Murray, & Fischhoff, 2010; Mills et al., 2008; Reyna, Estrada et al., 2011). They then give very different estimates when prompted to base their estimates on gist, such as beliefs about their level of risk. Biases and fallacies can be generated when gist representations of the probability of events replace, or are combined with, verbatim estimates of the probability of events, that is, experience (Brainerd, Reyna, & Aydin, 2012; Reyna & Mills, 2007a). Gist representations can violate coherence because they represent intensions or prototypes, rather than being subject to the constraints of extension or exemplar frequencies (Tversky & Kahneman, 1983). So, a woman who fits the stereotype of a feminist can be judged as more likely to be a feminist bank teller than a bank teller (a conjunction fallacy) because the gist of her description fits the former better than the latter. Stories do not have denominators.

Reminders about the subset relation between feminist bank tellers and bank tellers, however, reduce conjunction fallacies (Wolfe & Reyna, 2010). For example, as predicted, it reduces fallacies to remind people that this relationship between feminists and bank tellers is like the relationship between being left-handed and being a Republican. Also as predicted, monitoring and inhibition of fallacies are especially successful in the presence of cognitive prosthetics that allow classes to be kept straight, such as Venn diagrams or 2 x 2 contingency tables that represent classes discretely (e.g., Reyna, 1991; Wolfe & Reyna, 2010). Table 9.1 provides an example of how a subject might fill in such a 2 x 2 table. Symbolically, those discrete classes are the probability of A and B, probability of A and not B, probability of B and not A, and probability of neither A nor B.

Table 9.1 Hypothetical probability judgments using a 2 x 2 table: subjects enter all judgments

Feminist–Yes Feminist–No

Bank teller–Yes 19% 1% 20%
Bank teller–No 50% 30% 80%
69% 31% 100%

Note: The probability that Linda is a feminist bank teller is 19% (conjunctive probability). The probability that Linda is a feminist or a bank teller is 50% + 19% + 1% = 70% (disjunctive probability). The probability that Linda is a feminist assuming that she is a bank teller is 19/20% = 95% (conditional probability). The probability that Linda is a bank teller assuming that she is a feminist is 19/69% = 27% (conditional probability).

More generally, if people recognize the semantic gist of class relations, they can simplify their judgments and improve their coherence (Lloyd & Reyna, 2001; Reyna, Lloyd, & Whalen, 2001; Wolfe & Reyna, 2010). For example, having the genetic mutation for Huntington’s disease means that one will develop the disease, and vice versa (Reyna, Brainerd, Effken, Bootzin, & Lloyd, 2001). Therefore, the conditional probability of developing the disease given the mutation is 1.0 (and vice versa), the conjunctive probability is equal to the disjunctive probability, and the probabilities of having the disease without the mutation or the mutation without developing the disease are zero. The semantic relation is essentially one of identity (analogous to the relation between H2O and water). Reminding people that an identity relation between classes is “like the relationship between H2O and water” improves their performance; fallacies decline significantly (e.g., Wolfe & Reyna, 2010), although not as much as discretely representing classes.

As discussed, the relation between feminist bank tellers and bank tellers (or between cows and animals) is one of subset (or subclass) relations (Reyna, 1991). Gricean pragmatic explanations that people do not interpret these relations as subsets account for little variance when tested empirically (Brainerd & Reyna, 1990; Reyna, 1991; Reyna & Brainerd, 1991; Wolfe & Reyna, 2010). People lose track of the semantic relations and reminders (semantic analogies) are helpful. For example, having the gene for hemochromatosis (which causes excess accumulation of iron) does not necessarily mean that one will develop the disease; however, if one has the disease, one has the gene. The relation between the disease of hemochromatosis and having this gene is a subset relation, analogous to the relation between roses and flowers. Thus, the probability of having the disease (being a rose), but not having the gene (not being a flower), is zero, somewhat simplifying reasoning about probabilities. Finally, most patients with the BRCA gene develop breast cancer (the probability is not 1.0), but most patients with breast cancer do not have the BRCA gene. According to fuzzy-trace theory, therefore, the latter partially overlapping sets of relations (analogous to being a feminist and a bank teller) are the most confusing, and denominators are easily neglected.

In each of these examples – identical sets, subsets, and partially overlapping sets – categorical distinctions, not quantitative nuances, allow reasoning to be simplified. For example, if physical displays (e.g., pictures of seven cows and three horses) are removed, and children are forced to rely on their gist memory for the problem facts, their reasoning performance improves. They are more likely to apply the gist that cows are animals rather than the (irrelevant) verbatim details that there are seven cows and three horses (Brainerd & Reyna, 1990, 1995). These results illustrate that reductions in fallacies (e.g., with age) need not depend on conscious or unconscious monitoring of reasoning (De Neys, 2012; De Neys & Vanderputte, 2011), but, rather, on the interplay of parallel representations – which simultaneously produces increases in gist-based biases, such as conjunction fallacies, with age (e.g., Morsanyi & Handley, 2008; Reyna & Ellis, 1994; Reyna & Farley, 2006).

With respect to class-inclusion reasoning, theoretically significant factors have been actively manipulated in order to test causal mechanisms originating in fuzzytrace theory (e.g., Garcia-Retamero, Galesic, & Gigerenzer, 2010; Reyna, 1991; Wolfe & Reyna, 2010). These factors have included set relations (e.g., subset vs. overlapping relations), tagging of sets to separate classes (and hence reduce class-inclusion confusion), Venn diagrams, 2 x 2 tables (reasoners fill in the four cells with their own probability estimates, but the key is keeping classes distinct), and retrieval manipulations that cue reasoning principles. In critical experimental tests, frequency per se has not been shown to reduce fallacies (e.g., Barbey & Sloman, 2007; Reyna & Brainerd, 2008; Sloman, Over, Slovak, & Stibel, 2003). Frequencies seem to be helpful because they are confounded with external representations that discretely represent classes, thereby reducing the class-inclusion confusion predicted by fuzzy-trace theory. These external representations of discrete classes work equally well with probabilities and with frequencies to reduce errors such as conjunction fallacies, disjunction fallacies, conversion (or inversion) errors, and base-rate neglect (e.g., Lloyd & Reyna, 2001; Wolfe & Reyna, 2010; see Table 9.1).

However, three concepts must be distinguished: knowing and understanding a reasoning principle – competence; retrieving a reasoning principle when it is relevant (i.e., reasoning is cue-dependent); and being able to implement the principle successfully (Reyna & Adam, 2003). Although people’s behaviors contradict logical rules and constraints of probability theory (e.g., additivity of complementary probabilities or constraints on conjunctions or disjunctions of probabilities), they generally know and understand those rules and constraints. Studies separating competence, retrieval, and processing when people commit reasoning fallacies (e.g., Brainerd & Reyna, 1990, 1995) showed that people typically appreciate the qualitative implications of formal rules and constraints, despite violating them.

For example, people know and understand the conjunction rule, and can apply it reliably in many contexts (and its application is typically not conscious and deliberate; Reyna, 1991; Reyna & Mills, 2007a, 2007b). (The conjunction rule is simply that a conjunction of events cannot be more numerous or more probable than its constituent events.) Such reasoning competence could be called “logical” competence, but that is a misnomer in fuzzy-trace theory if it implies a content-free, explicit process. This competence involves intuitive (qualitative) understanding of principles that apply to mental representations of content; for example, knowing that greater frequency of occurrence implies greater probability (all other factors equal) or that subsets must be less numerous or less probable than sets to which they belong (assuming they are proper subsets). This intuitive competence is often present early in development, usually after initiation of formal schooling (around six years old in the US), although the knowledge is probably obtained from formal and informal sources.

Conclusions and overview

Intuition and impulsivity have long been juxtaposed with logic and conscious deliberation – the fast and slow processes of thought. For many scholars, only the slow and explicit kind of thinking has counted as reasoning. The most advanced reasoning was devoid of content, emulating formal logic or abstract algebraic structures (although some scholars have argued against pure formalism; Johnson-Laird, 2010). Slow thought allowed for deliberation. The appeal of methods such as verbal protocol analysis rested on this assumption that advanced knowledge was deliberate (i.e., conscious). In contrast, intuition was considered the province of childhood and the source of beguiling biases and fallacies that lingered as vestiges of childhood in adulthood.

Recently, the dichotomy between intuition and logic has been challenged, and some scholars have attempted to bring intuition and logic together in an uneasy alliance, with concepts such as explicit logical intuition or advanced System 1 automated reasoning (e.g., De Neys, 2012; Stanovich, West, & Toplak, 2011; Villejoubert, 2011). These efforts acknowledge shortcomings of standard dual processes. However, they do not account for the range of results about reasoning.

In fuzzy-trace theory, advanced reasoning resembles the intuitive process of understanding poetry more than it resembles engaging in formal logic or performing computations (Reyna & Brainerd, 1995, 2011). That is, intuition is the cornerstone of adult thought, capturing the meaningful gist of information, and operating in parallel with verbatim-based analysis. Content and context bias gist-based reasoning, as in framing effects, but these variations in interpretation often reflect insight borne out of experience.

A third set of processes monitors performance, looking for inconsistencies and inhibiting impulses. This third set of processes can be shown to be distinct from gist-based intuition and from verbatim-based analysis. Experimental techniques and mathematical models have been used to demonstrate that biases and fallacies occur despite reasoning competence, that gist-based biases increase with development, and that monitoring and inhibition simultaneously increase with development. These results show that intuition is not impulsivity, and explain how gist-based intuition supports healthy decision making.


1 Framing effects occur when preferences for the same option shift depending on wording. For example, imagine that 600 people are expected to die from a disease. In the “gain” frame, option A saves 200 people’s lives for sure, but option B offers a one-third probability of saving 600 people and a two-thirds probability of saving no one. In the loss frame, 400 people die for sure if option C is chosen, but option D offers a two-thirds probability of 600 people dying and a one-third probability of no one dying. For adults, preferences typically shift from preferring the sure option in the gain frame to preferring the risky option in the loss frame (Tversky & Kahneman, 1981; for framing effects in children, see Reyna & Ellis, 1994; for comparisons of adolescents’ and adults’ framing effects, see Reyna, Estrada et al., 2011).

2 Conjunction fallacies are defined as judging a conjunction of events as more probable than one or both events; for example, judging Linda to be more likely to be a feminist bank teller than a bank letter given the following description: “Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations” (Tversky & Kahneman, 1983).


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