CommentarylStanovich & West: Individual differences in reasoning The questionable utility of "cognitive ability" in explaining cognitive illusions

The nation of "cognitive ability" leads to paradoxical condusions when invoked to explain Inhelder and Piaget's research on dass indusion reasoning and research on the indusion rule in the heuristics-andbiases program. The vague distinction between associative and rule-based reasoning overlooks the human capacity for semantic and pragmatic inferences, and consequently, makes intelligent inferences look like reasoning eITors. \Vhy do most undergraduates appear to get the Linda problem wrong~ After all. this problem is meant to instantiate the inclusion rule, "perhaps the simplest and most fundamental principle of probability. ... If A indudes B then the probability of B cannot exceed the probability of A" (Kahneman & Tversky 1996, p. 58.5). Stano\ich & West (S&W) (l998b, p. 307) argue tlmt although the problem tests reasoning in accord with a simple rule, "correct responding on the Lnda problem ... is associated with higher cognitive ability." The finding that higher SAT scores are correlated with indusion responses in the Linda problem is a flagship exampie of their more general daim that there are two reasoning systems, one associative and the other rule-based, and that students with higher cognitive ability are more likely to give rule-based responses. In what folIows, 1 demonstrate that S&W's use of cogniti\e ability to e:-:plain violations of the indusion rule, when viewed in light of other findings on reasoning about dass indusion, gives rise to paradoxical condusions. Is the cognitive ability o( eight-year-olds higher than that o( undergraduates? In their dassie book The early growth of logic i1l the duld, Inhelder and Piaget (1964, p. 101) reported an experiment in wruch they showed fiveto ten-year-old children 20 pictures, four representing colored objects and 16 representing flowers. Eight of the 16 flO\vers were primulas, four yellow and four of other calors. The children were asked a list of questions about dass indusion relations, one of wruch was: "Are there more flowers or more primulas?" Only 47% of the fiveto seven-yearolds ga\'e answers in accord \vith dass indusion, tllat is, which reflected an understanding that the flowers were more numerous than the primulas. Among eight-year-olds, however, a majority (829'0) gave responses consiste~t \vith dass indusion. Inhelder and 678 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:5 Piaget (1964) conduded that "this kind of thinking is not peculiar. to professional logicians since the children themselves apply it with confidence when they reach the operationalleveI:' (p. 117). A couple of decades later, Tversky and Kahneman (1983) gave undergraduates at universities such as Stanford the description of aperson, Linda, and asked tllem to rank statements about Linda according to theirprobability. Among them were Linda "is a bank teller" (T) and "is a bank teller and is active in the feminist movement" (T&F). Only 11% of the adult participants ranked T as more probable than T&F, although T&F is induded in T. Here we encounter the puzzle. The Linda problem is analogous to the flowerproblem in that both represent an indusion relation (Reyna 1991, p. 319). Why, then, do children as young as eight (or nine and ten; Inhelder and Piaget were probably too optimistic about the onset ofdass-indusion reasoning; Reyna 1991) follow dass indusion, while undergraduates do not? To the extent that "correct" , responding in indusion problems is associated \vith higher cognitive ability, as S&\V's account suggests, we ought to condude that eight-year olds have higher cognitive ability than Stanford undergraduates. Not according to Piaget's theor)' of cognitive development, or for that matter, according to probably any other theory of cognitive development, much less according to common sense: concrete-operational children should trail far behind the undergraduates, who have reached the highest state of cognitive ability, the formal-operatonal stage. Is the cognitive ability o( second graders higher than that o( sixth graders? Perhaps the cognitive ability explanation would lead to less paradoxieal condusions if applied only to studies using the Linda and similar problems. In a pertinent study, Daviclson (1995) gave second, fourth, and sixth graders problems such as the Mrs. Hill problem. Mrs: Hili "is not in the best health and she has to wear glasses to see. Her hair is gray and she has wrinkles. She walks kind of hunched over." Then, tlle children were asked to judge how likely Mrs. Hili was to have various occupations, such as Mrs. Hili is "an old person who has grandchildren," and "an old person who has grandchildren and is a waitress at a 10cal restaurant." In Davidson's study, second graders gave more dass indusion responses than sixth graders (6.5% vs. 43%). Why? If "correct" responding in Linda-type problems is in fact associated with higher cogllitive ability, then we ought to condude that second graders have higher cognitive ability than sixth graders. Again, on any account of cognitive development and common sense, this condusion is implausible. Ironically, Davidson (199.5) interpreted the finding as evidence that children \vith higher cognitive ability (older children) are more Iikely to use the representativeness heuristic than children \Vitll lower cognitive ability (younger children). Yet tlle representativeness heuristic seems to epitomize what S&W refer to as the associative system, and thus its use should be correlated \vith lower cognitive ability. , Why do people violate the principle o( class inclusion in the Linda problem? Is there a way out ofthese paradoxes? In myview, notions such as "cognitive ability," which explain everything and nothing, will not be of much help to us in understanding people's reasoning abilities; nor will "dual-process tlleories of reasoning," unless underlying cognitive processes are cle<lfly specilled (for a critique of such theories, see Gigerenzer & Regier 1996). Problems such as Linda, tlle cab problem, and tlle standard Wason selection task are inherently anlbiguous (e.g., Birnbaum 1983; tIilton 1995). The Linda problem, for instance, is not a mere instantiation of the indusion rule. It is laden \vitll the ambiguity of natural language. Take the word "probability." In probabilistic reasoning studies, "probability" is typically assumed to be immediately translatable into mathematical probability. From its conception, however, "probability" has had more than one meaning (e.g., Shapiro 1983), and many of its meanings in contemporary natural language have little, if anything, to do \vitll mathematical probability (see Hertwig & Gigerenzer 1999). Faced \vith multiple possible meanings, participants must infer what experimenters mean when they use the term in problems such as Lnda. Not surprisingly, participants usually infer nonmathematical meanings (e.g., Commentary/Stanovich & West: Individual differences in reasoning possibility, believability, credibility) because the Linda problem is constructed so that the conversational maum of relevance renders the mathematical interpretation of "probability" implausible (Hertwig & Gigerenzer 1999). The failure to recognize the human capability for semantic and pragmatic inferences, still unmatched by any computerprogram, can lead researchers to misdassifY such intelligent inferences as reasoning elTors. In contrast to the probability instruction in the Linda problem, Inhelder and Piaget asked children whether there are "more flO\vers or more primulas." "More" refers directly to numerosity and does not leave open as many possible interpretations as the semantically ambiguous term "probability." Similarly, asking for "frequency" judgments in the Linda problem avoids the ambiguity of "probability" by narrowing down the spectrum of possible interpretations. This is a crucial reason why frequency representations can make conjunction effects disappear (Hertwig & Gigerenzer 1999; for another key reason, namely, the response mode, see Hertwig & Chase 1998). In sum, Stanovich & West present the Linda problem as support for their thesis that higher cognitive ability underlies COlTect judgments in reasoning tasks. Whether applied to research by Inhelder and Piaget or to research \\ithin the tradition of the heuristics-and-biases program, however, the notion of"cognith'e ability" gives rise to paradoxical conclusions. Rather than resort to ilI-specified terms and vague dichotomies, we need to analyze cognitive processes for instance, application of Gricean norms of conversation to the task of interpreting semantically ambiguous terms which underlie people's understanding of the ambiguous reasoning tasks. Otherwise, intelligent inferences \\ill continue to be mistaken for reasoning elTors.