H. Markovits ExperimentalP & W. © sychology 2007 Schroyens: Hogrefe 2007; Curious & Vol. Huber 54(1):38–43 Belief-Bias Publishers
A Curious Belief-Bias Effect Reasoning with False Premises and Inhibition of Real-Life Information Henry Markovits1 and Walter Schroyens2 1
Université du Québec à Montréal, Canada, 2University of Leuven, Belgium
Abstract. Many studies have shown that inferential behavior is strongly affected by access to real-life information about premises. However, it is also true that both children and adults can often make logically appropriate inferences that lead to empirically unbelievable conclusions. One way of reconciling these is to suppose that logical instructions allow inhibition of information about premises that would otherwise be retrieved during reasoning. On the basis of this idea, we hypothesized that it should be easier to endorse an empirically false conclusion on the basis of clearly false premises than on the basis of relatively believable premises. Two studies are presented that support this hypothesis. Keywords: reasoning, inference, belief
One of the more compelling conclusions of many of the studies that have looked at reasoning is the very strong effect that specific content has on the kinds of inferences that are made from what are formally identical inferential problems (e.g., Cummins, 1995; Cummins, Lubart, Alksnis, & Rist, 1991; De Neys, Schaeken, & d’Ydewalle, 2002; Janveau-Brennan & Markovits, 1999; Markovits, Fleury, Quinn, & Venet, 1998; Markovits & Quinn, 2002; Markovits & Vachon, 1990; Thompson, 2000). These results suggest that one important factor in understanding reasoning is the strong tendency to use existing knowledge about premises when making inferences. Although the specific formulation varies (Cummins, 1995; Markovits & Barrouillet, 2002; Oaksford, Chater, & Larkin, 2000; Thompson, 2000), it is clear that reasoning with concrete premises often involves active use of existing information about the premises used in reasoning. However, there is one important form of “logical” reasoning that cannot be easily accounted for solely by any such mechanism. Specifically, reasoning with false premises under the explicit logical instruction to “suppose that the premises are true” allows both adolescents and adults to often arrive at inferences that are at odds with their empirical knowledge. It is true that, in many instances, both children (Dias & Harris, 1988, 1990; Hawkins, Pea, Glick, & Scribner, 1984) and adults (George, 1995, 1997) make such inferences in a way that is consistent with the use of empirical knowledge, that is, they will often fail to make a logical inference when the premises are not empirically believable. A related effect is the tendency to accept or reject a possible conclusion on the basis of its believability (e.g., Evans, Barston, & Pollard, 1983; Markovits & Nantel, 1989; Oakhill & Johnson-Laird, 1985). However, it is also Experimental Psychology 2007; Vol. 54(1):38–43 DOI 10.1027/1618-3169.54.1.38
true that, with appropriate instructions, both children and adults can often make logical inferences that lead to empirically unbelievable conclusions (Leevers & Harris, 1999; Markovits & Bouffard-Bouchard, 1992; Markovits & Vachon, 1989; Vadeboncoeur & Markovits, 1999). In this case, a mechanism that relies on processes different from retrieval of knowledge about premises (or potential conclusions) can be used to understand how this kind of reasoning is possible. One hypothesis about how logical instructions are translated into inferential performance is that logical instructions to accept what are clearly false premises trigger inhibitory mechanisms that allow the reasoner to block retrieval of information that might normally be activated by the content of reasoning (Markovits & Barrouillet, 2002). There is, in fact, evidence that this is the case when reasoning with empirically false premises (Handley, Capon, Beveridge, Dennis, & Evans, 2004; Markovits & Doyon, 2004; Simoneau & Markovits, 2003). What an inhibitory model suggests is that when a reasoner is given a premise of the form “If P then Q,” for which there is information stored in long-term memory that Q is not a necessary consequence of P (i.e., cases of P and not-Q), logical instructions are used to inhibit retrieval of these cases in order to allow the reasoning process to rely solely on the presented premises. Failure to inhibit this kind of information will result in a tendency to use this information and produce responses that are empirically believable but logically inappropriate. A model of this kind can reconcile the clear tendency to rely on empirical knowledge about premises with the ability of children and adults to make logical inferences that contradict this knowledge. In the following we examine an interesting prediction that follows from this model. © 2007 Hogrefe & Huber Publishers
H. Markovits & W. Schroyens: Curious Belief-Bias
In most of the studies that have looked at the influence of believability of premises and conclusions, there is a general consistency between the two; often an empirically false, but valid, conclusion is generated from clearly false premises. However, it is the case that an empirically false conclusion can be derived from premises that are generally considered to be true. The specific example of this that we consider here is based on the difference between prototypical cases and atypical ones. Consider a major premise of the form “If something is P then it has characteristic Q” where Q is a characteristic that applies to prototypical cases of a given category. Such a statement will, thus, be quite believable, since it is statistically highly likely to be true (although not necessarily true in the strict sense). In this case, reasoners would process this kind of statement as highly believable, and there would be little attempt to inhibit retrieval of information about the category during reasoning. Suppose then that the minor premise following this form of major premise takes the form: “A is a P,” where A is an atypical case for which Q is not true. The resulting logical conclusion is that “A has characteristic Q,” which is empirically false. However, the minor premise would prompt potential retrieval of information that there are cases of P and not-Q, of which A is one. There would, thus, be a certain tendency to deny the conclusion. Compare this to a major premise of the same form, but where the relationship is clearly not true, i.e., “If P then Z,” where Z is not a prototypical characteristic, combined with a minor premise of the form “B is a P.” In this case, the initial statement would be processed as unbelievable and there would be a corresponding tendency to inhibit retrieval of information about possible cases of P and not-Q. Thus, when given the logical (but empirically false) conclusion that “B has Z,” a reasoner would have relatively little tendency to deny the resulting conclusion. The following are specific examples of these kinds of inference. If an animal is a mammal, then it has legs. A whale is a mammal. Thus, a whale has legs.
The conclusion in this case is false, although the major premise is true for most mammals. Processing this premise would not necessarily prompt inhibition of information that contradicts the premise. Thus, in this case, the information that “whales do not have legs” would remain accessible to reasoners when evaluating the conclusion. This would lead them to tend to reject the conclusion to a certain extent. Compare this to the following inference: If an animal is a mammal, then it has claws. A cow is a mammal. Thus, a cow has claws.
In this case, the conclusion is also clearly false, as is the major premise. In this case, it is assumed that there would be a strong tendency to inhibit retrieval of information about the category “mammal” while reasoning. This would © 2007 Hogrefe & Huber Publishers
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imply that the logical conclusion that a “cow has claws” should be accepted relatively easily, since retrieval of the fact that most mammals (including cows) do not have claws would be inhibited. Thus, in general, we would predict that it would be easier for reasoners who were under instructions to reason logically to accept an unbelievable, but logical, conclusion on the basis of a clearly unbelievable premise than to do so when the major premise is relatively believable.
Method Participants A total of 93 university students (23 males, 70 females; average age: 24 years 7 months) were given the booklets.
Procedure Booklets were distributed randomly to entire classes. Participants were given as much time as they required to respond to the problems.
Material Paper and pencil test booklets were prepared. In all of these, the first page asked for age and sex, followed by a fairly extensive set of instructions. In these, participants were informed that they were to respond to some inferential problems, and that in order to do so, they would have to consider the major premise as always true even if this was not the case in the everyday world. This was followed by a specific example “If something is a square, then it has four corners. X is a square. Conclusion: X has four corners.” Participants were told that they would have to indicate on a scale from 0 to 9 (corresponding to ratings of impossible to necessary), what the probability would be that the presented conclusion is true, given that the assertions used to make the conclusion are considered true. On each of the following four pages, two inferential problems were presented (for a total of eight). For the first booklet in the unusual condition, these eight problems were comprised of four filler items (corresponding, in order, to inferences of the form: DA (if P then Q, P is false), MT (if P then Q, Q is false), AC (if P then Q, Q is true), MT). The four experimental items all used the MP form (if P then Q, P is true) and were, in order: 1) If something is a mammal, then it has claws. Cows are mammals. Conclusion: Cows have claws. (MAMMAL) 2) If something is a plant, then it has blue flowers. Sunflowers are plants. Conclusion: Sunflowers have blue flowers. (PLANT) Experimental Psychology 2007; Vol. 54(1):38–43
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H. Markovits & W. Schroyens: Curious Belief-Bias
Table 1. Mean ratings for conclusions on the four experimental inferences and on the filler items combined in the unusual and prototypical conditions in Study 1 Condition
MAMMAL
PLANT
BIRD
ANIMAL
Total
Fillers
Unusual
7.65
7.55
7.71
7.59
7.60
6.49
Prototypical
5.68
7.18
6.48
6.84
6.54
6.26
3) If something is a bird, then it is red. Crows are birds. Conclusion: Crows are red. (BIRD) 4) If something is an animal, then it lays eggs. Bears are animals. Conclusion: Bears lay eggs. (ANIMAL) The first item was a filler, followed by a succession of one experimental followed by one filler item. A second version of this booklet was produced with the same problems, but presented in inverse order. For the first booklet in the prototypical condition, the same filler items were used. The four corresponding experimental items were, in order: 1) If something is a mammal, then it has legs. Whales are mammals. Conclusion: Whales have legs. 2) If something is a plant, then it regularly needs water. Cacti are plants. Conclusion: Cacti regularly need water. 3) If something is a bird, then it can fly. Ostriches are birds. Conclusion: Ostriches can fly. 4) If something is an animal, then it needs food regularly. Hibernating bears are animals. Conclusion: Hibernating bears need food regularly. The order of the eight items (four fillers, four experimental) was the same as the first unusual booklet. For this latter booklet, a second form was constructed by inverting the order of the problems. There were, thus, a total of four booklets.
Results Mean ratings for the four experimental problems in both the unusual and prototypical conditions were calculated, along with combined means for the filler items. These are presented in Table 1. As can be seen from this table, ratings for conclusions in the unusual condition are generally higher than those in the prototypical condition, although there is clear variation in the extent to which this is true. An ANOVA with ratings on the four experimental problem Contents as repeated measure and Problem type as the independent factor was performed. This indicated a significant main effect of problem type, F(1, 90) = 4.65, p < .05, and content, F(3, 88) = 4.09, p < .01, and a significant Problem type × Content interaction, F(3, 88) = 6.12, p < .01. An ANOVA with Problem type as independent variable was performed on the combined totals for the four filler items. Experimental Psychology 2007; Vol. 54(1):38–43
No difference was observed. Overall, these results generally support our basic hypothesis. However, there is a fair amount of variation in the extent of the differences observed on specific problems, although in no case was the rating for the prototypical form less then that for the unusual form. One final point was addressed. The unusual conclusions were specifically selected to be completely unbelievable. Prototypical conclusions were chosen to be as unbelievable as possible, but given the constraints of the method, these were, necessarily, at least somewhat believable. In order to verify this, we asked an independent sample of 18 university students to rate the believability of the eight conclusions used in this study on a scale from 0 to 8 (where 0 = unbelievable). Average ratings for the unusual conclusions were .90, while those for the prototypical conclusions were 1.50. A paired-value t test indicated that unusual conclusions were more unbelievable than were prototypical conclusions, t(17) = 1.90, p < .05. Overall, all conclusions were quite unbelievable, although the unusual conclusions were more unbelievable than the prototypical conclusions, as was expected.
Study 2 Although the results of the first study are clearly consistent with our hypothesis, there is some variability in the extent to which individual problems show the predicted pattern. There are some factors that might have influenced these results that were not controlled in the first study. In the first case, the major premise in the unusual condition was chosen to be relatively unbelievable (but not totally so), and it is possible that this variation may have had an influence. In addition, the minor premise in the unusual and prototypical forms differed. It is thus possible that some combination of these two factors might have influenced reasoners’ evaluations. We, thus, revised the original problem set in two ways. First, we constructed the major premises in the unusual condition to be totally unbelievable. We also used the same minor premise in both conditions.
Method Participants A total of 115 university students (31 males, 84 females; average age: 24 years 6 months) were given the booklets. © 2007 Hogrefe & Huber Publishers
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Table 2. Mean ratings for conclusions on the four experimental inferences and on the filler items combined in the unusual and prototypical conditions in Study 2 Condition
MAMMAL
PLANT
BIRD
AIRPLANE
Total
Fillers
Unusual
6.75
7.36
6.89
6.82
6.96
6.28
Prototypical
5.32
6.52
5.64
6.12
5.93
6.50
Procedure Booklets were distributed randomly to entire classes. Participants were given as much time as they required to respond to the problems.
Material Paper and pencil test booklets were prepared that were identical to those used in the first study, with the exception of the four experimental items. In the unusual condition, the following four items were used: 1) If something is a mammal, then it has wheels. Whales are mammals. Conclusion: Whales have wheels. (MAMMAL) 2) If something is a plant, then it has feet. Cacti are plants. Conclusion: Cacti have feet. (PLANT) 3) If something is a bird, then it has loudspeakers. Ostriches are birds. Conclusion: Ostriches have loudspeakers. (BIRD) 4) If something is an airplane, then it has hair. Gliders are airplanes. Conclusion: Gliders have hair. (ANIMAL). The corresponding items in the prototypical condition were: 1) If something is a mammal, then it has legs. Whales are mammals. Conclusion: Whales have legs. (MAMMAL) 2) If something is a plant, then it has leaves. Cacti are plants. Conclusion: Cacti have leaves. (PLANT) 3) If something is a bird, then it can fly. Ostriches are birds. Conclusion: Ostriches can fly. (BIRD) 4) If something is an airplane, then it has a motor. Gliders are airplanes. Conclusion: Gliders have a motor. (AIRPLANE).
Results Mean ratings for the four experimental problems in both the unusual and prototypical conditions were calculated, along with combined means for the filler items. These are presented in Table 2. As can be seen from this table, ratings for conclusions in the unusual condition are consistently higher than those in the prototypical condition. An ANOVA with conclusion ratings on the four experimental problem contents as repeated measure and Problem type as © 2007 Hogrefe & Huber Publishers
the independent factor was performed. This indicated a significant main effect of Problem type, F(1, 112) = 4.08, p < .05, and a main effect of Content, F(3, 110) = 9.04, p < .01. No other effects were significant. A similar analysis was performed on the combined ratings for the four filler items. No significant difference was obtained. As in the first experiment, the unusual conclusions were specifically selected to be completely unbelievable. Prototypical conclusions were chosen to be as unbelievable as possible, but given the constraints of the method, these were, necessarily, at least somewhat believable. In order to verify this, we asked an independent sample of 20 university students to rate the believability of the eight conclusions used in this study on a scale from 0 to 8 (where 0 = unbelievable). Average ratings for the unusual conclusions were .60, while those for the prototypical conclusions were 1.83. A paired-value t test indicated that unusual conclusions were more unbelievable than were prototypical conclusions, t(19) = 2.70, p < .001. Overall, all conclusions were quite unbelievable, although the unusual conclusions were more unbelievable than the prototypical conclusions, as was expected.
Discussion The results of these two studies are quite clear. When reasoning with false premises, reasoners are more willing to endorse highly unbelievable, but logical, conclusions that are inferred from a major premise that is clearly false than to endorse logical conclusions that are also unbelievable but are inferred from a major premise that is generally believable. The observed effect is made more convincing by the fact that the unusual conclusions were less believable than the prototypical conclusions. This is consistent with our predictions. At this point, it is worth examining in more detail the specific nature of the items that were used in these studies in order to look at the question of the potential loci of the obtained effects. Below, we present two comparable unusual and prototypical items. Unusual
Prototypical
If something is a mammal, then it has wheels.
If something is a mammal, then it has legs.
Whales are mammals.
Whales are mammals.
Conclusion: Whales have wheels.
Conclusion: Whales have legs.
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H. Markovits & W. Schroyens: Curious Belief-Bias
As can be seen from these examples, prototypical inferences have greater believability in both the major premise and the conclusion. Any model of belief-bias that relies on response bias based on evaluation of the believability of any combination of the individual components of the inferences, including the conclusion, would, thus, predict that prototypical conclusions would be more strongly affirmed than unusual conclusions. In both cases, of course, the inference form is identical, so that this cannot be a factor in the observed difference. While a direct use of response bias does not appear able to explain these results, other models could, in principle, do this. Klauer, Musch, and Naumer (2000) have proposed a complex model of belief-bias effects in reasoning that integrates several possible factors other than simple response bias. One of the differences between the unusual and prototypical premises is that the latter use semantically improbable relations (e.g., mammals and wheels). The Klauer et al. (2000) model specifically claims that semantic incongruity, of the kind found in unusual premises, can create difficulties in integrating the major and minor premises. In some cases, this could lead to an increase in the effect of response bias. However, as pointed out by a reviewer, semantic incongruity can induce a process of “ambiguous verification,” which would lead to a relative increase in premise acceptance, which would, in turn, be consistent with the present results. Such an explanation would imply that educated adult reasoners have problems forming an integrated representation of the relatively simple MP premises used in this study, something that would require some verification. It should also be mentioned that these results, and the inhibitory processes that are postulated, are consistent with Beller and Spada’s dual source theory (2003). This theory proposes that reasoners will use information derived from knowledge about the specific content without “logical” reasoning as one component of the reasoning process. However, whether or not this information is used depends on the interaction between reasoning processes and the pragmatics of the premises. When faced with premises that are semantically false, reasoners will infer from this that empirical knowledge is not appropriately used, and attempt to block any tendency to do this. The mechanism that allows this is quite consistent with the inhibition account that we use here. While there are clearly other ways of interpreting these results, the inhibition hypothesis that we present does predict these results in a direct way. The idea that reasoners must inhibit access to real-world knowledge when reasoning about clearly false premises (as is the case with the unusual inferences) has been supported by earlier studies (Markovits & Doyon, 2004; Simoneau & Markovits, 2003). The present results certainly support the potential usefulness of including an inhibitory component of this kind in any analysis of content-related reasoning.
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Acknowledgments This study was supported by a grant from the National Science and Engineering Research Council of Canada to the first author.
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Received May 22, 2005 Revision received February 8, 2006 Accepted February 9, 2006
Henry Markovits Psychology Department Université du Québec à Montréal C.P. 8888 Succ Center-Ville Montréal, Québec Canada H3C 3P8 Tel. +1 514 987-3000 Fax +1 514 987-7953 E-mail
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Experimental Psychology 2007; Vol. 54(1):38–43
