Individual differences in conditional reasoning: A ...

THINKING & REASONING, 2005, 11 (4), 305–325

Individual differences in conditional reasoning: A dual-process account Paul A. Klaczynski The Pennsylvania State University, University Park, PA, USA

David B. Daniel University of Maine at Farmington, ME, USA

Dual-process theories of conditional reasoning predict that relationships among four basic logical forms, and to intellectual ability and thinking predictions, are most evident when conflict arises between experiential and analytic processing (e.g., Stanovich & West, 2000). To test these predictions, 210 undergraduates were presented with conditionals for which the consequents were either weakly or strongly associated with alternative antecedents (i.e., WA and SA problems, respectively). Consistent with predictions, modus ponens inferences were not related to inferences on the uncertain forms (affirmation of the consequent, denial of the antecedent). On WA problems, modus tollens, affirmation of the consequent, and denial of the antecedent were related to each other and to verbal ability. Modus ponens was linked to verbal ability only when disabling conditions were activated. In accord with the predictions of Stanovich and West (2000), on most problems, thinking dispositions predicted variance in inferences independently from verbal ability. We argue that a largely automatic experiential processing system governs performance on modus ponens, unless disablers are activated. Consciously controlled analytic processing predominates on the uncertain forms and, under some conditions, on modus tollens.

Studies of conditional inferences have frequently concentrated on the conditions that elicit determinate and indeterminate inferences on four basic logical forms. The four forms share the major premise, if p, then q. Modus ponens (MP) involves the minor premise ‘‘p is true’’, and the conclusion ‘‘q is true’’. For modus tollens (MT), the minor premise is ‘‘q is not true’’ and Correspondence should be addressed to Paul A. Klaczynski, Department of Psychology, The Pennsylvania State University, University Park, PA, USA, 16802. Email: [email protected] # 2005 Psychology Press Ltd

http://www.tandf.co.uk/journals/pp/13546783.html

DOI: 10.1080/13546780442000196

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the conclusion is ‘‘p is not true’’. According to standard logic, MP and MT are valid logical forms. The minor premise and conclusion for the denial of the antecedent (DA) are ‘‘p is not true; therefore, q is not true’’. The affirmation of the consequent (AC) entails the minor premise ‘‘q is true’’, and the conclusion ‘‘p is true’’. The latter two forms are considered fallacious; their conclusions cannot be drawn with certainty. However, the practice of judging the correctness of inferences against the dictates of formal logic has been criticised extensively (see Evans, 2002; Evans & Over, 1996, 2004; Oaksford & Chater, 1994). Thus, for ease of presentation, we will subsequently discuss MP and MT as certain forms and AC and DA as uncertain logical forms; rather than labelling inferences as valid or invalid, we refer to inferences as determinate or indeterminate. Conditional inferences can be discussed not only in terms of logical correctness, but also in terms of ‘‘invited’’ inferences. Invited inferences are those that follow from pragmatic, natural language, or probabilistic interpretations of conditional statements. For instance, for the conditional ‘‘If a person exercises frequently, then that person will be in good shape’’, the invited inference for AC (Bill is in good physical shape) is ‘‘Bill exercises often’’; for DA (Bill does not exercise frequently), the invited inference is ‘‘Bill is not in good physical shape’’. In both cases, the invited inferences are determinate and thus are in conflict with the inferences based on material implication. By contrast, for MP and MT, the invited and logical inferences are often identical (however, see discussion below). Extant research (see Evans, 1989, 2002; Evans & Over, 1996; Klaczynski & Narasimham, 1998; Markovits & Barrouillet, 2002; Newstead, Handley, Harley, Wright, & Farrelly, 2004; Stanovich, 1999; Thompson, 1994, 2000) indicates the following: (a) drawing determinate inferences on MT problems is more difficult than on MP problems; (b) under a multitude of conditions, determinate inferences on the uncertain forms (AC and DA) are common and, by the standard logic view, fallacious; (c) strict deductive reasoning instructions increase responses that accord with standard logic; (d) under some conditions, children make more determinate inferences on the certain logical forms and fewer determinate inferences on the uncertain forms than adults; and (e) under some conditions, intellectual ability and actively openminded thinking dispositions predict inferences on MT, AC, and DA problems. In an effort to extend previous research, the present research was intended to tie together predictions derived from dual-process theories of conditional reasoning (e.g., Evans, 2002; Evans & Over, 2004; Klaczynski, Schuneman, & Daniel, 2004), theories that link semantic memory to reasoning (e.g., Cummins, 1995; Markovits, 2000), and theories of individual differences in reasoning (e.g., Newstead et al., 2004; Stanovich, 1999).

INDIVIDUAL DIFFERENCES

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THEORIES LINKING CONDITIONAL INFERENCES TO SEMANTIC MEMORY In this view, reasoning is highly determined by the contents of semantic memory (Cummins, 1995; Markovits, 2000; Markovits & Barrouillet, 2002). Disabling conditions are defined as semantic links that (subjectively) render a conditional false under certain circumstances (e.g., If a person exercises frequently but is a smoker, then that person will not be in good condition). In the absence of disabling conditions, determinate MP inferences are made by the vast majority of adults. However, when a conditional activates disabling conditions, adults often draw indeterminate inferences, especially on the MP form (Cummins, 1995; Janveau-Brennen & Markovits, 1999; see also Thompson, 2000). Responses to the indeterminate forms are also tied to semantic memory. Specifically, the accessibility of alternative antecedents (i.e., p1, p2, p3 . . . ) to a consequent (i.e., q) determines whether a conditional is represented as a conditional per se or as a biconditional (if and only if p, then q; or, alternatively, entailing probabilistic relationships; e.g., if q then usually p). In general, when no alternative antecedents are activated, reasoners work with natural language interpretations and accept the invited AC and DA inferences. When at least one alternative antecedent is strongly associated with a consequent, the probability of inhibiting invited inferences increases. Semantic memory reasoning theories therefore make the following predictions: (1) When conditionals do not activate disabling conditions, determinate inferences on the certain forms are more probable than when disabling conditions are activated; (2) when alternative antecedents are activated, determinate inferences on the uncertain forms are less probable than when no alternatives are activated; (3) across forms, inhibitory processes are critical determinants of whether determinate or indeterminate inferences are drawn (Handley, Capon, Beveridge, Dennis, & Evans, 2004; Markovits & Barrouillet, 2002).

DUAL-PROCESS THEORIES OF REASONING Premises common to all dual-process theories are that information processing operates in two distinct systems (labelled here the experiential and analytic processing systems), the two systems operate simultaneously and support each other under most circumstances, and one system is usually predominant over the other (Epstein & Pacini, 1999; Evans & Over, 1996; Klaczynski, 2001a; Klaczynski & Cottrell, 2004; Stanovich, 1999, 2003). The experiential system is largely automatic, requires little cognitive space, is minimally effortful, relatively fast, and operates on contextualised task representations that are rich in semantic content. The

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analytic system is under conscious control, effortful, operates according to abstract rules of inference, and involves the activation of decontextualisation and inhibitory abilities (Evans, 2002; Klaczynski, 2004; Stanovich, 1999; Stanovich & West, 2000)—thus, analytic processing deals with representations in which the logical structure of a task is separated from its social contents and conversational implicatures. The experiential system is typically predominant because it is the more cognitively economical system and because most responses triggered by experiential processing are often adaptive or, at least, not maladaptive (Evans & Over, 1996; Klaczynski, 2001b, 2004). Analytic processing is typically activated when the motivation for precise responses is high and/ or the task environment clearly requires logical analysis. On MP problems, the predominance of either system should lead to determinate inferences because the invited inferences and the logical inferences are the same. In the absence of disabling conditions, because it is the more cognitively economical system, experiential processing likely predominates on MP problems. However, when disabling conditions are activated, MP problems are more complex than when no disablers are activated. Experiential processing may predominate when disablers are activated (Evans & Over, 2004), but the additional complexity of representing MP when disablers are activated could also cue analytic system predominance. First, conscious awareness of disablers could lead to rejection of invited inferences and, consequently, to indeterminate inferences. Alternatively, awareness of disablers could engage the executive function abilities required to suppress them and thereby lead to determinate inferences. Although MT problems are more complex than MP problems, again either experiential or analytic processing may predominate. Given the minor premise, not q, experiential processing might entail the automatic activation of counterexamples in memory (e.g., for the conditional ‘‘if a person exercises frequently, then she is in good shape’’, and the minor premise ‘‘Alice is in poor shape’’, the availability of a general counterexample, such as ‘‘Many people in poor shape exercise a lot’’, would lead to the determinate inference, not p). On the basis of their findings (specifically, Experiment 3), Newstead et al. (2004) argued for experiential predominance on MT problems, as did Klaczynski et al. (2004). By contrast, Evans and Over (2004) suggest that adults often reason analytically on MT (particularly when strict logic instructions are given and participant intelligence is high). Specifically, reasoners begin by supposing that p and q are true. Given the minor premise, not q, the original supposition must be false; hence, the inference that p is true can be rejected. Alternatively, as with MP, if disablers are activated by MT problems, the original conditional may become a qualified conditional that allows p to sometimes be true if q is


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false. Analytic predominance could then occur in the two ways described previously for MP. On AC and DA, biconditional interpretations are common because they are more cognitively economical than complete conditional interpretations and because natural language often serves as a default mediator of interpretations. Because these interpretations are likely to cue experiential predominance, the invited inferences are often accepted. By contrast, if the analytic system is predominant, respondents should make indeterminate inferences. From this analysis, two opposing predictions can be offered. First, if people generally rely on the most economical (i.e., experiential) processing system on all four logical forms, then determinate inferences on MP and MT should relate positively not only to each other, but also to determinate inferences on the uncertain (AC and DA) forms. Second, and in contrast to the first hypothesis, Klaczynski et al. (2004) argued that experiential processing predominates on the certain forms and that analytic processing predominates on the uncertain forms. Thus, inferences on the certain forms should not be related to inferences on the uncertain forms. As discussed subsequently, each of these predictions is somewhat different when individual differences in intelligence and thinking dispositions are considered.1

INDIVIDUAL DIFFERENCES IN REASONING We thus far have suggested, consistent with Evans and Over (2004), that either experiential or analytic processing can predominate on all four logical forms. Although the experiential system is typically predominant, this predominance can be overridden by analytic processing. Indeed, Stanovich and West (1998a, 2000) showed that experiences of conflict (or the lack thereof) between the analytic and experiential systems are strong determinants of (at a given moment) system predominance. In addition, and as discussed in greater detail below, at least under some conditions (see 1 For ease of presentation, we discuss inferences as though they are produced entirely through experiential or analytic processing. However, both processing systems play roles in the production of conditional inferences. Thus, when we discuss responses produced by one system or the other, our intent is to imply that that system was predominant over the other when those responses were given. We should also note that more complex predictions about correlations among logical forms can be made, based, for example, on the claims of Evans and Over (2004, pp. 162–168). Those authors argue that inferences on all four forms can be based on either experiential or analytic processing but that analytic processing is likely to predominate (across forms) when (a) strict instructions to think logically are given and (b) participants are highly intelligent. Readers should note that, in our discussion of individual differences in reasoning, the conjectures of Evans and Over are consistent with many of our hypotheses. Nonetheless, it is also critical to note that our predictions do not pertain to situations in which strong instructions to think logically are given.

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Klaczynski, 2001a, 2004), judgements, decisions, and reasoning should be predicted by intelligence and ‘‘thinking dispositions’’ (Stanovich, 1999; Stanovich & West, 2000). Intelligence indexes the capacities to engage in analytic processing, effectively use working memory, and inhibit experiential responses. Thinking dispositions index intentional level differences in epistemic regulation (e.g., predispositions to use decontextualised representations and inhibit experiential processing). In the Stanovich and West (2000; Stanovich, 1999) theory, individual differences in reliance on experiential or analytic processing are evident most often when solutions produced by the two systems are in conflict. Neither intelligence nor thinking dispositions should be associated with inferences on MP problems because the invited and logical inferences are the same (hence, conflict is atypical). However, as we mentioned earlier, conflict may arise on MP and MT problems when disabling conditions are activated. Under these conditions, both intelligence and thinking dispositions should relate positively to determinate inferences. That is, once disablers have been activated, individuals who score higher on the individual difference measures should be more likely to suppress these disablers than individuals with lower scores. Individual differences were also expected to predict reliance on analytic and experiential processing on the uncertain forms. Specifically, because the invited and logical inferences on these problems bring experiential and analytic processing into conflict, and because complete conditional representations require more working memory capacity than biconditional representations (Markovits & Barrouillet, 2002), the individual difference measures should relate negatively to determinate AC and DA inferences. However, correlations were expected to be stronger when the consequents of conditionals were weakly (as opposed to strongly) associated with alternative antecedents. Specifically, when an alternative antecedent is strongly associated with a consequent, experiential processing should lead to rejection of invited inferences on the uncertain forms; analytic processing (i.e., suppositional reasoning) should also lead to rejection of invited inferences. Consequently, no conflict between the two systems is likely. When no alternative antecedents are available, experiential processing should pull for invited inferences for those of lower ability and thinking dispositions, and analytic processing should pull for logical inferences for individuals of higher ability and thinking dispositions.

PILOT STUDY We first created four types of problems. Specifically, our goal was to create conditionals with deontic and causal relationships that were closely equated in the probabilities of eliciting alternative antecedents.


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TABLE 1 Conditionals Rule type Causal Weak alternatives If a person exercises a lot, then she will be in good shapea If a person eats all the time, then he will gain weightb If a person cuts her finger, then her finger will bleeda If a person drinks something with sugar, then the taste will be sweetb Strong alternatives If a person eats healthy foods, then she will be in good shapeb If a person grows taller, then he will gain weighta If a person gets a thorn in her finger, then her finger will bleedb If a person drinks diet soda, then the taste will be sweeta Deontic Weak alternatives If a person is drinking alcohol, then he must be at least 21 years olda If a person borrows a library book, then she must have a library cardb If a judge puts a person in jail, then the person must be a criminala If a person drives a car, then she must have a driver’s licenseb Strong alternatives If a person rents a car, then he must be at least 21 years oldb If a person joins the book club, then she must have a library carda If a judge puts a person on probation, then the person must be a criminalb If a person drives a motorcycle, then she must have a driver’s licensea

Seconds

16.62 (4.35) 13.08 (5.12) 15.92 (5.12) 19.84 (9.22) 17.64 (6.05) 12.98 (3.38) 10.73 (3.07) 12.62 (4.65) 14.73 (5.44) 13.84 (5.96) 17.35 (3.72) 18.24 (7.65) 17.16 (5.85) 16.15 (5.79) 17.86 (4.39) 13.06 (3.92) 12.65 (5.12) 14.01 (5.72) 12.00 (4.84) 13.58 (6.50)

No. Alt

Mention

2.35 (0.67)

.35 (.21)

3.17 (1.43)

.92 (.28)

2.50 (1.25)

.13 (.34)

2.13 (1.03)

.08 (.28)

1.62 (1.10)

.29 (.46)

3.38 (0.83)

.89 (.19)

3.69 (1.46)

1.00 (.00)

3.38 (1.06)

.92 (.27)

3.46 (1.10)

.92 (.27)

2.96 (1.04)

.73 (.67)

2.15 (0.93)

.20 (.36)

2.04 (0.69)

.17 (.38)

1.67 (0.96)

.08 (.28)

1.75 (0.98)

.08 (.28)

2.96 (1.08)

.46 (.51)

3.32 (0.93)

.87 (.15)

2.92 (1.40)

.92 (.27)

2.46 (0.98)

1.00 (.00)

4.08 (2.28)

.85 (.37)

3.81 (1.20)

.69 (.47)

Causal and deontic conditionals with weak and strong antecedent – consequent association to alternative antecedents, time to generate an alternative antecedent, and numbers of alternative antecedents generated. Times are in seconds. Mention = probability that the antecedent in the ‘‘matched’’ consequent conditional was generated. Standard deviations are in parentheses. Superscripts denote the problem set in which each conditional was included.

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Participants were 39 undergraduates who were presented an antecedent generation task involving the conditionals shown in Table 1. Four deontic and four causal conditionals were presented in a booklet. About half of the participants worked with conditionals that contained consequents thought to be weakly associated with their antecedents and strongly associated with at least one alternative antecedent (‘‘strong alternative’’ [SA] conditionals). The remaining participants worked with conditionals whose consequents were thought to be strongly linked to their antecedents and weakly associated with alternative antecedents (WA conditionals). For each conditional in the first set, a ‘‘matched’’ conditional with the same consequent, but a different antecedent, was presented in the second set (see Table 1). Thus, if the consequent of a conditional was strongly linked to its antecedent, the same consequent in the second set was paired with a weakly associated antecedent. Participants produced as many alternatives they could in 1 minute. Antecedent – consequent association strength was assessed in three ways. First, we examined the numbers of alternative antecedents generated. Second, the likelihood that one of the alternatives generated on the SA (or WA) problems was the same as the antecedent that was actually used in the matched WA (or SA) conditional was examined. Third, we measured the time (on a stopwatch) taken to completely generate a first alternative antecedent. Inter-rater agreement on number of alternatives generated (based on the coding of 15 participants by two research assistants blind to the study’s hypotheses) was 91.7%. Inter-rater agreement on whether participants generated antecedents to the conditionals used in matched conditionals was 94.2%. Numbers of alternative antecedents, the likelihood that one of the alternatives generated was the antecedent on the matched set of conditionals, and mean times for generating a first alternative are presented in Table 1. A 2 (domain: deontic or causal) 6 2 (association strength: SA or WA) ANOVA showed that more alternatives were produced, the alternative in the ‘‘matched’’ set of conditionals was generated more often, and a first alternative antecedent was generated more quickly on the SA conditionals than on the WA conditionals, Fs(1, 37) = 35.18, 154.54, 23.92, respectively, ps 5 .001. No other effects were statistically significant.

MAIN STUDY Participants A total of 210 students were recruited from introductory psychology classes. Students were awarded class credit for participating. Experimental sessions


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lasted between 25 and 40 minutes. Sessions were conducted with groups of two to seven participants.

Materials Reasoning task. Two sets of problems (see Table 1) were used. Within each problem set, two problems contained deontic conditionals and two contained causal conditionals. Within each problem domain, there was one SA conditional and one WA conditional. Problem set was not included in subsequent analyses because initial analyses revealed that it had no effects (smallest p = .23). Within each problem set, the four rules were presented in one of four counterbalanced orders. Rules were presented on separate pages of a fivepage booklet (instructions were on the first page). Participants were told that they would read a number of rules and that, for each rule, they would be asked some questions that they should use the rule to answer. Participants were also instructed that, for the purposes of this study, they were to assume that the rules were true and that, even if they did not believe that the rules were always true, they should respond to the questions as though the rules were always true. Note that, according to Evans (2002; Evans & Over, 2004), these are considered ‘‘weak’’ deductive reasoning instructions. Information that affirmed or denied the antecedent, or that affirmed or denied the consequent, was then presented, followed by a question about whether the invited inference could be drawn (‘‘yes’’, ‘‘no’’, or ‘‘can’t be certain’’). In the instructions, participants were informed that ‘‘can’t be certain’’ responses could be correct if they believed that no conclusion followed from the information that was provided. For example, for the rule ‘‘If a person drives a car, then she must have a driver’s license’’, the four questions (presented in counterbalanced order across participants) were: ‘‘Amy is driving a car. Does she have a driver’s license?’’ (MP) ‘‘John does not have a driver’s license. Is he driving a car?’’ (MT) ‘‘Sarah is not driving a car. Does she have a driver’s license?’’ (DA) ‘‘Peter has driver’s license. Is he driving a car?’’ (AC)

For each question, participants provided written justifications. For MP and MT, these were coded for the presence of disabling conditions. Responses were coded as disablers when participants noted that when certain circumstances arose, p could be true without entailing q. These justifications called into question the truth of the rules despite explicit instructions to treat the rules as though they were always true, for example, ‘‘Amy could have a driver’s permit and then she could drive a car without a license.’’ Two

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undergraduate judges, blind to the study’s hypotheses, coded the justifications. Inter-rater agreement (based on 30 participants, i.e., 120 justifications) was 88.3% for disabling conditions on MP problems and 92.1% for disablers on MT problems. For AC and DA, justifications were coded for mention of alternative antecedents. Responses were scored as involving alternative antecedents if specific alternatives were noted (e.g., ‘‘She could have been driving a motorcycle’’) or if the general idea that alternatives could exist was mentioned (e.g., ‘‘She could have been driving something else’’). Inter-rater agreement on alternatives was 85.4% for AC and 90.4% for DA. Disagreements were resolved through discussion with the first author. Verbal ability. As a proxy for individual differences in intelligence, the PMA Verbal Meaning test (Thurstone, 1962) was administered prior to problem presentation. This test was selected because vocabulary is the best single predictor of global intelligence scores and because the test is moderately correlated with measures of fluid intelligence and strongly correlated with other measures of crystallised intelligence (Klaczynski & Gordon, 1996; Schaie & Willis, 1996). For each of 64 items, the task was to select which of four words had the same meaning as a target word. Five minutes were given to complete as many items as possible. To test some of our predictions regarding intellectual ability, participants were categorised into low, medium, and high ability groups (see also Newstead et al., 2004). Decontextualised thinking. To assess individual differences in reliance on analytic processing, the Stanovich and West (1997, 1998a) Thinking Disposition Questionnaire (TDQ) was administered (to approximately half the participants before the reasoning problems and immediately after the vocabulary test; to the remaining participants after the reasoning problems). Each of 131 items is rated on a 6-point Likert-style scale (1 = strongly disagree; 6 = strongly agree). Although the TDQ contains several subscales (e.g., actively open-minded thinking, need for cognition), following the practice established by Stanovich and West, we used a single composite score in all analyses. Cronbach’s alpha for the TDQ was .76.

RESULTS We present our findings in four sections. Analyses of determinate inferences on each logical form are presented first. Second, we present a brief analysis of disabling justifications on MP and MT and alternative antecedent justifications on AC and DA. For each analysis in these sections, 2 (alternative antecedent strength: WA or SA) 6 2 (domain: deontic or causal) 6 3 (ability group: low, medium, high)


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analyses of variance were conducted. Next, correlational analyses of relationships among inferences across forms are presented, as are analyses of the relationships of determinate inferences on each form to verbal ability (VA) and thinking dispositions (TD). In the final section, we return to the role of disabling justifications, arguing that these may mediate the links between the certain forms and the individual difference measures.

Effects of alternative antecedent association strength and problem domain Mean numbers of determinate inferences on each form are presented in Table 2. Modus ponens. No main effects or interactions were significant, largest F(2, 207) = 2.54, p = .08. Modus tollens. The domain 6 alternative antecedent interaction bordered on statistical significance, F(1, 207) = 3.82, p = .052, as fewer determinate inferences were made on WA deontic problems than on WA TABLE 2 Mean numbers of determinate inferences by problem domain, alternative antecedent association strength, and verbal ability WA Causal MP Low ability Medium ability High ability MT Low ability Medium ability High ability AC Low ability Medium ability High ability DA Low ability Medium ability High ability

.83 .85 .82 .82 .74 .75 .69 .77 .32 .37 .32 .26 .29 .40 .26 .18

(.38) (.36) (.38) (.39) (.44) (.43) (.46) (.42) (.47) (.49) (.47) (.44) (.45) (.49) (.44) (.39)

SA Deontic .78 .73 .72 .89 .65 .63 .54 .80 .37 .48 .40 .20 .34 .40 .32 .30

(.42) (.45) (.45) (.31) (.48) (.50) (.50) (.40) (.48) (.50) (.49) (.40) (.47) (.49) (.47) (.46)

Causal .77 .81 .74 .78 .66 .63 .61 .75 .23 .21 .31 .18 .19 .22 .19 .12

(.42) (.40) (.44) (.42) (.47) (.46) (.49) (.43) (.42) (.41) (.46) (.39) (.39) (.42) (.41) (.33)

Scores could range from 0 to 1. Standard deviations are in parentheses.

Deontic .80 .88 .69 .82 .69 .71 .63 .74 .22 .23 .22 .20 .24 .25 .26 .22

(.50) (.33) (.46) (.39) (.46) (.46) (.49) (.44) (.41) (.43) (.42) (.40) (.43) (.43) (.44) (.41)

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causal problems (p = .038; see Table 2). Although the effect of ability group was not significant (p = .081), ability actually had a curvilinear effect, F(2, 207) = 5.06, p = .026. The low (M = .68; SD = .28) and high (M = .76; SD = .25) ability groups made more determinate inferences than the medium (M = .62; SD = .29) ability group. If age indexes ability indirectly (at least under some conditions; see Kokis, Macpherson, West, & Stanovich, 2002), these data are consistent with U-shaped developmental trends in MT that have sometimes been reported (e.g., Janveau-Brennan & Markovits, 1999; O’Brien & Overton, 1982). Affirmation of the consequent. As expected, more determinate inferences were made on WA problems than on SA problems, F(1, 207) = 20.47, p 5 .001. However, the effect of alternative antecedents was qualified by an interaction with ability group, F(2, 207) = 3.78, p = .024. Additional analyses showed that, in the low and medium ability groups, determinate inferences more frequent on WA than on SA problems (ps 5 .01; for high ability, p = .44). Denial of the antecedent. Determinate inferences were more frequent on WA problems than on SA problems, F(1, 207) = 11.76, p = .001, and on deontic problems than on causal problems, F(1, 207) = 3.85, p = .051. The effect of ability group approached significance (p = .06). In sum, replicating previous research, determinate inferences on the uncertain forms were less common when alternative antecedents were strongly associated with consequents than when few or no alternatives were available. More intriguing are the findings that the lack of alternative antecedents decreased indeterminate AC inferences only for low and medium ability individuals and that verbal ability related to determinate MT inferences only among the low and medium ability groups. Our findings provide little support for deontic theories of reasoning (e.g., Cosmides, 1989; Cummins, 1996). However, the findings regarding the deontic problems should be treated cautiously (see also Thompson, 1994, 2000) because the problems were not embedded in the types of rich social contexts used in most studies of deontic reasoning and, in contrast to most studies of deontic reasoning, we did not use variants of Wason’s (1966) selection task to measure inferences (see, however, Almor & Sloman, 1996; Klaczynski & Narasimham, 1998). Analyses of justifications. Mean numbers of disabling and alternative antecedent justifications appear in Table 3. Disabling conditions on MP and MT problems. MP disabling justifications were more common on deontic than on causal problems, F(1, 205) = 3.86,


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TABLE 3 Mean numbers of disabling conditions and alternative antecedent justifications by problem domain and alternative antecedent association strength WA

Disablers MP MT Alternative antecedent AC DA

SA

Causal

Deontic

Causal

Deontic

.21 (.41) .18 (.39)

.26 (.44) .20 (.40)

.22 (.41) .24 (.43)

.23 (.42) .21 (.41)

.29 (.44) .27 (.44)

.20 (.40) .24 (.43)

.47 (.50) .40 (.49)

.45 (.49) .35 (.48)

Scores could range from 0 to 1. Standard deviations are in parentheses.

p = .05. No effects were significant for MT disablers (smallest p = .11). Not surprisingly, MP disablers were negatively related to MP inferences, MT inferences, and MT disablers, rs = – .58, – .29, .29, respectively, ps 5 .001. Similarly, MT disabling conditions were linked to MP and MT inferences, rs – .52, – .48, respectively, ps 5 .001. Alternative antecedent justifications on AC and DA problems. For both AC and DA, alternative antecedents were generated more on SA than on WA problems, Fs(1, 205) = 35.98, 16.15, ps 5 .001. No other effects were significant (smallest p = .16). Alternatives on AC and DA problems were related negatively to determinate inferences on both AC and DA problems (for AC, rs = – .39, – .34, ps 5 .001, respectively; for DA, rs = – .18, – .33, ps 5 .01, respectively).

Relationships among inferences and to the individual difference measures In Table 4, we present correlations among determinate inferences on the four logical forms and the correlations of each form to VA and TD. Consistent with recent developmental research (Klaczynski et al., 2004), MP was related to MT; on neither the WA nor the SA problems was MP related to the uncertain forms. Note, however, that the MP – MT correlations within WA and SA problems were significantly stronger than the correlations between the WA and SA problems (z = 19.79, p 5 .001). Although the correlations between MP and verbal ability were not, in themselves, significant, the positive correlation on WA problems was significantly different from the negative correlation on SA problems (p 5 .01).

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.52***

7.13 7.14*

WA – AC 7.21** 7.16* .77***

WA – DA .25*** .18** .05 .09

SA – MP .29*** .32*** 7.13 7.08 .48***

SA – MT 7.05 7.14* .40*** .32*** 7.02 .01

SA – AC 7.06 7.16* .42*** .36*** 7.03 7.07 .58***

SA – DA

WA = Few alternative antecedents; SA = many alternative antecedents; VA = verbal ability; TD = thinking dispositions. *p 5 .05 **p 5 .01 ***p 5 .001

WA – MP WA – MT WA – AC WA – DA SA – MP SA – MT SA – AC SA – DA VA

WA – MT

.11 .22** 7.26*** 7.24*** 7.12 .10 .07 7.17*

VA

TABLE 4 Correlations among determinate inferences on each logical form, verbal ability, and decontextualized thinking

.33*** .24** 7.25*** 7.18** .25*** .17* .11 7.21** .15*

DT


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Like MP, on both WA and SA problems, MT was positively related to TD. As the table indicates, whereas MT on the SA problems was unrelated to the uncertain forms, MT on WA problems was negatively (albeit modestly) associated with AC and DA. On WA problems (but not on SA) problems), MT and verbal ability were positively related. Across the WA and SA problems, AC and DA were positively correlated. As with the MP – MT relationship, these correlations were significantly stronger within the WA and SA problems than between the WA and SA problems (ps 5 .001). Further, verbal ability and TD were more closely related to AC and DA inferences on the WA problems than on the SA problems. For each variable that was linked to both verbal ability and TD, hierarchical multiple regression analyses indicated that TD predicted variance in inferences above and beyond that explained by verbal ability (smallest b = .14, p 5 .04). As detailed further in the Discussion, these patterns of correlations provide rather clear support for dual-process theories of conditional reasoning.

Disabling conditions as mediators of the relationships between the certain logical forms and the individual difference measures We further explored the MT – ability correlation and the previously reported null correlations between MP and ability by examining disabling conditions as possible mediators of these associations. Specifically, because indeterminate, experiential responses (invited by disabling conditions) conflict with determinate, analytic responses on MP and MT, and because disabling justifications may signify that such conflicts have arisen, we expected that high verbal ability and high TD participants for whom disablers were activated groups would inhibit indeterminate responses better than lower verbal ability and TD participants. That is, despite the activation of disabling conditions, we expected higher ability and TD participants to make determinate MP and MT inferences. To examine this proposal, we split participants into two MP and two MT groups. For both MP and MT, participants were assigned into ‘‘disablers activated’’ groups when they mentioned disablers on more than 50% of their justifications (for MP, N = 64; for MT, N = 47); the ‘‘disablers inhibited’’ groups consisted of the remaining participants (for MP, N = 146; for MT, N = 163). In support our conjecture, in the ‘‘disablers activated’’ groups, the MP – verbal ability and MP – TD correlations were significant, rs = .28, .46, ps 5 .01, .05, respectively. In further support of our hypotheses, MP related negatively to DA in the ‘‘disablers activated’’ group (r = – .25, p 5 .05), but not in the ‘‘disablers inhibited’’ group. Although correlations were in the

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same direction for MT, perhaps owing to the smaller size of the ‘‘disablers activated’’ group, the MT – verbal ability, MT – TD, and the MT – DA correlations only approached significance (rs = 21, .27, .28, ps = .08, .06, .057, respectively). Surprisingly, in the ‘‘no disablers’’ group, verbal ability was modestly and negatively linked to MP (r = – .18, p 5 .05), a finding that parallels developmental evidence that MP inferences decline with age under some conditions (Janveau-Brennan & Markovits, 1999). By contrast, TD was positively related to MP (r = .35, p 5 .001). Multiple regression analyses indicated that, in both the ‘‘disablers activated’’ and ‘‘not activated’’ groups, TD predicted variance in MP inferences beyond that accounted for by verbal ability (bs = .43, .32, ps 5 .001). For MT in the ‘‘no disablers’’ group, no link between verbal ability and determinate inferences was evident (r = .07), but the MT – TD correlation was significant (r = .21, p 5 .01).

DISCUSSION The present findings extend previous research on conditional reasoning in several ways. First, on both causal and deontic problems, we replicated findings that inferences on the certain forms are linked to disabling conditions (although, unlike previous research, we did not experimentally manipulate disablers; e.g., Cummins, 1995) and that inferences on the uncertain forms are tied to the availability of alternative antecedents. In line with the theories of Thompson (1995, 2000) and Evans (2002; Evans & Over, 2004), it appears that disablers on the certain forms and alternative antecedents on the uncertain forms affect the manner in which conditionals are represented. On the certain forms, disablers may lead to relatively complex representations that include qualifications to a conditional (e.g., p is not represented as sufficient for q) and lead to indeterminate—and thus neither logical nor invited—inferences. On the uncertain forms, alternative antecedents allow for complete conditional representations; the lack of alternatives gives rise to biconditional representations that, in turn, result in determinate—and logically invalid—inferences. Our second major finding serves to qualify these claims. First, MP was related positively to MT, but was not related to AC or DA. The null correlations with the uncertain forms are consistent with those reported by Klaczynski et al. (2004) and suggest experiential system predominance on MP, at least when strict deductive reasoning instructions are not given (Evans & Over, 2004). Yet these correlations do not tell the entire story. First, the significant differences between MP – MT correlations within the WA and SA problems and MP – MT correlations between the WA and SA problems imply the operation of different processes as a function of alternative antecedent availability. In these cases, however, the predominant


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processing system is likely determined not so much by the MP and MT forms as by the availability (or lack thereof) of alternative antecedents on the uncertain forms. Second, and more importantly, when disablers were activated, verbal ability and DA were linked negatively to MP and, marginally, MT. Consistent with the hypothesis that disablers create experiential-analytic conflict, and the Stanovich and West (1998a, 2000) prediction that differences between ability groups are most apparent when conflict arises, it was primarily individuals of higher verbal ability (and thinking dispositions) who drew determinate conclusions in the ‘‘disablers activated’’ group. These findings support arguments that, when conflict arises, higher ability and thinking disposition individuals can suppress experiential processing interference better than individuals with less ability and self-reported biases toward contextualised thinking (Evans & Over, 2004; Handley et al., 2004; Klaczynski, 2001a; Newstead et al., 2004; but see Klaczynski & Gordon, 1996). In addition, our findings indicate that experiential processing is usually, but not always (i.e., for high ability and TD individuals when disablers are activated), predominant on MP. Determinate MT inferences also may be based on either experiential or analytic processing predominance. Given that q is false, reasoners can rely on automatically activated counterexamples and thus infer that p is false on the basis of predominantly experiential processing. Alternatively, the MT form may demand more complex processing than MP because some level of hypothetical thinking is required to infer that, if q is not true, p must not be true. MT problems may thus engage suppositional reasoning abilities wherein reasoners hypothesise that two contradictory states of affairs (p and q; not q) are true. The contradiction is resolved and the truth status of the conditional is preserved by inferring that p must be false. Although the relationships of MT to AC and DA (particularly when conditionals had few alternative antecedents, a situation we discuss in more detail below) suggest that reasoners typically rely on a suppositional process, the correlations between MT and the individual difference measures (rs = .17, .21, ps 5 .05, for MT – verbal ability and MT – thinking dispositions, respectively) suggest that reasoning by supposition was characteristic of only higher ability and thinking disposition participants. This conjecture is further supported by indications that the MT – verbal ability relationship was curvilinear, suggesting experiential predominance (i.e., reliance on counterexamples) among low ability individuals and analytic predominance (i.e., suppositional reasoning) among high ability participants. Finally, different processing routes to determinate MT inferences were also indicated by the data on disabling justifications (i.e., when disablers were activated, higher ability participants were able to suppress them and make determinate inferences; by contrast, lower ability individuals may have had difficulty inhibiting the interference created by

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disablers and/or may have automatically accepted disablers as a basis for inferences; for a more detailed discussion, see Evans & Over, 2004, Ch. 6). As with each of the certain forms, our data suggest that the uncertain forms are processed analytically by some individuals and experientially by others. First, as noted earlier, only on WA conditionals did MT relate to AC and DA. This finding is important because, when no alternative antecedents were available, the most typical responses to the uncertain forms were determinate inferences; the negative link to MT suggests that participants who reasoned by supposition on MT also did so on AC and DA. This may be because the lack of alternatives triggers analytic – experiential conflict— the experiential ‘‘pull’’ for invited inferences on the uncertain forms conflicts with inferences based on logical task analysis—at least among higher VA/ TD participants. The finding that lower ability participants made more determinate AC and DA inferences on the WA than on the SA problems adds additional credence to this claim. Specifically, when alternatives were not available, those of lower verbal ability tended to accept invited inferences, suggesting that these individuals processed the uncertain forms experientially and perhaps did not experience analytic – experiential conflict. By contrast, when a conditional’s consequent was strongly associated with alternative antecedents, analytic – experiential conflict is unlikely because both logical analysis and reliance on semantic memory call for indeterminate inferences. Finally, evidence that the AC – DA correlations within the WA and SA problems were stronger than the same correlations between WA and SA problems supports the hypothesis that, under different task conditions, different processes predominated on the uncertain forms. In sum, our findings indicate individual differences in the tendency to inhibit experiential processing on each logical form (see Markovits, Doyon, & Simoneau, 2002; Newstead et al., 2004; and Handley et al., 2004, for other additional evidence that ability, inhibitory abilities, and working memory capacity are associated with conditional reasoning). Although the conditions under which the individual difference measures (especially verbal ability) predicted inferences were different for the certain and uncertain forms, the process common to each of these findings is the experience of analytic – experiential conflict. In general, when conflict is not elicited by task content (e.g., alternative antecedents are available, disablers are not activated), individual differences in reasoning are minimal (Stanovich, 1999; Stanovich & West, 2000). Two questions remain: What do individual differences in verbal ability actually index? And, why did thinking dispositions predict inferences across forms, even when (theoretically) analytic – experiential conflict did not occur on some problems? In response to the first question, the PMA Verbal Meaning test, although somewhat outdated, is a good indicator of crystallised intelligence (Schaie & Willis, 1996). In addition, Klaczynski and Gordon (1996) reported that the test


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correlates moderately well with measures of fluid intelligence and well with overall IQ (r = .64; and, as noted previously, verbal ability is the best single predictor of general intelligence). Consequently, although caution should be taken in interpreting our findings, we consider the verbal meaning test a very rough indicator of the capacities to engage in analytic reasoning by suppressing experiential processing interference. If this claim is granted, then our findings extend those of Stanovich and West (1997, 1998a, 1998b) and others (e.g., Handley et al., 2004; Newstead et al., 2004) to the realm of conditional inferences. Consistent with Stanovich and West (e.g., 1997, 1998a; see also Newstead et al., 2004), thinking dispositions predicted significant variance on problems that elicited analytic – experiential conflict beyond that accounted for by verbal ability. This finding is consistent with Stanovich and West’s (1998a) analysis of correlations among various tasks from the ‘‘heuristics and biases’’ literature (see Kahneman, Slovic, & Tversky, 1982). Specifically, Stanovich and West (see also Klaczynski, 2001a) also found that ability (indexed by SAT scores) and thinking dispositions accounted for significant variance on tasks involving, for instance, counterfactual reasoning, syllogistic reasoning, and covariation detection. One of the main points taken from these data is that, if computational limitations are indexed by measures of general ability, such limitations cannot entirely account for performance on a variety of reasoning and decision tasks. Rather, dispositional tendencies to actively regulate one’s thinking, decontextualise logical structures from potentially misleading content, and rely on analytic processing in complex problem situations, explain variance in reasoning independently from general ability. However, thinking dispositions also predicted inferences on problems not believed to elicit conflict. Although we are not entirely certain of the reasons for these unexpected correlations, one possibility is that TD indexes dispositions to be intellectually engaged. It may be that, because more intellectual engaged individuals were less likely than less engaged individuals to make careless mistakes (e.g., misreading minor premises), they made more logical inferences on most problems. This suggestion, however, is in need of more careful study. To conclude, our findings suggest that the Klaczynski et al. (2004) argument that inferences on the certain forms are based on predominantly experiential processing and, on the uncertain forms, on predominantly analytic processing, is overly simplistic. In addition, our data partially support the theory of Evans and Over (2004) that analytic reasoning is often predominant on MT and the uncertain forms. Specifically, it appears that only individuals, higher in verbal ability and thinking dispositions, reason by supposition and by inhibiting disablers on MT. Similarly, although MP inferences are most often governed by experiential processing, higher ability,

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higher thinking disposition individuals rely more on analytic processing when conditionals activate disabling conditions. Manuscript received 29 September 2003 Revised manuscript received 20 October 2004

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