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A test of a two-stage model of the evaluation of conditional hypotheses.

This paper tests a model of performance in tasks involving the evaluation of conditional hypotheses using items of information suggested by the experimenter. The model is also used to explain how performance in such tasks changes from early adolescence to adulthood. This introduction will first describe the origin of the model in question and its relation to other views of such tasks and then use it to make some predictions about performance in conditional evaluation and related tasks. The task being examined is important in its own right as it involves a kind of inductive reasoning that is common both in everyday life and in scientific reasoning. As it is notorious that even well-educated adults have difficulty in performing correctly on such tasks, the practical benefits of understanding the origins of such difficulties and thus of devising ways of remediating them are considerable, particularly for science education. The model under investigation is also of more general psychological interest as it forms part of a wider theory about human logical competence that is significantly different from other approaches and appears to overcome some of their difficulties. Some indication of these more general implications of the study will be given at the conclusion of the paper.

In the most usual task of the kind under consideration, originally due to Johnson-Laird and Tagart (1969), subjects are given explicitly or implicitly universally quantified conditionals of the form "If one of a class of events X occurs, then one of a class of events Y occurs." Such conditionals are termed explicitly quantified when they contain explicit wording indicating that the statement is intended to cover all events of a certain kind. The commonest linguistic format of this kind used in formal studies has been "All Xs are Ys," though "Every X is a Y" and "If X occurs, then Y always occurs" are also formats of this kind. A universally quantified conditional is termed inexplicitly quantified when it has the same sense as such explicitly quantified conditionals but no explicit quantifying language is used, as in "If I eat breakfast, I don't eat lunch" and "If there is a triangle on the card, then it is colored red." For the second of these to be universally quantified we have to refer to the context. If it is applied to a set of cards, then it is universally quantified, but if it is applied to only one card then it is not. In the tasks under consideration, following presentation of the conditional statement, subjects are given four kinds of information with which to evaluate it. The conditional statement plays the role of a hypothesis and the pieces of information are used to evaluate it. The four kinds of information are: an example of X with one of Y;, an example of Y without one of X;, an example of X without one of Y, an occasion when neither occurs. Subjects are ideally offered the response options "Supports," "Tells you nothing," or "Disproves," used by Johnson-Laird and Tagart (1969). These are both the most logical reactions to the different kinds of information and those most often given when subjects are asked to produce their own replies.

This kind of task is distinct from information search tasks in which subjects are given a conditional hypothesis and then asked what kinds of information they would search for to test it. The most widely used task of this second kind is Wason's (1966) selection task. Although the present study was mainly designed to throw light on the process of information use with conditional hypotheses, some comments will be made in the concluding section regarding its implications for the study of search tasks.

Two approaches to conditional evaluation tasks involving information use have been prominent in psychological literature: the Piagetian approach, which is best summarized by Overton (1990); and that of Johnson-Laird (1986) and Johnson-Laird and Byrne (1991). The model to be examined here is more recent and is best summarized in Langford (1 992, in press-b). Four issues are of most significance in distinguishing between the three approaches; the analysis suggested of the language in which the task is framed; the way empirical results from such tasks are described and which of the conflicting claims about the results obtained from such tasks that are available in the literature are given credence by the theorist; the method used to assess interpretations of the meaning of the initial hypothesis on the part of subjects; the strategy or strategies that subjects are thought to bring to bear in deciding the implications of different items of information for the hypothesis. These issues will now be reviewed.

The analysis of the language of presentation favored by Langford (1 992, in press-b) has already been given above. It is evidently an empirical question as to whether explicitly and inexplicitly quantified conditionals and the various possible wordings available within each type are understood and processed in the same way. Much of the literature on conditional evaluation tasks involving information use involves either or both small and unrepresentative samples or other difficulties, such as the use of inappropriate response options (see Langford, 1992). The studies that involved the least problems of these kinds are those of Langford (in press-a, in press-b), which found that the explicitness of quantification has little influence on findings. The conclusion that the explicitness of quantification has minimal impact on the meanings that subjects take from conditionals is also reinforced by findings from tasks designed to give a direct assessment of such meanings (Langford, 1992). The only substantial exception to this conclusion is that explicitly quantified conditionals of the kind "Only Ys are Xs" are apparently interpreted somewhat differently from other kinds of conditional (Johnson-Laird & Byrne, 1989). In what follows it will be assumed that the more usual linguistic formulations of conditionals are under discussion.

The traditions of research on information use tasks with conditionals summarized in Overton (1990) and Johnson-Laird and Byrne (1991) are defective in their analyses of the language of such tasks. Their main failing is that they do not distinguish clearly enough between universally quantified conditionals, that are to be understood as true of all examples in a given universe of discourse, and singular or atomic conditionals that refer to a single pair of events. One significant error that has resulted from this is that both traditions refer to evaluation tasks involving information use as providing truth table analyses of the meanings of the conditionals assessed. This is a conceptual error, as philosophers only claim that entering the truth values of two particular events into a conditional will give its truth table if it is a singular or atomic conditional (a classic statement of this is contained in Wittgenstein, 1922; all modern textbooks on formal logic agree upon it). The truth table of a conditional is a table giving the truth values it assumes given all possible combinations of the truth and falsity of the antecedent and consequent. These combinations are: an example of X with one of Y, Y without X, X without Y, and neither event. For a singular conditional like "If I go out today, then I will get your shopping," these events make the conditional true, true, false and true, respectively. For a universally quantified conditional like "If I go out, then I will get your shopping," understood as applying to a certain range of days, such combinations of single events have no immediate relation to the truth table of the conditional at all. Whether we adopt the substitutional or the standard approach to quantification in logical semantics, to get the truth table of a universally quantified conditional we must review all possible examples within the universe of discourse (substitutional semantics is generally attributed to Wittgenstein, 1922, though he later abandoned it; reviews of standard semantics can be found in Hodges, 1983; Martin, 1987). A universally quantified conditional is true if there is no example of the antecedent without the consequent and false if there is such an example.

Overton (1990), Johnson-Laird (1986), and Johnson-Laird and Byrne (1991) provide only very partial reviews of empirical work on the evaluation of conditional hypotheses in information use tasks, focusing chiefly on their own, admittedly substantial, contributions. In a wider ranging review of the literature Langford (1992) concluded that, if we eliminate studies using small or unrepresentative samples and inappropriate response options, the predominant patterns of reply to the four kinds of information already listed are as follows. The first pattern is termed conjunctive-like and is "Supports, -, -, -," where - indicates any response; the second is termed biconditional-like and is "Supports, disproves, disproves, -"; the third is conditional-like and is "Supports, any reply except disproves, disproves, -."

The three approaches under consideration all agree that subjects may adopt three broadly differing interpretations of conditionals. Although Overton and Johnson-Laird describe these in their singular form, they will be given here in the quantified form advocated previously. For the conditional "If X occurs, then Y occurs," the conjunctive interpretation is that the expression means "Every event is X and Y'; the biconditional meaning is "If and only if X occurs, then Y occurs"; the conditional meaning is the logician's meaning of "If X occurs, then Y occurs," which implies that any combination of events may occur other than X without Y. The approaches agree that these interpretations tend to occur in this order during the development of the individual. Where they differ most is that, as already mentioned, Overton (1990) and

Johnson-Laird and Byrne (1991) think that conditional evaluation tasks give a direct index of the meaning of inexplicitly quantified conditionals by providing subjects' truth table interpretations. This idea should be rejected. Problems with their use of this task to index common interpretations are further increased by their reliance on the misleading surveys of the findings from such tasks just discussed. Johnson-Laird has also studied subjects' interpretations of explicitly quantified conditionals like "All the Xs are Ys" using more direct methods (see especially Johnson-Laird & Bara, 1984). Here again he found that conjunctive, biconditional, and conditional interpretations predominated. However, Johnson-Laird and Bara (1984) themselves pointed out that the tasks used to provide direct indices of such interpretations are themselves open to some question, mainly on the grounds that they unduly constrain subjects' replies and do not ask subjects to distinguish the necessary from the possible inclusion of a combination of events within the universe of discourse. Langford (1992) provided an even more extensive survey of this literature and concluded that these problems were serious enough to warrant greater reliance on an alternative method of assessing interpretations of both explicitly and inexplicitly quantified conditionals that asks subjects to say which combinations of events are necessarily, possibly, or definitely not included in the relevant universe of discourse if a conditional statement is true. This constrains subjects' possible replies considerably less than the other methods used and distinguishes the necessary from the possible occurrence of a combination. Results obtained using this task by Langford (1992, in press-b) and Langford and Hunting (in press) show that whereas the most common interpretations do resemble the traditional "conjunctive," "biconditonal," and "conditional" interpretations, they are considerably more varied than usually thought.

The fourth issue to be addressed is the strategy subjects are thought to use in interpreting information in conditional evaluation tasks involving information use. Overton (1990), Johnson-Laird (1986), and Johnson-Laird and Byrne (1991) see no need to consider this as a distinct phase of processing as they think such tasks provide truth tables. However, once we accept that the task cannot provide such tables when implemented with universally quantified conditionals, it is almost inevitable that we move to a two-stage model of task performance in which the meaning of the hypothesis is first interpreted and the implications of items of information are then assessed using some strategy for information use. Langford (1 992, in press-b) points out that one important dimension of such strategies is likely to be whether or not the stated hypothesis is tested against an alternative hypothesis or considered alone. He claimed that, in a task involving certain "nonstandard" conditionals that are implied rather than directly stated in the instructions, subjects often adopt a strategy of devising a plausible alternative hypothesis and using the testing strategy that if a combination of events is at least possible under both hypotheses it tells you nothing, but if it is possible under one and not the other it supports the hypothesis that makes it possible and disproves the other. However, in the usual conditional evaluation task he suggests that quantified conditionals are assessed using the following strategy, based on consideration of the target hypothesis alone: Combinations of events that must sometimes occur under the hypothesis support it; those that may occur support it or tell you nothing; those that cannot occur disprove it. The application of this strategy to the most common kinds of interpretation produces the three common patterns of response found in empirical studies of conditional evaluation tasks involving information use.

The object of the present study was to present simulated versions of the most common interpretations subjects give to standard conditional hypotheses, phrased in language that makes their meaning as unambiguous as possible. These were offered without suggested alternatives, as the model under investigation assumes that standard conditionals are usually dealt with without reference to such alternatives. The model of performance in such tasks of Langford (1992, in press-b) predicts common patterns of response to such simulated interpretations of conditionals. A second prediction depends on the assumption that the tendency to test against alternative hypotheses is similar for the simulated interpretations and standard conditionals. If this is so, the overall range and relative frequency of patterns of response when evaluating standard conditionals can be predicted from an assessment of the relative frequency of interpretations and patterns of response when evaluating simulated versions of these interpretations. Advocates of the approaches of Overton (1990) and Johnson-Laird and Byrne (1991) would conclude that the simulations of inexplicitly quantified conditionals offered here do not simulate the meanings of such conditionals as they understand them. This makes it impossible for these approaches to make this second prediction in regard to such conditionals. A third prediction, also only made by the two-stage model, is that individuals' patterns of response when evaluating a standard conditional are, to some extent, predictable from an assessment of the meaning they give to such a conditional and the pattern of response they give to a simulation of that meaning. However, both Newstead (1989) and Langford and Hunting (in press) provide indications that such predictions are likely to be only moderately successful, as interpretations appear to fluctuate considerably from occasion to occasion. These predictions were examined in relation to the two age ranges 12-13 and 19-29 years to assess the impact of developmental changes in hypothesis interpretations on results.

Method

Subjects

Eighty subjects were interviewed at each of the age ranges 12-13 and 19-29 years. The school age subjects were selected from students attending three state schools and one private Catholic school in the Melbourne metropolitan region by interviewing whole classes of students whose teachers had volunteered to participate in the project. The university age students were undergraduate students at La Trobe University, Melbourne, who were obtained by personal approach in the main university concourse. The university students were a selected group, compared to the general population, which may have amplified developmental trends.

Design

Half the subjects at 12-13 years and half at 19-29 years received the first interview described below and half the second. For half of those receiving each interview presentation was in the order described below, for half in a partially reversed order described in the procedure section. School age subjects were divided into groups of 20, with 3 such groups drawn from state schools and 1 from the Catholic school. Within each such group five subjects were assigned at random to each of the conditions just described.

Procedure

Each interview was read to subjects individually, who also had a written sheet containing the questions and pictures described below. Subjects were told before the interview they could ask questions if the meaning of any question was not clear. The first interview began "Suppose I have some packs of cards that contain only the following four kinds of cards." Then followed pictures of four rectangular cards, showing: an A in the left half and a B in the right; nothing in the left half and a B in the right: an A in the left half and nothing in the right; nothing in either half. Underneath each picture was its name, the names being; AB, -B, A-, and --. Item 1 in the first interview was: "I show you a pack of these cards and make the claim that it certainly contains AB cards, may contain -B and -- cards, but certainly does not contain A- cards. Suppose I shuffle the pack and turn over the top card. It is -B. Does this: (a) support my claim, (b) tell you nothing, (c) disprove my claim." The object of these instructions was to present a simulated version of a universally quantified conditional hypothesis in language that, unlike that usually used in presenting such hypotheses, is susceptible of little misinterpretation. This was then followed by the same question regarding the information that A-, AB, and -- cards had been turned over. items 2-4 presented the following hypotheses: "It certainly contains AB cards, may contain -- cards, but certainly does not contain -B or A cards"; "it certainly contains AB cards, may contain -B and -- cards, but certainly does not contain A- cards"; "it certainly contains AB cards, but certainly does not contain -B, A-, or -- cards." The studies of Langford (in press-a, in press-b) suggest that these items simulate common meanings given to conditional hypotheses other than the standard logic interpretation simulated in the first item. Items 5 and 6 presented for evaluation the universally quantified conditional hypotheses "Suppose I claim to have a pack of cards for which it is true that if there is an A on the left of the card, then there is a B on the right"; and ". . . for which it is true that all those with an A on the left have a B on the right." items 7 and 8 were tasks of the kind advocated by Langford (1992) and Langford and Hunting (in press) for evaluating the meanings given to quantified logical expressions. Items 7 and 8 asked subjects to indicate on a diagram consisting of pictures of the four kinds of card which kinds must be and which might be in a pack of which the above two statements, respectively, are true. The first part of Question 7 ran "Would you now please show on the diagram below which kinds of cards you think must be in a pack for which it is true that if there is an A on the left then there is a B on the right. Please do this by putting ticks below the pictures." The second part of Question 7 asked the same question for "which kinds of cards you think might be in a pack . . ." At the end of the interview subjects were asked, for each question, "Can you tell me how you went about answering this question?" The second interview asked the same questions about cards showing a black or white cat on the left and a black or white dog on the right. Half the interviewees received the interviews in the order given above and half with Items 1-6 in reverse order followed by Items 7 and 8 in reverse order, with order of information types within items 1-6 also reversed.

Results and Discussion

Items 1-4 simulated conditional-like (first version), biconditional-like, conditional-like (second version), and conjunctive-like interpretations, of conditionals, respectively. Details of the numbers of subjects choosing the interpretations corresponding to Items 1-4 at Items 7 and 8 now follow, with the interpretations corresponding to Items 1-4 listed in that order within each age group. For Item 7: 12-13-year-olds - 0, 8, 3, 36; 19-29-year-olds - 10, 21, 7, 18. For item 8: 12-13-year-olds - 1, 6, 4, 39; 19-29-year-olds - 11, 22, 4, 20. The interpretations simulated by Items 1 and 2 (conditional-like and biconditional-like) increase in frequency with age for both items, ps < .01, .05, for Item 7, and ps <.01, .05, for Item 8, by chi squared. The interpretation corresponding to item 4 (conjunctive-like) decreases with age for both items, ps < .01. These are similar to age trends noted in other studies (see Johnson-Laird & Bara, 1984; Langford, 1992 for reviews).

Common patterns of reply at items 1-4 were all consistent with use of the strategy suggested by Langford (1992, in press-b): cards that must sometimes occur under the target hypothesis provide support, those that may occur provide support or tell you nothing, those that cannot occur disprove the hypothesis. Subjects were considered to conform to a pattern if they showed at most two deviations from it. The most common patterns at Item 1 were: for 12-13-year-olds, 25 used the first, 28 the second; these figures for 19-29-year-olds were 26, 31. For Item 2 corresponding figures were: 12-13-year-olds 22, 30; 19-29-year-olds 34, 29. For Item 3 figures were: 12-13-year-olds 30, 27; 19-29-year-olds 35, 36. The hypothesis presented in item 4 contained no card that was in the "may occur" category and thus the only common pattern was the first. This occurred 57 times for the 12-13-year-olds and 62 times for the 19-21 -year-olds. There was little sign of appreciable age trends in the occurrence of patterns.

Patterns of reply at Items 5 and 6, which involved evaluation of standard conditionals, were coded into the common patterns outlined by Langford (1992, in press-b), which are the following replies to examples of X and Y, Y without X, X without Y, neither X nor Y: "Supports, any reply except disproves, disproves,-"; "Supports, disproves, disproves, -"; and "Supports, -, -, -," where - is any response. The following numbers of subjects' replies conformed to these three patterns respectively for Item 5: at 12-13 years, 1, 6, 35; at 19-29 years, 8, 29, 19. For Item 6 these numbers were: at 12-13 years, 0, 7, 37; at 19-29 years, 10, 27, 15. Frequency of the first (conditional-like) and second (biconditional-like) patterns increased with age for both items and that of the third (conjunctive-like) pattern decreased, ps < .01 by chi squared. These developmental findings are in accordance with trends in the occurrence of these patterns noted by Langford (in press-a, in press-b).

We now turn to prediction of these patterns of response from the meanings subjects gave to conditionals at items 7 and 8 and their responses to the simulated versions of the most common of these meanings given at Items 1-4. As already mentioned, it is not certain that the instructions used in these items produce just the same degree of reliance on testing hypotheses without recourse to alternatives as the presentation of hypotheses in standard conditional language. When asked how they went about answering questions, only 4 from 160 subjects reported use of alternative hypotheses in assessing either of the conditionals at Items 5 and 6, and between 15 and 20 did at Items 1-3 and none did at item 4. Although the differences between the proportions using alternatives at Items 5 and 6 and those using them at Items 1-3 are not significant, there is some sign that such use was more common at the latter items. However, this relatively minor discrepancy would not have much effect on the analysis of patterns of response that follows.

The dominant pattern of reaction to the simulated conjunctive interpretation presented in item 4 was "supports, disproves, disproves, disproves," whereas the predominant conjunctive-like reactions to the conditional evaluation task at Items 5 and 6 were, as in other studies, "supports, -, -, -," where - is any response. One origin of the greater variability in replies at the last three places, in tasks where the hypothesis is presented as a standard conditional, is probably the less common interpretations that involve some combination of "might" and "cannot occur" at these places. Such replies occurred in: 8 subjects of 12-13 years and 9 subjects of 19-29 years at Item 7; and 6 of 12-13 years and 7 of 19-29 years at Item 8. But even taking these interpretations into account, we would still expect a strong leaning to the "disproves" reply in the last three places within the conjunctive pattern, which was not found in this or earlier studies. This suggested that it may be incorrect to assume that when subjects do not pick either "must be in the pack" or "may be in the pack" during the tasks assessing interpretations, they have a definite opinion that the combination cannot be in the pack. In order to further assess this possibility a follow-up study was conducted in which forty 12-13-year-olds were given the items assessing the meanings of the two kinds of standard universally quantified conditional, half for cards with letters and half for cards with animals, in an alternative format in which they were offered the alternatives "must be in the pack," "may be in the pack," "cannot be in the pack," and "uncertain." This showed that, for the "if ..., then ..." conditionals, 23 of these subjects gave the pattern "must occur, X, X, X," for examples of the four kinds of information already listed, where X can be either "uncertain" or "cannot occur." All but four of these subjects gave at least one "uncertain" reply and 41 of a total of 69 replies at the last three places were "uncertain." Replies were similar for explicitly quantified conditionals of the form "all those with an A on the left have a B on the right,." This suggests that much of the variability in replies at the last three places for standard conditionals, among subjects who adopt a conjunctive interpretation, is because of uncertainty about the status of the last three kinds of combination.

The biconditional interpretation assessed in Item 2 ("must, cannot, cannot, may occur") gave rise, when presented for evaluation in that item, to the two patterns of reply "supports, disproves, disproves, tells you nothing" and "supports, supports, disproves, supports." This accounts for most of the biconditional-like pattern found in information use tasks ("supports, disproves, disproves, -"), except there are no "disproves" replies in the fourth place. The reply "supports, disproves, disproves, disproves" will, however, often occur in response to the conjunctive interpretation assessed in Item 4 ("must, cannot, cannot, cannot occur"). The conditional-like pattern in evaluation tasks ("supports, any reply except disproves, disproves, -") would arise from the conditional-like interpretations of conditionals realized in Items 1 and 3 ("must, may, cannot, may occur" and "must, may, cannot, cannot occur"). When presented for evaluation at Items 1 and 3 these gave rise to the response patterns: "supports, tells you nothing, disproves, tells you nothing"; "supports, supports, disproves, supports"; "supports, tells you nothing, disproves, disproves"; "supports, supports, disproves, disproves."

These findings confirm that most of the replies categorized as conditional-like, biconditional-like, and conjunctive-like in tasks requiring the evaluation of standard conditional hypotheses originate from corresponding conditional-like, biconditional-like, and conjunctive-like interpretations of these hypotheses. However, it should be emphasized that the names given to patterns of evaluation responses by Langford (1992, in press-b) are partially misleading, as some replies falling into some patterns appear to result from interpretations other than those implied by the pattern name. Notwithstanding this point, the tendency for the first two kinds of pattern to increase with age and for the third to decrease with age during adolescence can be explained as a product of corresponding developmental changes in the interpretations given to such hypotheses, as most examples of each pattern can be expected to arise from the corresponding interpretation.

The most plausible explanation for the developmental changes in interpretation just mentioned is a modified version of Inhelder's and Piaget's (1956) explanation proposed by Langford (1992, in press-b). Inhelder and Piaget (1956) thought that biconditional interpretations of causal conditional hypotheses are common in early adolescence because adolescents prefer to think in terms of definite monocausal relations between a single causal antecedent (e.g., variations in the length of a pendulum) and a single causal consequent (e.g., variations in the rate of oscillation). True conditional interpretations are later constructed from these connections between pairs of events via the realization that the consequent may have an additional possible cause, thus occurring in the absence of the original antecedent. Taking account of the presence or absence of two possible antecedents and a consequent involves eight possible combinations of events, which is beyond the processing capacity of younger adolescents. This makes them consider only one possible antecedent at a time, thus producing the biconditional interpretation that the consequent occurs if and only if the antecedent does. Langford (1992, in press-b) suggests that such definite connections between a single antecedent and a single consequent are preferred in dealing with all kinds of conditionals, but that the popularity of biconditional interpretations even among undergraduate samples suggests that the processing limitations that Inhelder and Piaget (1956) believed tended to disappear in mid-adolescence persist into adulthood. The conjunctive interpretation seems to represent an even more drastic attempt to limit the number of combinations of events considered by envisaging only "X with Y." The findings described here suggesting that subjects adopting conjunctive interpretations tend to be confused about the other combinations of the presence and absence of the two events support this view.

A popular alternative explanation of the tendency to convert conditionals to biconditionals ascribes it chiefly to discourse expectations, arguing that subjects take the implication, from Grice's (1975) maxim of quantity, that had the speaker expected that a second antecedent might be relevant they would have mentioned it (Fillenbaum, 1986; Geis & Zwicky, 1971; Knifong, 1974; Politzer, 1986; Rumain, Connell, & Braine, 1983). This is, however, contradicted by the studies of Byrnes and Overton (1986) and Langford (in press-a, in press-b), showing that deliberate mention of a second antecedent has little or no effect on performance in conditional evaluation tasks involving information use.

To gauge the possibility of predicting individual evaluations of standard quantified conditionals from assessed interpretations of such expressions, patterns of replies to Items 5 and 6 were coded according to the definitions of the three patterns of responses to information use tasks just discussed. If a subject interpreted Items 7 or 8 according to one of the four common interpretations realized in Items 1-4 then their behavior on the corresponding item from Items 1-4 was used to predict their behavior at Items 5 and 6. Thus if a subject interpreted the statement "if there is an A on the left, then there is a B on the right (of the card)" at Item 7 to mean the interpretation given in Item 2, then it was predicted that when asked to evaluate this hypothesis at Item 5 the subject would give the same pattern of responses as he or she gave at Item 2. For the "if ..., then ..." expression given in Item 5, the contingency coefficients relating predicted and observed occurrences of the three patterns of reply (conditional-like, biconditional-like, and conjunctive-like) were .45, .48, and .42 respectively, ps < .001. Percentages of 56, 64, and 66 of occurrences of these patterns at this item were correctly predicted, respectively. Corresponding coefficients for the explicitly quantified conditionals evaluated at Item 6 ("all those with an X on the left, have a Y on the right") were .46, .49, .46, ps < .001. Percentages of 58, 66, and 69 of occurrences of the three patterns at Item 6 were predicted. The relatively modest size of these contingency coefficients is probably caused by the fluctuations in interpretations of the same expression from one occasion to the next postulated by Newstead (1989) and Langford and Hunting (in press) and directly observed in informal studies by the present author.

In summary, the study supported all three kinds of prediction made by the two-stage model. The alternative approaches to conditional evaluation tasks of Johnson-Laird (1986), Johnson-Laird and Byrne (1991), and Overton (1990) are unable to make the second and third of these predictions in relation to inexplicitly quantified conditionals.

Concluding Discussion

The view of conditional evaluation tasks involving information use advocated here is part of a more general view of the development of logical reasoning in adolescence outlined by Langford (1992, in press-b) and Langford and Hunting (in press). This section will discuss the implications of the present study for this more general view.

Universally quantified conditionals like "All the Xs are Ys" and "If X occurs, then Y occurs" are part of fully quantified first order predicate logic, which is logic that deals with statements like "This event or object has quality X' and then combines them using the standard logical functors "if," "and," "or," and "not" and the quantificational notions "all," "some," "no." The meaning of expressions from this kind of logic is assumed to be represented by beliefs about the necessity, possibility, or impossibility of the existence of certain combinations of events within the relevant universe of discourse. As with conditionals, so for other kinds of expression we find considerable variation in the content of such beliefs between subjects, partly for developmental reasons of the kind discussed in the preceding section in relation to conditionals, but also partly because logic is not intensively taught in modern Western education systems and the meaning of logical expressions is acquired in an indistinct manner through everyday conversational exchanges. Thus Langford and Hunting (in press) reported that interpretations of the expressions "Some Xs are Ys" and "No Xs are Ys" tend to vary considerably among undergraduates.

It is a reasonable generalization of the approach to inductive information use tasks advocated here to suggest that in any such task involving expressions from quantified first order predicate logic, one of the various information use strategies suggested here is brought to bear upon whatever combinatorial representation of the hypothesis is formed. This suggests the research program of discovering which factors are responsible for encouraging use of a particular strategy (a range of likely parameters is discussed by Langford, 1992) and further examination of the combinatorial representations formed given a particular speech act conveying information about the hypothesis.

Inductive use of conditionals in information search tasks has been explored in a preliminary way within the present approach. In such tasks subjects are given a universally quantified conditional as a hypothesis and asked which kinds of information they would search for to test it. Initial findings from studies in progress by the author suggest that, once we remove certain artificial difficulties and ambiguities in Wason's (1966) information search task and most of its descendants in the literature, a majority of undergraduate subjects are capable of using the following search strategies for conditional (and presumably other) hypotheses quite efficiently. To find support for a hypothesis you should check combinations that are at least possible under the hypothesis to see if they exist, and you may also want to check that no impossible combinations exist. To disprove a hypothesis you should check impossible combinations to see they do not exist. The artificial difficulties and ambiguities in Wason's selection task that need to be removed to obtain these results are: use of a hypothesis that can involve the antecedent being on top of a card and the consequent underneath or vice versa (this is removed by using hypotheses similar to those used in the present study stating "If there is an X on the left of the card then there is a Y on the right"); the subject is not offered a choice of information types but a choice of which cards to turn over, having to infer which information types this could yield (this is overcome by offering a direct choice of the four possible combinations of the presence and absence of the two events involved in the conditional); Wason's instructions fail to indicate whether "testing" means searching for confirmation or disconfirmation of the hypothesis (this is overcome by making one request to look for information that would support the hypothesis and another to look for information that would disprove it); standard ways of scoring the task take insufficient account of the wide range of interpretations that subjects give to a conditional hypothesis (this can be partially overcome by employing a task to evaluate the subject's interpretation of the hypothesis similar to those used in the present study). This demonstration of a fairly high degree of rationality in a less artificial information search task than the Wason selection task using abstract standard "if ..., then ..." conditionals contrasts markedly with the prevailing belief that the average undergraduate is quite irrational in their search behavior for such expressions (for reviews see Cheng & Holyoak, 1985, 1989; Evans, 1989; Jackson & Grigggs, 1990; Johnson-Laird & Byrne, 1991).

The present approach has also been applied to deductive reasoning. By taking account of variations in the interpretation of expressions used as premises in syllogistic reasoning, employing the meaning evaluation technique advocated here, Langford and Hunting (in press) were able to use an adaptation of the model of syllogistic reasoning proposed by Johnson-Laird and Bara (1984) and Johnson-Laird and Byrne (1991) to provide much more detailed predictions regarding syllogistic production data than achieved by Johnson-Laird and his collaborators. The two approaches are much more compatible in this area than in that of inductive reasoning as syllogistic reasoning typically involves explicitly quantified expressions and Johnson-Laird and Byrne (1991) assume that such expressions are primarily represented in the combinatorial form advocated here.

References

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Author:Langford, Peter E.
Publication:The Psychological Record
Date:Mar 22, 1993
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