We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: “MP”, Affirmation of the Consequent “AC”) and denial problems (Denial of the Antecedent “DA”, and Modus Tollens “MT”). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are reliable effects of (...) a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

We tested the hypothesis that choices determined by Type 1 processes are compelling because they are fluent, and for this reason they are less subject to analytic thinking than other answers. A total of 104 participants completed a modified version of Wason's selection task wherein they made decisions about one card at a time using a two-response paradigm. In this paradigm participants gave a fast, intuitive response, rated their feeling of rightness for that response, and were then allowed free time (...) to reconsider their answers. As we predicted, answers consistent with a matching heuristic were made more quickly than other answers, were given higher FOR ratings, and received less subsequent analysis as measured by rethinking time and the probability of changing answers. These data suggest that reasoning biases may be compelling because they are fluently generated; this is turn creates a strong FOR, which acts as a signal that further analysis is not necessary. (shrink)

Does reasoning occur on the Wason selection task, or are card selections determined purely on the basis of heuristic processes? To answer this question two relevance-based theories of reasoning are compared: (1) the theory of Evans (1984, 1989; Evans & Over, 1996), which takes the heuristic viewpoint, and (2) the theory of Sperber, Cara, and Girotto (1995), which takes the reasoning viewpoint. In three experiments, the effect of removing matching cards from the selection task array is examined. It is argued (...) that the Sperber et al. theory makes clearer predictions about the results of these manipulations, which are confirmed, and that the Evans theory can only accommodate them if it allows the operation of reasoning processes. The results are also discussed in relation to Roth's (1979) account of the selection task, mental models theory, and information gain theory. (shrink)

Yama (2001) argued that the matching bias effect was an amalgam of a genuine matching effect and a set size effect. However, Evans (2002) pointed out some problems with Yama's argument. One was on the matching index used in Yama (2001). The others concerned a gap between Yama's (2001) interpretation of matching bias and Evans' (1998) recent discussions that had placed emphasis on the problem of implicit negation. I reply to these claims taking Oaksford (2002) into consideration. Further, I propose (...) a framework connecting context, goal, utility, and relevance, and including a hierarchical structure of goals. I argue that theories of reasoning can be developed and extended with the framework. (shrink)

It has been reported as a robust effect that people are likely to select a matching case in the Wason selection task. For example, they usually select the 5 case, in the Wason selection task with the conditional "if an E, then a not-5". This was explained by the matching bias account that people are likely to regard a matching case as relevant to the truth of the conditional (Evans, 1998). However, because a positive concept usually constructs a smaller set (...) than its negative one does (a rarity assumption), it is more effective to get information on the truth of the conditional in a positive set than in a negative set. Thus the optimal data selection account can also explain the effect. The set size of Q and matching by introducing negation were manipulated independently in four experiments. From the results it was inferred that the so-called matching bias was an amalgam of two different cognitive components-relevance judgement by matching and optimal data selection. (shrink)

We report two studies on the effect of implicitly versus explicitly conveying affirmation and denial problems about conditionals. Recently Evans and Handley (1999) and Schroyens et al. (1999b, 2000b) showed that implicit referencing elicits matching bias: Fewer determinate inferences are made, when the categorical premise (e.g., B) mismatches the conditional's referred clause (e.g., A). Also, the effect of implicit affirmation (B affirms not-A) is larger than the effect of implicit denial (B denies A). Schroyens et al. hypothesised that this interaction (...) is due to uncertainty in the case-wise affirmation of the contrast class of negated elements involved in implicit affirmations. In Experiment 1 we tested this hypothesis by manipulating the set size of the conditional clauses. The results confirm that binary sets, where the contrast class is a singleton, eliminate the differential effect of implicit affirmation and denial. With non-binary sets the interaction is not modulated by the scope of the contrast class (3, 5, 9 elements). Experiment 2 further investigated the role of contrast classes by using class inclusion to construct implicit affirmations (Mammal vs Mammal or Monkey) and implicit denial (No-Mammal vs Mammal or Monkey), in addition to the standard implicit problems mediated by contrast-class inclusion [(No-)Mammal/No-Mammal; Reptile; Snake). Findings indicate that class inclusion (Mammal/Monkey; Reptile/ Snake) only marginally affects performance, and is independent of the type of problem. This would suggest that the implicitness problem-type interaction is dependent on constructing contrast classes. However, the experiment failed to replicate the interaction, even on the subset of problems repeating the abstract letter/number format of Experiment 1. Moreover, with the natural binary set-sizes (vowels/consonants) the implicitness effect was eliminated entirely. (shrink)

In this paper the arguments for optimal data selection and the contrast class account of negations in the selection task and the conditional inference task are summarised, and contrasted with the matching bias approach. It is argued that the probabilistic contrast class account provides a unified, rational explanation for effects across these tasks. Moreover, there are results that are only explained by the contrast class account that are also discussed. The only major anomaly is the explicit negations effect in the (...) selection task (Evans, Clibbens, & Rood, 1996), which it is argued may not be the result of normal interpretative processes. It is concluded that the effects of negation on human reasoning provide good evidence for the view that human reasoning processes may be rational according to a probabilistic standard. (shrink)

Two experiments are reported that employed think-aloud methods to test predictions concerning relevance effects and rationalisation processes derivable from Evans' (1996) heuristic-analytic theory of the selection task. Evans' account proposes that card selections are triggered by relevance-determining heuristics, with analytic processing serving merely to rationalise heuristically cued decisions. As such, selected cards should be associated with more references to both their facing and their hidden sides than rejected cards, which are not subjected to analytic rationalisation. Experiment 1 used a standard (...) selection-task paradigm, with negative components permuted through abstract conditional rules. Support was found for all heuristic-analytic predictions. This evidence was shown to be robust in Experiment 2, where "select - don't select" decisions were enforced for all cards. Both experiments also clarify the role played by secondary heuristics in cueing the consideration of hidden card values during rationalisation. We suggest that whilst Evans' heuristic-analytic model and Oaksford and Chater's (e.g., 2003) optimal data selection model can provide compelling accounts of our protocol findings, the mental models theory fares less well as an explanation of our full dataset. (shrink)

We propose that the pragmatic factors that mediate everyday deduction, such as alternative and disabling conditions (e.g. Cummins et al., 1991) and additional requirements (Byrne, 1989) exert their effects on specific inferences because of their perceived relevance to more general principles, which we term SuperPs. Support for this proposal was found first in two causal inference experiments, in which it was shown that specific inferences were mediated by factors that are relevant to a more general principle, while the same inferences (...) were unaffected by factors not relevant to the general principle. These results were extended to deontic inferences in two further experiments. Taken together, these findings show that unstated superordinate principles play a significant role in certain types of reasoning. Questions raised by the findings for the main theoretical approaches are discussed. (shrink)

In certain contexts reasoners reject instances of the valid Modus Ponens and Modus Tollens inference form in conditional arguments. Byrne (1989) observed this suppression effect when a conditional premise is accompanied by a conditional containing an additional requirement. In an earlier study, Rumain, Connell, and Braine (1983) observed suppression of the invalid inferences "the denial of the antecedent" and "the affirmation of the consequent" when a conditional premise is accompanied by a conditional containing an alternative requirement. Here we present three (...) experiments showing that the results of Byrne (1989) and Rumain et al. (1983) are influenced by the answer procedure. When reasoners have to evaluate answer alternatives that only deal with the inferences that can be made with respect to the first conditional, then suppression is observed (Experiment 1). However, when reasoners are also given answer alternatives about the second conditional (Experiment 2) no suppression is observed. Moreover, contrary to the hypothesis of Byrne (1989), at least some of the reasoners do not combine the information of the two conditionals and do not give a conclusion based on the combined premise. Instead, we hypothesise that some of the reasoners have reasoned in two stages. In the first stage, they form a putative conclusion on the basis of the first conditional and the categorical premise, and in the second stage, they amend the putative conclusion in the light of the information in the second premise. This hypothesis was confirmed in Experiment 3. Finally, the results are discussed with respect to the mental model theory and reasoning research in general. (shrink)

Yama (2001) has presented an ingenious series of experiments in which he attempts to separate two accounts in the literature of the cause of "matching bias" in conditional reasoning. One account is that the bias arises from the way in which people process negations and the other is that it is due to the larger set sizes associated with negative propositions, rather than negation per se . Yama's experiments show influences of both negation and set size, from which he concludes (...) that both factors contribute to the matching bias that is normally observed. In this note, it is argued that this conclusion is at odds with other findings in the literature, particularly those investigating implicit negation as the cause of the bias. Introducing explicit negations has been shown to remove matching bias completely and not partially, as Yama's account must predict. A possible reconciliation is proposed in terms of subtle contextual differences introduced by Yama's experiments. (shrink)

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (shrink)

The phenomenon known as matching bias consists of a tendency to see cases as relevant in logical reasoning tasks when the lexical content of a case matches that of a propositional rule, normally a conditional, which applies to that case. Matching is demonstrated by use of the negations paradigm that is by using conditionals in which the presence and absence of negative components is systematically varied. The phenomenon was first published in 1972 and the present paper reviews the history of (...) research and theorising on the problem in the subsequent 25 years. Theories of matching bias considered include those based on several broad frameworks including the heuristic-analytic theory, the mental models theory, the theory of optimal data selection, and relevance theory as well as the specific processing-negations account. The ability of these theories to account for a range of phenomena is considered, including the effects of linguistic form, realistic content, and explicit negation on the matching bias effect. Of particular importance are recent findings showing that the bias is observable on a wider range of linguistic forms than has generally been thought, and that it is almost entirely dependent on the use of implicit negation in the logical cases to which rules are applied. The reasons for the general suppression of matching when realistic content is used are, however, unclear and a need for further research is identified here. It is concluded that matching bias is a highly robust effect which is closely connected with the problem of understanding implicit negation. Most of the theories in the literature are unable to account for at least some of the major phenomena discovered in research on the bias. The accounts that fare best are those that posit local effects of negation, including the heuristic-analytic and processing negations theories. (shrink)

Recent empirical studies raise methodological concerns about the use of intuitions in philosophy. According to one prominent line of reply, these concerns are unwarranted since the empirical studies motivating them do not control for the putatively characteristic phenomenology of intuitions. This paper makes use of research on metacognitive states that have precisely this phenomenology to argue that the above reply fails. Furthermore, it shows that empirical findings about these metacognitive states can help philosophers make better informed assessments of their warrant (...) for relying on intuitions in inquiry. (shrink)