Two reasoning mechanisms for solving the conditional Fallacies

There are two different reasoning mechanisms for solving ‘ifthen’-problems: one is based on likelihood-estimates and is rather heuristic; the other one takes counterexamples into account and is analytic in nature. Based on the difference in input of the two reasoning mechanisms we found that the AC problem is mainly solved by using likelihood-information, whereas the DA problem is rather solved using counterexample-information. Mental models adepts have proposed some explanations to account for the differences in processing difficulty and speed between AC and DA. Considering the reasoning mechanism for AC and DA from a dual process perspective provides an extra explanation for the observed effects. This study indicates that framing observations in a dual process account can provide additional explanations for well-known phenomena. Introduction Reasoning with conditional sentences is one of the central activities of our daily life. By using conditionals people are able to predict and explain the occurrence of simple as well as complex effects. There are situations in which these inferences are made in an effortless and unconscious manner, in other situations reasoners consciously initiate a range of steps leading to a conclusion. This difference can be framed within the general idea of dual processes (see e.g., Evans & Over, 1996; Sloman, 1996; Stanovich & West, 2000). The dual process theories bear a family resemblance in distinguishing two types of cognitive processes. One process operates in a fast, heuristic, implicit way and leads to pragmatic conclusions. The other process is characterized by rather slow, analytic and explicit way of processing and yields more normative answers. In general the dual process theories suffer from a trade-off between scope and precision. The theories apply to a whole range of tasks: text comprehension, attribution, induction as well as deduction tasks, but in their general formulation they are not suited to make precise predictions in specific task contexts (see e.g., Sloman, 1996; Osman, 2002). The present article focuses on how simple everyday causal conditional arguments are solved. There are four conditional problem types: (1) modus ponens, MP: ‘if p, then q’, ‘p’, ‘q follows’ (2) modus tollens, MT: ‘if p, then q’, ‘not q’, ‘not p follows’ (3) affirmation of the consequent, AC: ‘if p, then q’, ‘q’, ‘p follows’ and (4) the denial of the antecedent, DA: ‘if p, then q’, ‘not p’, ‘not q follows’. These four conclusions are the default conclusions; when reasoners give this conclusion, we say that they accept the inference. In classical logic, MP and MT are considered valid inferences, whereas AC and DA are labeled fallacious. The distinction between valid inferences and ‘fallacies’ does not hold in everyday reasoning. The distinction valid/invalid is based on the material implication interpretation of the ‘ifthen’ connector: ‘p’ is sufficient but not necessary for ‘q’. In everyday (causal) reasoning there are sentences of all four possible combinations of sufficiency and necessity, so the material implication interpretation is just one out of four possible interpretations of ‘if-then’. In general, instead of considering the formal structure of the argument, reasoners draw a conclusion based on the problem content, namely whether the cause is necessary and/or sufficient for the effect (see e.g., Cummins, Lubart, Alsknis, & Rist, 1991; Thompson, 1994; Cummins, 1995; Newstead, Ellis, Evans, Dennis, 1997). Although the truth-functionality of the material implication does not apply to everyday reasoning in general, some reasoners can still take the logical validity of the inferences into account. Markovits and Barrouillet (2002) and De Neys, Schaeken, and d’Ydewalle (2003) claim that skilled reasoners can inhibit ‘relevant’ disabling information when they are solving MP and MT; even when the cause is not sufficient for the effect, MP and MT are still accepted. To avoid this possible interference of logical validity on the reasoning mechanism the present research will be confined to the solving of the so-called fallacies, AC and DA. To find out how AC and DA are solved, we elaborate on the question posed by Cummins (1995): Can naive human reasoning best be characterized as an inductive probabilistic process or is our naive understanding based on the consideration of alternative causes and disabling conditions? To answer this question the two processes are linked to two recent theories on deduction: the mental model account and the probabilistic account. The two processes are brought together in the dual process theory formulated by Evans and Over (1996), but the specification can also be linked to other dual process accounts. There is already evidence for this dual process specification for causal conditional reasoning: it was found that the heuristic reasoning mechanism delivers a fast output and uses likelihood-information as input, whereas the analytical process takes more time to produce a conclusion and takes counterexamples into account (Verschueren, Schaeken, & d’Ydewalle, 2003a). In this specification both reasoning mechanisms that Cummins proposed can be recognized: The heuristic process corresponds roughly to the inductive probabilistic process, whereas the analytical process focuses on counterexample retrieval. In general the characteristics of the two reasoning mechanisms for causal reasoning are summarized in Table 1. Table 1: Characteristics of the specified dual process theory.