Conditional reasoning: The necessary and sufficient conditions.

Abstract

AbstractFive experiments investigated two theories of conditional reasoning. The pragmatic schema theory posits that conditional reasoning is mediated by context-sensitive inference rules. According to the contextual cuing theory, inferences are based on a mental model that represents necessity and sufficiency relations. Both schematic relations and necessity relations predicted responses on Wason's four-card selection task. In contrast, after the effects of perceived necessity had been partialled out, schematic relations did not predict responses to either a conditional arguments task, or a task in which subjects judged the similarity of and only statements. These findings question the assumption that reasoning is mediated by schematic rules, which presumably apply regardless of task. However, there was evidence to suggest that both schematic variables and the availability of counter-examples may be important in evaluating necessity relations, suggesting an alternative role for schematic-based interpretations in reasoning.Conditional reasoning involves drawing inferences about situations in which the occurrence of one event is conditional upon the occurrence of another event (e.g., if the car runs out of gas, then it stalls). Despite the apparent simplicity of this task, two decades of research have revealed that people reason inconsistently: They sometimes draw invalid inferences; at other times, they fail to draw valid inferences. The purpose of this research was to evaluate two current explanations for this variability in conditional reasoning performance. Cheng and Holyoak's (1985) pragmatic schema theory proposes that conditional reasoning performance is mediated by context-specific inference rules, and predicts that inference patterns will vary as a function of the reasoning schema that is evoked. According to the contextual cuing theory, the types of inferences made will vary as a function of the necessity and sufficiency of the conditional relation.These approaches are similar in that both propose a means of integrating the interpretation of conditional relations with the underlying inferential processes. However, they emphasize different interpretational variables (pragmatic context vs necessity/sufficiency), and propose different mechanisms for the generation of deductive inferences (abstract rules vs counter-examples). The purpose of this paper is to test predictions that contrast the two views, andto develop a theoretical position that integrates these two perspectives into a single framework.Conditional Reasoning PatternsConditional reasoning involves drawing inferences from conditional relations that are usually phrased p, then q, and are typically assessed using one of two tasks. The Wason selection task requires subjects to find the information necessary to determine whether a conditional relation is true or false (Wason, 1968). For example, if the rule was a card has a vowel on one then it has an even number on the other side, then finding an odd number opposite a vowel violates the rule. The conditional arguments task, on the other hand, requires subjects to evaluate the validity of inferences derived from a conditional rule.For a conditional arguments task, the subject is presented with a conditional relation, and is then asked to evaluate the validity of four logical questions or arguments, termed Modus Ponens (MP), Modus Tollens (MT), Denying the Antecedent (DA), and Affirming the Consequent (AC). Each argument involves an affirmation or negation of the antecedent (p) or consequent (q), as is illustrated below:1) If this tree is a spruce, then it has needles.MP: This tree is a spruce. Does it have needles? (YES)DA: This tree is not a spruce. Does it have needles? (MAYBE)AC: This tree has needles. Is it a spruce? (MAYBE)MT: This tree does not have needles. Is it a spruce? (NO)According to standard, propositional logic, the correct responses to the MP, DA, AC, and MT questions are yes, maybe, maybe, and no respectively. …