Two meanings of “if”? Individual differences in the interpretation of conditionals

Abstract

This work investigates the nature of two distinct response patterns in a probabilistic truth table evaluation task, in which people estimate the probability of a conditional on the basis of frequencies of the truth table cases. The conditional-probability pattern reflects an interpretation of conditionals as expressing a conditional probability. The conjunctive pattern suggests that some people treat conditionals as conjunctions, in line with a prediction of the mental-model theory. Experiments 1 and 2 rule out two alternative explanations of the conjunctive pattern. It does not arise from people believing that at least one case matching the conjunction of antecedent and consequent must exist for a conditional to be true, and it does not arise from people adding the converse to the given conditional. Experiment 3 establishes that people's response patterns in the probabilistic truth table task are very consistent across different conditionals, and that the two response patterns generalize to conditionals with negated antecedents and consequents. Individual differences in rating the probability of a conditional were loosely correlated with corresponding response patterns in a classical truth table evaluation task, but there was little association with people's evaluation of deductive inferences from conditionals as premises. A theoretical framework is proposed that integrates elements from the conditional-probability view with the theory of mental models.

Probability in reasoning: A developmental test on conditionals

“…However, as we noted above, it is interesting to note that about 30% of adults adopt a conjunctive response in truth-table tasks when the alternative responses are reduced to a true/false choice instead of allowing for the ''irrelevant'' response (Gauffroy & Barrouillet, 2011). Even more interestingly, Oberauer et al (2007) observed that the adoption of a conjunctive response pattern in a two-valued truthtable task correlates with the tendency for conjunctive responses in the probability task. By contrast, the adoption of a material implication reading of the conditional in the two-valued truth-table task correlated with the conditional probability response in the probability task.…”

“…Evans et al (2003) reported about 50% of conditional probability patterns and about 43% of conjunctive patterns, whereas Oberauer and Wilhelm (2003) in their Experiment 3 identified only 44% of their participants as clearly conforming to the conditional probability response, whereas 34% privileged conjunctive responses. Oberauer, Geiger, Fischer, and Weidenfeld (2007) reported 57% of their participants exhibiting a conditional probability response in their Experiment 1, and 70% in their Experiment 3. Interestingly, Oberauer and Wilhelm (2003) asked their participants to assess both the probability of the conditional and the conditional probability.…”

Reasoning with conditionals: Does every counterexample count? It’s frequency that counts

“…Another, more recent approach to the understanding of conditionals advocates a probabilistic view, according to which conditionals are evaluated by comparing ruleconfirming instances of the pq conjunction with exceptional instances of the p¬q conjunction (Evans & Over, 2004;Evans et al, 2005;Oberauer et al, 2007). In this line of research, a probabilistic truth table task has been established that presents explicit frequency information about exceptional cases.…”

“…Participants are then asked to evaluate their belief in the conditional statement considering the frequency information given. In several studies Oberauer, Geiger, Fischer, & Weidenfeld, 2007;Oberauer & Wilhelm, 2003), the conditional probability P(q|p) had the largest influence on people's belief judgments.…”

The modulation of conditional assertions and its effects on reasoning

“…Likewise, many theorists have proposed that the probability of a conditional is the corresponding conditional probability of its consequent given its antecedent (e.g., Evans, Handley, Neilens, & Over, 2007;Evans, Handley, & Over, 2003;Hadjichristidis et al, 2001;Over, Hadjichristidis, Evans, Handley, & Sloman, 2007;Oberauer & Wilhelm, 2003). Oberauer and his colleagues have argued that the model theory needs to be revised in order to explain their participants' judgements of the probabilities of conditionals, which usually corroborated the conditional probability hypothesis (Oberauer, Geiger, Fischer, & Weidenfeld, 2007). However, according to the model theory, these judgements reflect the small-scope principle-that is, individuals take a question of the form:…”