How people interpret conditionals: Shifts toward the conditional event.

Abstract

We investigated how people interpret conditionals and how stable their interpretation is over a long series of trials. Participants were shown the colored patterns on each side of a 6-sided die and were asked how sure they were that a conditional holds of the side landing upward when the die is randomly thrown. Participants were presented with 71 trials consisting of all combinations of binary dimensions of shape (e.g., circles and squares) and color (e.g., blue and red) painted onto the sides of each die. In 2 experiments (N₁ = 66, N₂ = 65), the conditional event was the dominant interpretation, followed by conjunction, and material conditional responses were negligible. In both experiments, the percentage of participants giving a conditional event response increased from around 40% at the beginning of the task to nearly 80% at the end, with most participants shifting from a conjunction interpretation. The shift was moderated by the order of shape and color in each conditional's antecedent and consequent: Participants were more likely to shift if the antecedent referred to a color. In Experiment 2 we collected response times: Conditional event interpretations took longer to process than conjunction interpretations (mean difference = 500 ms). We discuss implications of our results for mental models theory and probabilistic theories of reasoning.

Probability in reasoning: A developmental test on conditionals

“…It should be noted that an alternative explanation of this developmental trend has been recently proposed by Fugard et al (2011) who suggest an inhibitory account. The trend from a conjunctive to a defective biconditional and then a defective conditional response would reflect a narrowing of the hypothetical scope.…”

“…Empirical evidence supporting this proposal is based on a probabilistic truth table task (hereafter, the probability task) in which participants are asked to assess the probability of an If p then q conditional from the probabilities of the four truth-table possibilities p & q, p & not-q, not-p & q, not-p & not-q. Several studies observed that a majority of adults judge the probability of the conditional as the conditional probability P(q|p), that is the probability of p & q divided by the summed probabilities of p & q and p & not-q (Evans, Handley, & Over, 2003;Fugard, Pfeifer, Mayerfofer, & Kleiter, 2011;Oberauer & Wilhelm, 2003;Over, Hadjichristidis, Evans, Handley, & Sloman, 2007).…”

“…Thus, it could be argued that our task mainly solicited counterfactual-based reasoning, hence the strong development we observed, instead of the probabilistic reasoning theorized by the new paradigm psychology of reasoning. However, this same task is usually considered as providing one of the strongest evidence supporting the probabilistic view of reasoning (Evans et al, 2005;Fugard et al, 2011). Moreover, the dual-process view advocated by Verschueren et al (2005) and Markovits (2014) establishes a clear demarcation between deductive and probabilistic forms of reasoning, whereas one of the ultimate claims of the new paradigm is that deductive processes are probabilistic in nature.…”

Statistical models as cognitive models of individual differences in reasoning

“…Other research has explored how people can be trying to solve different tasks, for instance, because they interpret the task in different ways (Adler 1984;Politzer 1986;van Lambalgen 2004, 2005;Stenning and Cox 2006;Fugard, Pfeifer, Mayerhofer, and Kleiter 2011). Consider, for example, the premises, 'if the wireless router is switched on, then I can connect to the Internet' and 'the wireless router is switched on'.…”

Reasoning as we read: Establishing the probability of causal conditionals

“…One group based their belief on P(q|p), while the other, slightly smaller group based their belief on P(pq) (see also Oberauer & Wilhelm, 2003;Politzer, Over, & Baratgin, 2010, for similar findings). It has since been shown that adults who initially judge a conditional as P(pq) tend to switch to a P(q|p) interpretation as more and more trials are presented (Fugard, Pfeifer, Mayerhofer, & Kleiter, 2011). The influence of P(pq) has been attributed to a form of shallow processing (Evans et al, 2003) and also to individual differences in cognitive ability (Evans, Neilens, & Over, 2008); however, this effect has not been consistently replicated in the literature (Evans, Handley, Neilens, & Over, 2007).…”