The meaning(s) of conditionals: conditional probabilities, mental models, and personal utilities

Five experiments were conducted to test the hypothesis that people understand conditional statements ("if p then q") as indicating a high conditional probability P(q|p). Participants estimated the probability that a given conditional is true (Experiments 1A, 1B, and 3) or judged whether a conditional was true or false (Experiments 2 and 4) given information about the frequencies of the relevant truth table cases. Judgments were strongly influenced by the ratio of pq to p¬q cases, supporting the conditional probability account. In Experiments 1A, 1B, and 3, judgments were also affected by the frequency of pq cases, consistent with a version of mental model theory. Experiments 3 and 4 extended the results to thematic conditionals and showed that the pragmatic utility associated with believing a statement also affected the degree of belief in conditionals but not in logically equivalent quantified statements