On the Evaluation of If p then q Conditionals

We propose that when evaluating conditionals, people construct an imaginary world that contains the antecedent, and then evaluate the plausibility of the consequent being true in the same world. Thus, when asked for an estimate of the probability of the conditional, people should produce the conditional probability of its consequent given its antecedent. We contrast this view with a view based on the theory of mental models, in which the judged probability of a conditional is derived from the proportion of models in which the premises are true. Study 1 examined this hypothesis by comparing probability estimates for (i) category-based conditional arguments (e.g. If robins have ulnar arteries then sparrows have ulnar arteries), (ii) corresponding conditional probabilities in the form of suppositions (e.g. Suppose you knew that robins have ulnar arteries. How likely would you think it was that sparrows have ulnar arteries?) and (iii) the argument strength of corresponding inductive arguments (e.g. Fact: Robins have ulnar arteries. Therefore: Sparrows have ulnar arteries. How convincing do you find this argument?) All three estimates were highly correlated, a finding that supports our hypothesis. The similarity between the two categories (e.g. robins and sparrows) was also manipulated. Similarity affected all three estimates equally, similar items being given higher estimates than dissimilar items. This finding indicates that similarity is one basis for the plausibility judgements. Study 2 tested our hypothesis using conditional statements with known probabilities. The results favoured our hypothesis. We discuss these results in terms of philosophical and psychological views of conditionals, and suggest that they bring together kinds of reasoning that are traditionally studied separately, such as conditional reasoning, induction, and judgements of probability.