‘If’, ‘or’, and the possibilities they refer to: A new paper in JEP:LMC

Ruth Byrne and Phil Johnson-Laird published a new paper in the Journal of Experimental Psychology: Learning, Memory, and Cognition that describes studies on the real and counterfactual possibilities that if and or refer to. The paper’s abstract is here:

The theory of mental models postulates that conditionals and disjunctions refer to possibilities, real or counterfactual. Factual conditionals, for example, “If there’s an apple, there’s a pear,” parallel counter- factual ones, for example, “If there had been an apple, there would have been a pear.” A similar parallel underlies disjunctions. Individuals estimate the probabilities of conditionals by adjusting the probability of their then-clauses according to the effects of their if-clauses, and the probabilities of disjunctions by a rough average of the probabilities of their disjuncts. Hence, the theory predicts that estimates of the joint probabilities of these assertions with each of the four cases in their partitions will be grossly subadditive, summing to over 100%. Five experiments corroborated these predictions. Factual conditionals and disjunctions were judged true in the same cases as their counterfactual equivalents, and the sum of their joint probabilities with cases in the partition ranged from 240% to 270% (Experiments 1a, 1b). When participants were told these probabilities should not sum to more than 100%, estimates of the probability of A and C, as the model theory predicts, were higher for factual than counterfactual conditionals, whereas estimates of the probability of not-A and not-C had the opposite difference (Experiment 1c). Judgments of truth or falsity distinguished between conditionals that were certain and those that might have counterexamples (Experiment 2a), whereas judgments of the likelihood of truth reflected the probabilities of counterexamples (Experiment 2b). We discuss implications for alternative theories based on standard logic, suppositions, probabilistic logic, and causal Bayes networks.

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