The psychology of inferring conditionals from disjunctions: A probabilistic study

There is a new probabilistic paradigm in the psychology of reasoning that is, in part, based on results showing that people judge the probability of the natural language conditional, if  AAthen  BB, P(ifAthenB), to be the conditional probability, P(B∣A)P(B∣A). We apply this new approach to the study of a very common inference form in ordinary reasoning: inferring the conditional if not  -AAthen  BB from the disjunction AAor  BB. We show how this inference can be strong, with PP(if not  -AAthen  BB) “close to” P(AorB), when AAor  BB is non-constructively justified. When AAor  BB is constructively justified, the inference can be very weak. We also define suitable measures of “closeness” and “constructivity”, by providing a probabilistic analysis of these notions.

► Inferring if not  -AA then BB from AAor  BB is probabilistic strong when AAor  BB is non-constructively justified.
► When AAor  BB is non-constructively justified, the probability of the conditional, P(ifnot-AthenB), is “close” to the probability of the disjunction, P(AorB).
► A measure of closeness μμ is given for the extent to which P(ifnot-AthenB) is “close” to P(AorB).
► A measure of constructivity cc is given that is “high” for constructive inferences and low for non-constructive inferences.
► The representation of P(ifnot-AthenB) in terms of P(AorB) and P(not-A), or in terms of μμ and cc, is the same.