Deductive updating is not Bayesian.

Abstract

One of the major debates concerning the nature of inferential reasoning is between counterexample-based theories such as mental model theory and probabilistic theories. This study looks at conclusion updating after the addition of statistical information to examine the hypothesis that deductive reasoning cannot be explained by probabilistic inferences. In Study 1, participants were given an initial "If P then Q rule" for a phenomenon on a recently discovered planet, told that "Q was true," and asked to make a judgment of either deductive validity or probabilistic likelihood of the putative conclusion that "P is true." They were then told the results of 1,000 observations. In the low-probability problem, 950 times P was false and Q was true, whereas 50 times P was true and Q was true. In the high-probability problem, these proportions were inverted. On the low-probability problem, probabilistic ratings and judgments of logical validity decreased. However, on the high-probability problem, probabilistic ratings remained high whereas judgments of logical validity significantly decreased. Confidence ratings were consistent with this different pattern for probabilistic and for deductive inferences. Study 2 replicated this result with another form of inference, "If P then Q. P is false." These results show that deductive updating is not explicable by Bayesian updating.