Uncertainty and conjunction fallacies
This chapter examines conjunction fallacies. This phenomenon is a topic in the psychology of reasoning and is not strictly linguistic, but it is related to pragmatics. Monads are shown to capture conjunction fallacies compositionally, which has eluded prominent prior theories. The chapter contrasts a monad built around the probability semiring with one built around a simpler semiring, the one semiring. The choice between the probability and one semirings partially predicts experimental participants’ behaviour. This points to an explanation in terms of the satisficing heuristic, rather than the representativeness heuristic. The chapter explores two options for fully predicting the results. The first is to use Gricean pragmatics in addition to the one semiring. The second is to use alternative underlying semirings for the monad: tropical semirings. This alternative compositional solution achieves a highly satisfying fit with aggregate psychological data and preserves an interesting duality between the logical operations of conjunction and disjunction. Some exercises are provided to aid understanding.