How to infer possibilities: A reply to Oaksford et al. (2018)

Individuals draw conclusions about possibilities from assertions that make no explicit reference to them. The model theory postulates that assertions such as disjunctions refer to possibilities. Hence, a disjunction of the sort, A or B or both, where A and B are sensible clauses, yields mental models of an exhaustive conjunction of possibly A, possibly B, and possibly both A and B, which each hold in default of information to the contrary. Oaksford, Over, and Cruz (this issue) are critical of the model theory and defend a probabilistic approach to reasoning. In this reply, we deal with their three main claims: (a) Our results concern only the periphery of their probabilistic theory. We show that they refute their theory insofar as it applies to possibilities. (b) The model theory leads to logical absurdities. We rebut this criticism as it applies to the model theory in Hinterecker, Knauff, and Johnson-Laird (2016), and explain why standard modal logics, which concern possibilities, do not set appropriate norms for inferences about them. (c) The algorithm for reasoning based on models needs a normative theory. In fact, it has such a theory, but the demand for "a specification of a sound, complete, and decidable normative system" is chimerical for everyday reasoning. (PsycINFO Database Record (c) 2019 APA, all rights reserved).