Abstract

Which premisses should we use to start our inquiries? Which transitions during inquiry should we take next? When should we switch lines of inquiry? In this paper, I address these open questions about inquiry, formulating novel norms for such decisions during deductive reasoning. I use the first-order predicate calculus, in combination with Carnap’s state description framework, to state such norms. Using that framework, I first demonstrate some properties of sets of sentences used in deduction. I then state some norms for decisions made during deductive reasoning, establishing initial benchmarks for efficient deduction by ideal reasoners. When deciding which transition to make next, reasoners should choose the most informative transition, the one that maximally reduces uncertainty in the sense of ruling out the largest number of state descriptions relevant to their inquiry. Finally, inspired by optimal foraging theory, I show that, under certain assumptions of ignorance, reasoners should change premiss sets when their information intake drops below the global average information intake across premiss sets.