Imperatives lie at the heart of both practical and moral reasoning, yet they have been overshadowed by propositions and relegated by many philosophers to the status of exclamations. One reason for this is that a sentence’s having literal meaning seems to require its having truth-conditions and ‘Keep your promises!’ appears to lack such conditions, just as ‘Ouch!’ does. One reductionist attempt to develop a logic of imperatives translates them into declaratives and construes inferential relations among the former in terms of inferential relations among the latter. Since no such reduction seems fully to capture the meaning of imperatives, others have expanded our notion of inference to include not just truth – but also satisfaction – preservation, according to which an imperative is satisfied just in case what it enjoins is brought about.
A logic capturing what is distinctive about imperatives may shed light on the question whether an ‘ought’ is derivable from an ‘is’; and may elucidate the claim that morality is, or comprises, a system of hypothetical imperatives. Furthermore, instructions, which are often formulated as imperatives (‘Take two tablets on an empty stomach!’), are crucial to the construction of plans of action. A proper understanding of imperatives and their inferential properties may thus also illuminate practical reasoning.
Subgradients of algebraically convex functions: a Galois connection relating convex sets and subgradients of convex functions