A logical account of free choice imperatives∗ Maria Aloni and Ivano Ciardelli Institute for Logic, Language, and Computation, University of Amsterdam
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[email protected] But how many kinds of sentence are there? Say assertion, question, and command? { There are countless kinds [... ] Wittgenstein, PU, x23 Abstract Since Ross's observation that the instruction Post this letter does not entail Post this letter or burn it, imperatives have constituted a challenge for the logician. Building on ideas from inquisitive semantics, we propose an account in which imperatives are regarded as partial specifications of a set of options. We show that this account avoids Ross's paradox and gives rise to a sensible notion of imperative entailment. 1 A na¨ıve attempt A hypothesis What is the meaning of an imperative sentence, such as Close the door? In the case of a declarative sentence, its meaning is usually taken to lie in its truth condi- tions, which define what a state of affairs must be like in order for the sentence to be true. In this view, we can think of a declarative sentence as a partial specification of a certain state of affairs. Technically, states of affairs are modeled by means of the notion of a possible world, and truth conditions for sentences come in the form of a definition of a satisfaction relation j=, relating possible worlds to sentences. If j'j = fw j w j= 'g denotes the set of worlds where the declarative sentence ' is true, then ' may be formally thought of as partially specifying a state of affairs by locating it within the set j'j.