I motivate and characterize an intensional semantics for ‘ought’ on which it does not behave as a universal quantifier over possibilities. My motivational argument centers on taking at face value some standard challenges to the quantificational semantics, especially to the idea that ‘ought’-sentences satisfy the principle of Inheritance. I argue that standard pragmatic approaches to these puzzles are either not sufficiently detailed or unconvincing.

In classical logic, the proposition expressed by a sentence is construed as a set of possible worlds, capturing the informative content of the sentence. However, sentences in natural language are not only used to provide information, but also to request information. Thus, natural language semantics requires a logical framework whose notion of meaning does not only embody informative content, but also inquisitive content. This paper develops the algebraic foundations for such a framework. We argue that propositions, in order to embody (...) both informative and inquisitive content in a satisfactory way, should be defined as non-empty, downward closed sets of possibilities, where each possibility in turn is a set of possible worlds. We define a natural entailment order over such propositions, capturing when one proposition is at least as informative and inquisitive as another, and we show that this entailment order gives rise to a complete Heyting algebra, with meet, join, and relative pseudo-complement operators. Just as in classical logic, these semantic operators are then associated with the logical constants in a first-order language. We explore the logical properties of the resulting system and discuss its significance for natural language semantics. We show that the system essentially coincides with the simplest and most well-understood existing implementation of inquisitive semantics, and that its treatment of disjunction and existentials also concurs with recent work in alternative semantics. Thus, our algebraic considerations do not lead to a wholly new treatment of the logical constants, but rather provide more solid foundations for some of the existing proposals. (shrink)

The semantics for a deontic action logic based on Boolean algebra is extended with an interpretation of action expressions in terms of sets of alternative actions, intended as a way to model choice. This results in a non-classical interpretation of action expressions, while sentences not in the scope of deontic operators are kept classical. A deontic structure based on Simons’ supercover semantics is used to interpret permission and obligation. It is argued that these constructions provide ways to handle various problems (...) related to free choice permission. The main result is a sound and complete axiomatization of the semantics. (shrink)

This paper refutes the widespread view that disjunctions of imperatives invariably grant free choice between the actions named by their disjuncts. Like other disjunctions they can also express a correlation with some factual distinction, but as with modalized declaratives used for non-assertive speech acts this needs to be indicated explicitly. A compositional analysis of one such indicator, depending on, constitutes the point of departure for a uniform analysis of disjunctions across clause types. Disjunctions are analyzed as sets of propositional alternatives (...) that correlate with a partition that the speaker may or may not be able to indicate explicitly. Free choice arises as the specific case where the partition is induced by the preferences of the addressee. (shrink)

Disjunctions in the scope of possibility modals give rise to a conjunctive inference, generally referred to as ‘free choice.’ For example, Emma can take Spanish or Calculus suggests that Emma can take Spanish and can take Calculus. This inference is not valid on standard semantics for modals in combination with a Boolean semantics for disjunction. Hence free choice has sparked a whole industry of theories in philosophy of language and semantics. This paper investigates free choice in sentences involving a non-monotonic (...) modified numeral, under which we embed a possibility modal scoping over disjunction. One example is Exactly one student can take Spanish or Calculus. As we point out, the presence of certain readings of these sentences is a key test for a prominent approach, which analyzes free choice as a kind of scalar implicature. We report on two experiments investigating the readings of such sentences, using an inferential task. Our results are challenging for the implicature approach. We sketch two possible solutions within this approach, either adopting a different recent implicature algorithm, or exploring a different meaning for modified numerals with exactly. Both of them suffer from a variety of problems. We then discuss a third solution, which exploits a recent account of free choice based on homogeneity. This approach can account for our results, in combination with plausible assumptions about homogeneity projection, though it too has open issues with related cases. Regardless of which solution is chosen, non-monotonic contexts turn out to be an important test case for theories of free choice, implicature, and modified numerals. (shrink)

We discuss the semantic significance of a puzzle concerning ‘ought’ and conditionals recently discussed by Kolodny and MacFarlane. We argue that the puzzle is problematic for the standard Kratzer-style analysis of modality. In Kratzer’s semantics, modals are evaluated relative to a pair of conversational backgrounds. We show that there is no sensible way of assigning values to these conversational backgrounds so as to derive all of the intuitions in Kolodny and MacFarlane’s case. We show that the appropriate verdicts can be (...) derived by extending Kratzer’s framework to feature a third conversational background and claiming that the relevant reading of ‘ought’ is sensitive to this parameter. (shrink)