Option 1: Information-Sensitive Ordering Sources

Dowell (2012, 2013) suggests supplementing Kratzer’s semantics by making the ordering source of the subjective ‘should’ dependent on information-states. In cases like (8), where a should-sentence is true since it is true in light of a subject’s information-state, but not in light of the facts, the ordering source ranks worlds in light of the subject’s evidence, not in light of the facts. An ordering source sensitive to Sean’s lack of knowledge about the whereabouts of the miners is thought to rank a world where he blocks neither shaft higher than one where he blocks one of the shafts, even if the miners happen to be in that shaft. On this picture, the subjective ‘should’ is contextually sensitive to information-states in the sense that it is contextually sensitive to ordering sources, which again are sensitive to contextually salient information-states.

Before I move on to other suggestions of how to alter Kratzer’s semantics to accommodate information-sensitivity, a note on terminology. Dowell (2013: 158) draws the distinction between the subjective and objective deontic ‘should’ such that the hallmark of the subjective ‘should’ is that it is information-sensitive, whereas the objective ‘should’ isn’t since its ordering source is realistic. On my terminology, and the one of Kolodny and MacFarlane (2010: 117) and Wedgwood (forthcoming: sec. 4), on the other hand, the deontic ‘should’ is in general information-sensitive and the subjective and the objective ‘should’ are both instances of this information-sensitivity. The objective ‘should’ is also relativized to an information-state, but one that represents all the facts. I call this the

fully realistic information-state. This might not be anybody’s information-state (or only God’s), but since information-sensitivity is a merely technical term, I don’t see why we shouldn’t construe the objective ‘should’ as a limiting case of information-sensitivity.

Dowell does not provide any motivation for her terminology, except that Angelika Kratzer suggested this to her in personal communication (Dowell 2013: 158, n. 22), and I don’t think that there is some substantial disagreement here.

Dowell defines the objective ‘should’ as having an ordering source that is insensitive to somebody’s information-state, which is the same as having a ordering source that is sensitive to the fully realistic information-state. Thus, this all comes down to what we understand as an information-state. Following Kolodny and MacFarlane (2010: 117) and Wedgwood (forthcoming: sec. 4), I use the term in a more flexible fashion.

A further remark on terminology: when I speak of thesubjective ‘should’, I only mean cases where ‘should’ is relativized to the subject’s information-state, unlike Dowell, who calls any instance of the deontic ‘should’ that is relativized to an information-state that represents somebody’s evidence, be it the subject’s, the speaker’s or the collective evidence, ‘subjective’. Where ‘should’ is relativized to, for example, the collective evidence, I call it collective. Again, I think this is a merely terminological issue and that nothing major hinges on this.16

Jennifer Carr (2015) argues that Dowell’s twist on Kratzer’s semantics has the problem that it does not get the following sentence right:

(10) If they are in shaft 1, I should block shaft 1.

Our intuition is supposed to be that (10) is correct. But imagine we are in a context in which Sean’s information-state is salient. In this context, (10) will turn out wrong. On Kratzer’s standard account of conditionals, the ‘if’-clause of an indicative conditional restricts the modal base of the modal in the consequent. The truth-conditions for an indicative conditional with a necessity modal in the consequent read on this picture as follows (Kratzer 1991: 648):

If JIfφ, shouldψK

w,c,f,g _{= 1 iff}

JshouldψK

w,c,f+_,g

= 1, where for any worldv, w,

f+(w) =f(w)∪ {v : _Jφ_Kc,f,g,v = 1 }.

The expression with the curly brackets represents the set of worlds in which ‘φ’, the antecedent, is true. Thus, (10) is true at w iff Sean is blocking shaft 1 in all the g(w)-best worlds in the set that contains all and only those worlds in the modal background ∩f(w) in which the miners are in shaft 1. But this is not the case since ‘should’ is subjective and the ordering sourceg therefore ranks worlds

16

For more on the subjective and objective ‘should’, see chapter 3. For more on the collective ‘should’, see chapters 5 and 6.

in which Sean blocks neither shaft still higher than those where Sean blocks shaft 1. One might argue that whenever (10) is uttered, the context changes such that ‘should’ becomes objective. In light of a realistic ordering, worlds where Sean blocks shaft 1 are ranked best. Carr replies that, intuitively, there is no change in the contextually salient priorities, i.e., in the ordering source, in the following discourse where (8) precedes (10):

(8) I should block neither shaft.

(10) If they are in shaft 1, I should block shaft 1.

Silk (2014) defends a proposal along the lines of Dowell, even though in a formally far more detailed manner. He suggests that the ordering sources g does not only take a world of evaluation as an argument, but also a contextually provided information-state, which ranks worlds in light of it. The problem Carr describes for Dowell’s account is avoided by the assumption that an ‘if’-clause updates not only the modal background of the ‘should’ in the consequent, but also the information-state thatgtakes as an argument.17 It would restrict this information- state to worlds in which the miners are in shaft 1. An ordering source which is determined by this updated information-state will rank those worlds best where Sean blocks shaft 1, which will make (10) true (Silk 2014: 707).

Carr’s (2015) own proposal is to have three, instead of two parameters. The first parameter is an information-state, which is in her model a pair of a modal background, i.e., the intersection of the propositions the modal base is mapped on to, and a probability function that assigns probabilities to the worlds in this modal background. The second parameter is a value function, which maps worlds to numbers, i.e., evaluates them. The third parameter is a decision rule. Decision rules rank the worlds in the modal background based on the probability function and the value function. For example, if the decision rule is to maximize expected utility, it ranks those worlds in the modal background best which according to the probability function of the first parameter and the value function of the second have the highest expected utility. (8) is predicted to be true on this account if we assume that the decision rule that is provided by the context in combination with Sean’s information-state ranks worlds in which he blocks neither shaft highest.

17

In cases where the modal background is epistemic, the information-state and the modal background will be identical.

This will, for example, be the case if the principle is to maximize expected utility. Since Sean has no clue whether the miners are in shaft 1 or 2, Sean’s probability distribution assigns the propositions <The miners are in shaft 1> and <The miners are in shaft 2>a probability of 0.5, respectively. Assuming that the value function assigns saving all miners a value of, let’s say, 10, and saving 9 a value of 9, blocking neither shaft has an expected utility of 9 and blocking shaft 1 and blocking shaft 2 respectively an expected utility of 5.

(10) is correct, too, because the ‘if’-clause updates the information-state such that (i) the modal background is restricted to worlds where the miners are in shaft 1 and (ii) the probability function P r is updated toP r∗=P r(· | The miners are in shaft 1). This updated information-state will assign a probability of 1 to the propositions that the miners are in shaft 1. If the decision rule is, again, to maximize expected utility, this will yield the result that blocking shaft 1 is ranked highest and (10) accordingly true because blocking shaft 1 has the highest expected utility out of all alternative actions relative to the probability function

P r∗.

Notice that Carr’s account avoids any kind of commitment to a specific decision rule. It is not part of her semantics that the decision rule in the context of (8) or (10) is, for example, maximization of expected utility. Rather, she argues that the reason (8) and (10) are true is because the contexts of their utterance provide decision rules that make (8) and (10) true. The decision rule does not have to be ‘Maximize expected utility!’ Which decision theoretic principle ‘should’ expresses in these contexts is on Carr’s picture a matter of metasemantics, i.e., of how contextual parameters are resolved, not of the semantics of ‘should’ itself. This will be of relevance in the next subsection when we look at alternatives to Carr’s (2015) account.

Despite these differences, Carr’s (2015) theory incorporates information- sensitivity in a fashion very similar to Dowell (2013) and Silk’s (2014). As Carr (2015: 705) points out, her decision rules are generalizations of Kratzer-like ordering source; they perform the same function of ordering worlds in the modal background. Like Dowell (2013) and Silk (2014), Carr (2015) makes this ordering sensitive to a contextually provided information-state. The three hence account for the information-sensitivity of ‘should’ in the same way: the contextually provided ordering source ranks in light of a contextually provided information-state.

The reader might have noticed that all of these three different theories gloss over the distinction between ‘must’ and ‘should’. They all work within Kratzer’s standard semantics for ‘must’ and ignore the additional technical steps necessary to account for ‘should’, such as adding a second ordering source (von Fintel and Iatridou ms, 2008), treating ‘should’-sentences as hidden conditionals (Silk 2012), or changing the modal force of the quantifier (Finlay 2014, forthcoming). The same is true of the theories we’ll turn to in the next subsection. I assume the authors do so for the sake of simplicity and because it is reasonably clear how their treatments of information-sensitivity can be applied to the more complex semantic accounts of ‘should’. For example, all these accounts of ‘should’ rely on ordering sources in some way or another, so the treatments of information- sensitivity discussed in the present subsection can be applied to these accounts by making the relevant ordering sources information-sensitive. In the remainder of this chapter, I will follow these authors’ lead: in the next section 2.6, where I will discuss the doxastic ‘should’, I will first explain how the semantic accounts for the deontic ‘should’ mentioned can be applied to the doxastic ‘must’ and ‘should’; but when I explain, in the next step, how the models of information-sensitivity discussed here and in the next subsection can be applied to the doxastic ‘should’, I will ignore the difference between ‘must’ and ‘should’. This will save us getting into a lot of irrelevant complications.