Option 2: DP Models

Cariani et al. (2013) deviate farther from Kratzer’s account by adding a third parameter, a decision problem. I therefore call their model and the very similar one by Charlow (2013)decision problem models—or short,DP models. A decision problem is a function from a world to a set of ‘choosable’ actions. Choosable actions are those actions that an agent can do knowingly. For example, if I am faced with the problem of whether to turn right or left in worldw, this decision problem will mapwonto the following set of propositions: {<I turn left>,<I turn right>}. It is crucial that the modal background is epistemic, not circumstantial on Cariani et al.’s account. That is, the modal background is the set of worlds compatible with the speaker’s knowledge. The decision problem forms a partition on the modal background by dividing it into cells representing the actions that

are choosable for the agent. In the miners case, this is the decision set ∆miners:

∆miners: {<Sean blocks shaft 1>, <Sean blocks shaft 2>, <Sean

blocks neither shaft>}.

It is important that the proposition<Sean saves all miners>is not an element of it. This is so since saving all miners is not an action that Sean can do knowingly, given his ignorance about where the miners are. Finally, Cariani et al. (2013: 231) represent the ordering background for the miners case as the set Γminers:

Γminers: {<All miners are saved>, <At least 9 miners are saved>,

<At least 8 miners are saved>,...,<At least 1 miner is saved>}

Γminers ranks those propositions in the decision set ∆miners highest that entail

the most of the propositions in Γminers. Consequently, the proposition<blocking

neither shaft>is ranked highest since it entails all propositions in Γminers except

for <All miners are saved>. The other two propositions entail none of the propositions in Γminers. Remember that the modal background is epistemic and

thus contains both worlds where the miners are in shaft 1 and worlds where they are in shaft 2. Thus, the cell <Sean blocks shaft 1> of the modal background contains both worlds where Sean blocks shaft 1 and the miners are in shaft 1 and worlds where he blocks shaft 1 and they are in shaft 2. Thus,<Sean blocks shaft 1>entails none of the propositions in Γminers since it also holds at worlds

where no miners are saved. The same holds for<Sean blocks shaft 2>. Therefore,

<Sean blocks neither shaft> is ranked highest and (8) turns out true.18

(10) is also correct since its ‘if’-clause restricts the modal background of the ‘should’ in the consequent to worlds where the miners are in shaft 1. The propositions describing Sean’s choosable actions within this modal background thus all only contain worlds in which the miners are in shaft 1. The proposition

<Sean blocks shaft 1>, which is part of this restricted decision set, therefore entails all propositions in the ordering background. If Sean blocks shaft 1 and the

18

Charlow (2013) pursues a similar strategy. Following von Fintel and Iatridou (ms, 2008)’s suggestion to add a second ordering source to the semantics for ‘should’, he claims that the second ordering source ranks actions in contexts where the ‘should’ is sensitive to an information-state on basis of whether they are choosable in Cariani et al.’s sense. Blocking neither shaft is then said to be the action which is the highest ranked if the first ordering source, which ranks according to how many lives are saved, and the second one are merged.

miners are in shaft 1, this is guaranteed to save all 10 miners, and thus at least 9 miners, etc. The proposition is accordingly ranked highest and (10) true.

The information-sensitivity of ‘should’ is in this theory captured by the fact that which actions are choosable depends (i) on the knowledge, i.e., the information- state, of the subject the respective should-sentence is about and (ii) the epistemic modal background.

Carr (2015) objects to this proposal by Cariani et al. (2013) (and the similar one by Charlow 2013) that it carries a commitment to a specific decision-theoretic principle. ‘Sean should block shaft 1’ will turn out false even if Sean knows that there is an objective chance of 97% that the miners are in shaft 1. In this case, he cannot knowingly perform the action of saving all 10 miners since for this he would need to know that they are in shaft 1, which he doesn’t. The action<Sean blocks shaft 1>contains some worlds in which the miners are in shaft 2 since his knowledge does not rule this possibility out, even though he considers it highly unlikely. Again, blocking neither shaft will thus be the highest ranked action since it entails the most propositions in the ordering background.

This consequence of Cariani et al.’s account expresses a commitment to the decision-theoretic principle Maximin, which requires choosing that action whose worst possible outcome is the best among the worst possible outcomes of all alternative actions. Blocking shaft 1 has in the described scenario the highest expected utility (0.97×10 lives saved) compared to the alternative options of blocking neither shaft (1.0×9 lives saved) and blocking shaft 1 (0.03×10 lives saved). However, the worst possible outcome of blocking shaft 1 or blocking shaft 2, which is that no miners are saved, is worse than the worst possible outcome of blocking neither shaft, which is that 9 miners are saved. So Cariani et al.’s semantics has a commitment built into it to the Maximin principle, rather than for example the principle of maximizing expected utility. As Carr argues, however, such normative issues shouldn’t be part of the semantics of the term ‘should’. In other words, which decision-theoretic principle is correct should not be a matter of the meaning of ‘should’.19

I think there is a further problem with DP models: they cannot account for cases where the speaker is speaking relative to an information-state that is not their own. Consider the following variant of Miners:

Miners-CCTV.Everything is as inMiners, except that the physicist is not at the mine, but watches Sean via CCTV. After Sean utters (8), the physicist says:

(11) Yes, Sean should block neither shaft. Given what he knows, this is the only responsible thing to do.

The first sentence of (11) rings true, since the physicist apparently means by it that Sean should block neither shaft in light of his evidence, even though she knows that the miners are in shaft 1. According to DP models, (11) is false though. To see this, let’s remember what the decision set is:

∆miners: {<Sean blocks shaft 1>, <Sean blocks shaft 2>, <Sean

blocks neither shaft>}.

As ∆miners is a partition on the epistemic modal background, which is the set

of worlds compatible with the speaker’s, i.e., the physicist’s, knowledge,<Sean blocks shaft 1>only contains worlds in which the miners are in shaft 1. It follows that, just as in Miners, <Sean blocks shaft 1> entails all propositions in the ordering background Γminers and that it is hence ranked the highest. It follows

that (11) is false as <Sean blocks neither shaft>is not ranked highest.

In reply to this problem, a defender of a DP model could give up the assumption that the epistemic modal background must be the set of worlds compatible with the speaker’s knowledge. For example, assume that when the physicist utters (11), the epistemic modal background is the set of worlds compatible with Sean’s knowledge, rather than hers; the reason for this could be that the physicist is trying to talk about what Sean should do in light of his knowledge, rather than in light of hers. If the decision set ∆miners is a partition on Sean’s, rather than

the physicist’s, epistemic background,<Sean blocks shaft 1>will contain both worlds where the miners are in shaft 1 and where they are in shaft 2. As a result,

<Sean blocks shaft 1>won’t entail <All miners are saved>and thus won’t be the highest ranked cell, but rather<Sean blocks neither shaft>will.

To sum up, we have seen that Cariani et al. (2013) and Charlow’s (2013) DP models struggle to account for cases where a better-informed speaker talks about what an agent should do in light of their inferior evidence. While the just

suggested move might fix this for the practical ‘should’, I will argue in the next section that it does not for the doxastic ‘should’.