In this chapter we have sketched out an analysis which treats modals as quantifiers over possible worlds. This analysis helps to explain why modals are similar to quantifiers in certain ways, for example, in the scope ambiguities that arise when they are combined with other quantifiers.
The analysis also helps to explain the unusually systematic pattern of “polysemy” observed in the English modals, as well as the fact that this same pattern shows up in many other languages as well. This is not how polysemy usually works. Under Kratzer’s analysis, the English modals are not in fact polysemous, but rather indeterminate for type of modality. The strength of the modal (necessary vs. possible) is lexically entailed, but the type of modality (epistemic vs. deontic etc.) is determined by context.
Modals in French and many other languages work in much the same way as the English modals; but this is certainly not the case for all languages, perhaps not even for a majority of them. However, the quantificational analysis can account for these other languages as well. Strength of modality is represented in the quantifier operator, while type of modality is represented in the restriction on the class of possible worlds. Either or both of these can be lexically specified in particular languages, or for specific forms in any language.
Epistemic modality is different in certain ways from all the other types (known collectively as root modality). Some authors have claimed that epistemic modality is not part of the propositional content of the utterance. We argued that this is wrong, based on the fact that epistemic modality can be questioned and challenged, and (at least in some languages) can be negated as well. We return to these issues in the next chapter, where we discuss the difference between markers of epistemic modality vs. markers of evidentiality (source of information).
Further reading
Von Fintel 2006 and Hacquard (2011) provide very useful overviews of the semantic analysis of modality, as well as references to much recent work on this subject. Hacquard in particular provides a good introduction to Kratzer’s treatment of modals. Matthewson (2016) presents an introduction and overview with frequent references to Salish and other languages whose modals are quite different from those of English. De Haan 2006 presents a helpful typological study of modality. A brief introduction to modal logic can be found in Garson (2016); recent textbooks on the subject include Blackburn et al. (2008) and van Benthem (2010).
Discussion exercises
A: Deontic vs. epistemic modality. Identify the type of modality in the following statements:
1. You must leave tomorrow.
2. You must have offended the Prime Minister very seriously.
3. You must be very patient.
4. You must use a Mac.
5. You must be using a Mac.
B: Ambiguous type of modality. Use the restricted quantifier notation to express two possible types of modality (deontic vs. epistemic) for the following sentences:
1. Arnold must trust you. (assume “h” = hearer)
2. You may annoy Mr. Roosevelt.
3. You must be very patient.
C: Scope ambiguities. Use the restricted quantifier notation to express the two possible scope relations for the indicated reading of the following sentences:
1. No terrorist must enter the White House. [deontic]
2. Many prisoners must be released. [deontic]
3. Every candidate could be disqualified. [epistemic]
Homework exercises
A: Epistemic vs. deontic modality. For each of the sentences below, describe two contexts: one where the modal would most likely have an epistemic reading, the other where the modal would most likely have a deontic reading:
1. Arnold must not recognize me.
2. Henry ought to be in his office by now.
3. Baxter may support Suharto.
4. George should be working late tonight.
5. You have to know how to drive.
B: Restricted quantifier representation. Use the restricted quantifier notation to express two types of modality (epistemic vs. deontic) for the following sentences. For convenience, you may use the abbreviation “sp” to refer to the speaker and “h” to refer to the hearer.
1. You must exercise regularly.
2. I should be on time this evening.
3. Rick may not remain in Casablanca.
C: Scope ambiguities
(1) Use the restricted quantifier notation to express the deontic reading of the two indicated interpretations for the following sentence:
No professors must be fired.
a. ¬∃x[PROFESSOR(x) ∧ □ FIRED(x)]
b. □ ¬∃x[PROFESSOR(x) ∧ FIRED(x)]
(2) Use the restricted quantifier notation to express the two possible scope interpretations for the epistemic reading of the following sentences:
a. Every student could graduate.
b. Some of the suspects must be guilty
