A Modal Approach to the Semantics of GEN

Kratzer’s modal approach can be used as an influential way of thinking about the semantics of GEN in a quantificational theory of generic sentences. In a series of writings, Kratzer (1977, 1978,

8 _{This brief exposition of the Kratzerian modal approach draws mainly on Portner (2009). It is not intended to} be used here, as formalizing the manifestations of genericity in MSA is a future project. It gives, however, a workable framework for formalizing genericity in MSA in other projects.

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1981, 1986, 1991a, 1991b, 2012) developed a theory of modals and conditionals, which is accepted as the canonical model by a good number of formal semanticists working in this realm of semantics. A major assumption of this theory is that modals are not lexically ambiguous, but rather interpreted differently relative to a set of background information or assumptions, which she dubbed

“conversational backgrounds.” This indicates that the different flavors of modals, epistemic, deontic, bouletic, circumstantial, etc., do not emerge from the ambiguous lexical contributions of the modals themselves, but rather are taken over from the contextually-dependent backgrounds of the particular contexts that wrap these modal propositions.

Kratzer (977) made a point of departure from modal logic pertaining to the role assigned to context. In modal logic, context is assumed to determine the correct word out of the set of lexically ambiguous modal words like should, for example, by helping the addressee choose the correct ‘should’, among the many ‘shoulds’,which the speaker had in mind when uttering the sentence. In Kratzerian theory, however, context determines the set of worlds that a modal like should quantifies over, and hence explicating the flavor or sense of the modal. Therefore, context not only provides a set of indices of indexical features of meaning like the identity of speaker, addressee, time, or place at which the sentence is used, but plays a pivotal role in determining the accessibility relation function, and hence the sense or flavor of the modal. According to Kratzerian theory, the different modals vary in terms of the possible worlds with which they are compatible. The modal May, for example, is compatible with both epistemic and deontic accessibility relations, while Might is compatible with epistemic but not with deontic accessibility relation.

Kratzer (1977) claims that although the interpretation of a modal is often gleaned implicitly from context and conversational backgrounds, it can be fixed sometimes by explicit linguistic expressions like “in view of what I know, or in view of the rules of the secret committee”. These expressions work as a function f from the set of all possible worlds W to the set of all propositions that the speaker knows in w, in the case of the epistemic interpretation. This interpretation can be explicitly provided by an expression like the following: “in view of what I know” = for any w, f(w)=

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the set of propositions which the speaker knows in w. Formally, in context c, what I know expresses a function f such that:

(i) The domain of f is that subset of W in which the speaker of c exists. (ii) For any w in the domain of f, f(w) = { P: the speaker knows p in w}

As standard in possible world semantics, a proposition is interpreted as a set of possible worlds in which that proposition is true, so for p to be true in w, w must be a member of p. Since f(w) yields a set of propositions, i.e., a set of sets of worlds, and we only need a single set of worlds, we can use a known trick in logic to get that set. We resort to intersecting all of the propositions in the set, and eventually get one proposition, i.e., a single set of worlds in which all the propositions are true. Given this conversational background function f, the accessibility relation of a modal is defined as follows: for any worlds w and v, v is the set of worlds accessible from w iff every proposition in f(w) is true in v. So if we take f(w) to be epistemic, f(w) represents all the facts known by the speaker in w, and v is accessible from w iff all the facts known by the speaker in w are true in v. More

precisely, the set of worlds accessible from w is ∩f(w).

The second major idea of Kratzerian modal theory pertains to the simple dichotomy entertained in modal logic between the set of worlds accessible and the other set of worlds which is not accessible. In modal logic, the set of accessibility relation functions that determine the sense of the modal is determined by a semantic rule that applies to all modals with no change. Thus,

pragmatics plays fewer roles than semantics in this model; it only provides the indexical features of meaning of a proposition through context. In Kratzerian theory, however, the tables are turned; pragmatics plays the main role in determining the set of worlds over which modals quantify. Kratzer (1981) argues that the simple dichotomy is insufficient and problematic, and suggests an ordering mechanism of the set of all possible worlds W that modals quantify over. According to this

assumption, the set of worlds is not simply dichotomized, but rather ranked through the interaction of two conversational backgrounds.

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In Kratzer’s (1981) revised model, a sentence is interpreted according to two conversational backgrounds: the MODAL BASE f which provides a set of relevant worlds, those in ∩ 𝑓(𝑤), and background g which is an ORDERING SOURCE ≤ 𝑔(𝑤) which ranks these worlds as closer or distant from some ideal world. The specifications of both the modal base and ordering source are determined contextually. For example epistemic modal base combines with an ordering source related to information as ‘what the normal course of events is like’, some reports or beliefs. A stereotypical ordering source might be related to information as ‘in view of the normal course of events’. A

circumstantial modal base combines with an ordering source related to laws, goals, plans, and wishes: what the law provides, what is good for you, what our goal is, what is moral, and what have you. Consider the illustrative example in (43) below:

(43) Given the state of your health, you should stay at home.

The sentence in (43) can be paraphrased as follows: “In view of your state of health (circumstantial modal base), and in view of what is best for your health (ordering source), you should stay at home”. In other words, the set of worlds in ∩ 𝑓(𝑤) which is top-ranked according to

≤ 𝑔(𝑤) is the set of accessible worlds in a simple modal sentence. The definition of ordering source in Kratzerian theory indicates that every comparable sequence among worlds in the relevant set of worlds reaches a point as we move towards the ‘ever-better’ worlds in which a proposition is true. In sum, in Kratzerian approach the semantics of modal verbs incorporates three parameters. The MODAL FORCE parameter determines whether the modal verb is represented universally or existentially; i.e., whether it expresses necessity or possibility. The MODAL BASE or conversational background determines the set of accessible worlds. And the ORDERING SOURCE parameter ranks these worlds as closer to or distant from some ideal world. The specification of both the modal base and the ordering source is determined pragmatically.

7.1.2 Application of Kratzer’s Approachto the Semantics of GEN

Greenberg (2003) argues that applying Kratzer’s approach to the semantics of GEN operator has three main advantages. First, it captures the law-likeness nature of characterizing sentences

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through the universal quantification over all possible worlds. Second, it accounts for the exception- tolerance of characterizing sentences since it allows the universal quantification to quantify over individuals in the most normal worlds only; this is attained through the ordering source parameter. Finally, it naturally accounts for the variety of flavors or kinds of rules (44) which characterizing sentences can express through the modal base which can vary as, epistemic, deontic, instrumental, mathematical, linguistic, etc., and give different interpretations.

(44) a. A cat meows. (epistemic)

b. A driver watches traffic laws. (deontic)

c. A taxpayer pays state and federal income taxes. (legal) d. A queen is the wife or widow of a king. (linguistic) e. An even number can be divided evenly into groups of two. (mathematical)

Kratzer’s (1981) modal framework can be adopted to informally account for the truth

conditions of generics in MSA in this project, and to build formal models in the future. This approach is suggested by Krifka et al. (1995:52) to be used to calculate the truth conditions of generic sentences like (45), as in (46):

(45) A lion has a bushy tail.

(46) 𝑮𝑬𝑵 [𝑥1 … 𝑥𝑖, 𝑦1 … 𝑦𝑖" ](𝑹𝒊𝒔𝒕𝒓𝒊𝒄𝒕𝒐𝒓, 𝒎𝒂𝒕𝒓𝒊𝒙 )" 𝑖𝑠 𝑡𝑟𝑢𝑒 𝑖𝑛 𝑤 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑡𝑜 𝑎 𝑚𝑜𝑑𝑎𝑙 𝑏𝑎𝑠𝑒 𝐵𝑤 𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟𝑖𝑛𝑔 𝑠𝑜𝑢𝑟𝑐𝑒 ≤ 𝑤 𝑖𝑓𝑓: 𝐹𝑜𝑟 𝑒𝑣𝑒𝑟𝑦 𝑥1 … 𝑥𝑖 𝑎𝑛𝑑 𝑒𝑣𝑒𝑟𝑦 𝑤′ ∈ 𝐵𝑤 𝑠. 𝑡 𝑹𝒆𝒔𝒕𝒓𝒊𝒄𝒕𝒐𝒓 [𝑥1 … 𝑥𝑖 ]𝑖𝑠 𝑡𝑟𝑢𝑒 𝑖𝑛 𝑤′_{, 𝑡ℎ𝑒𝑟𝑒 𝑖𝑠 𝑎 𝑤𝑜𝑟𝑙𝑑 𝑤}′′_{𝑖𝑛 𝐵} w 𝑠. 𝑡. 𝑤′′ ≤w 𝑤′, 𝑎𝑛𝑑 𝑓𝑜𝑟 𝑒𝑣𝑒𝑟𝑦 𝑤𝑜𝑟𝑙𝑑 𝑤′′′ ≤w 𝑤′′, ∃𝑦1 … 𝑦𝑖 𝑴𝒂𝒕𝒓𝒊𝒙 [ (𝑥1) … (𝑥𝑖), 𝑦1 … 𝑦𝑖]] 𝑖𝑠 𝑡𝑟𝑢𝑒 𝑖𝑛 𝑤′′′ .

(Where Bw is the modal base, and 𝑤′′ ≤w 𝑤′ means that 𝑤′′ is closer to the ideal world determined by the ordering source than 𝑤′)

According to the definition in (46) the sentence in (45) means that, “everything which is a lion in the worlds of the modal base is such that, in every world which is most normal according to the ordering source, it will have a bushy tail.” It is noteworthy, that the definition in (46) does not presuppose that there are lions in the actual world. In addition, it does not require that every single lion must have a bushy tail. Only lions in worlds which are ranked closer to the ideal world are counted, hence capturing exception tolerance of characterizing generics.

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