A radically different approach to defining the meaning of if was proposed by Kratzer (1986), based on a suggestion by D. Lewis (1975). As we mentioned in Chapter 14, Lewis analyzes adverbs like always, sometimes, usually, never, etc. as “unselective quantifiers”, because they can quantify over various kinds of things. He points out that conditional clauses can be used to specify the situations, entities, or units of time which are being quantified over, as illustrated in (27). However, it is difficult to say exactly what the if means in such examples.
(27) a. If it is sunny, we always/usually/rarely/sometimes/never play soccer.23
always: ∀d [SUNNY(d) → (we play soccer on d)]
sometimes: ∃d [SUNNY(d) ∧ (we play soccer on d)]
usually: ⁇?
b. If a man wins the lottery, he always/usually/rarely/sometimes/never dies happy.
always: ∀x [(MAN(x) ∧ WIN(x,lottery)) → DIE_HAPPY(x)]
sometimes: ∃x [MAN(x) ∧ WIN(x,lottery) ∧ DIE_HAPPY(x)]
usually: ⁇?
Example (27a) is a standard conditional whose antecedent expresses the proposition SUNNY(d), using d as a variable for days. The adverbs always, sometimes, etc, specify the quantifier part of the meaning. The word if seems to name the relation between the antecedent and the consequent; but with always this relation is expressed by →, with sometimes the relation is expressed by ∧, and with adverbs like usually and rarely there is no way to express the relation in standard logical form. A similar problem arises in (27b). What these examples show is that we cannot identify any consistent contribution of the word if to the meaning of the sentence in this construction.
Using the restricted quantifier notation allows us to give a uniform analysis for such sentences, regardless of which adverb is used. As shown in (28), the antecedent of the conditional clause contributes material to the restriction on the quantifier, and the consequent specifies the material in the scope of the quantifier. But notice that there is no element of meaning in these expressions corresponding to the word if. Lewis concludes that in this construction, if “has no meaning apart from the adverb it restricts.”
(28) If a man wins the lottery, he always/usually/rarely/sometimes/never dies happy.
always: [all x: MAN(x) ∧ WIN(x,lottery)] DIE_HAPPY(x)
sometimes: [some x: MAN(x) ∧ WIN(x,lottery)] DIE_HAPPY(x)
usually: [most x: MAN(x) ∧ WIN(x,lottery)] DIE_HAPPY(x)
rarely: [few x: MAN(x) ∧ WIN(x,lottery)] DIE_HAPPY(x)
never: [no x: MAN(x) ∧ WIN(x,lottery)] DIE_HAPPY(x)
Kratzer (1986) proposed that Lewis’s analysis could be extended to all indicative (i.e., non-counterfactual) standard conditionals. If the conditional sentence contains a quantifier-like element in the consequent, the word if serves only as a grammatical marker introducing material that contributes to the restriction on the quantifier. This is illustrated in (29) for normal quantifier phrases, and in (30) for epistemic and deontic modality
(29) a. Every student will succeed if he works hard.
[all x: STUDENT(x) ∧ WORK_HARD(x)] SUCCEED(x)
b. No student will succeed if he goofs off.
[no x: STUDENT(x) ∧ GOOF_OFF(x)] SUCCEED(x)
(30) a. If John did not come to work, he must be sick. [epistemic necessity]
[all w: (w is consistent with what I know about the actual world) ∧ (the normal course of events is followed as closely as possible in w) ∧ (John did not come to work in w)] SICK(j) in w
b. If John did not come to work, he must be fired. [deontic necessity]
[all w: (the relevant circumstances of the actual world are also true in w) ∧ (the relevant authority’s requirements are satisfied as completely as possible in w) ∧ (John did not come to work in w)] FIRED(j) in w
Kratzer suggests that when a conditional sentence does not contain an overt quantifier-like element, the presence of if leads the hearer to assume a default quantifier. In some contexts, this default element would be epistemic necessity, as in (31a). In other contexts, the default element could be generic frequency, as in (31b).24
(31) a. If John left at noon, he’s home by now. [implied: epistemic necessity]
[all w: (w is consistent with what I know about the actual world) ∧ (the normal course of events is followed as closely as possible in w) ∧ (John left at noon in w)] HOME(j) in w (by time of speaking)
b. If John leaves work on time, he has dinner with his family. [implied: generic frequency]
[all d: (d is a day) ∧ (John leaves work on time in d)] John has dinner with his family in d
Kratzer (1986: 11) summarizes her proposal as follows:
The history of the conditional is the story of a syntactic mistake. There is no two-place if … then connective in the logical forms for natural languages. If -clauses are devices for restricting the domains of various operators. Whenever there is no explicit operator, we have to posit one.
Her point is that the conditional meaning, the sense of relationship between antecedent and consequent, is not encoded by the word if. Rather, it comes from the structure of the quantification itself. The function of if is to mark certain material (the antecedent) as belonging to the restriction rather than the scope of the quantifier.
The proposal that if “does not carry any distinctive conditional meaning”25 may get some support from the observation that conditional readings can arise in sentences where two clauses are simply juxtaposed without any marker at all, as seen in (32–33).
(32) Examples of juxtaposed conditionals from LanguageLog:26
a. “Listen,” Renda said, “we get to a phone we’re out of the country before morning.”
b. “He could have been a little rusty early on, and then the inning he gave up four runs I think he kind of lost his composure a little bit,” Orioles manager Sam Perlozzo said. “He just did a little damage control in that situation, we’re OK.”27
(33) INIGO: We’re really in a terrible rush.
MIRACLE MAX: Don’t rush me, sonny.
You rush a miracle man, you get rotten miracles.28
23 D. Lewis (1975).
24 Examples from Von Fintel (2011). As we will see in Chapter 21, the English simple present tense has special properties which explain the generic frequency interpretation of examples like (31b).
25 Von Fintel (2011).
26 http://itre.cis.upenn.edu/~myl/langu...es/004521.html
27 AP Recap of Toronto-Baltimore game of May 22, 2007; David Ginsburg, AP Sports Writer.
28 From the 1987 movie The Princess Bride.
