Quantificational Readings of Indefinites with FOCUSED Creation Verbs Tamina Stephenson Semantics Generals Paper, March 2005
1. “Quantificational” Readings of Indefinites The central data for this paper involves the availability or unavailability of a certain reading of indefinite objects in English sentences. This kind of reading comes up in sentences with adverbial quantifiers such as usually, and can be brought out most clearly in examples like (1). (1)
I usually love a sonata by Dittersdorf.
[Diesing (1992): 113]
The salient reading of (1) says, roughly, that in most cases when I hear a sonata by Dittersdorf, I love it. I will follow Diesing (1992) in referring to this kind of reading of an indefinite object as a “quantificational” reading. The key property of these readings is that the adverb seems to quantify at least in part over individuals that satisfy the description of the indefinite object – in the case of (1), over sonatas by Dittersdorf. In Diesing’s approach using tri-partite structures, these readings are derived from LFs where the indefinite object is mapped to the restrictor clause rather than the nuclear scope. Diesing observes that a quantificational reading of an indefinite object is possible in a sentence like (2) as indicated in (2.ii), but not in (3). (2)
I usually read a book about slugs. (i) ≈ [On Tuesdays] What I usually do is read a book about slugs. (ii) ≈ When I encounter a book about slugs, I usually read it. = “quantificational reading”
(3)
I usually write a book about slugs. (i) ≈ [In the summer] What I usually do is write a book about slugs. ] (ii) ≠ When I encounter a book about slugs, I usually write it / I’m usually the one who wrote it
Diesing’s explanation of this contrast is that indefinites in restrictor clauses carry a preexistence presupposition – that is, in (2) and (3), the indefinite a book about slugs requires the domain of quantification to consist of preexisting books about slugs. Since verbs of creation by definition involve bringing their objects into existence, she reasons, 1
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they are thus incompatible with these readings. This explanation has intuitive appeal, and some version of it tends to strike people as obvious. After all, it’s difficult to even come up with a sensible paraphrase for a reading of (3) that would be parallel to (2.ii), and when you try to do so you get the feeling that the problem is just that books don’t exist until they’re written. Nevertheless I will show that this line of explanation cannot be correct. The problem with Diesing’s type of explanation is that a quantificational reading for sentences like (3) actually becomes available if you put contrastive focus on the verb of creation. Consider the examples in (4). (4)
(a)
I usually [HANDwrite]FOC a book about slugs. = When I write a book about slugs, I usually do it by hand.
(b)
I usually write a book about slugs [on the COMPUTER]FOC. = When I write a book about slugs, I usually do it on the computer.
(c)
I usually [KNIT]FOC a scarf. = When I make a scarf, I usually do it by knitting.
These sentences can be used to say something like “out of the scarves that I eventually make, most of them are created by knitting,” or “out of the books about slugs that I eventually write, most of them are created on a computer.” In other words, sentence (4.a) is quantifying at least in part over a set of books about slugs, and saying that I handwrite most of them; similarly, sentence (4.c) is quantifying at least in part over a set of scarves, and saying that I knit most of them. According to Diesing’s analysis, this should be impossible, since the indefinite ought to require that the books and scarves already exist before I write or knit them. Thus Diesing predicts that the indicated readings for the sentences in (4) should not be possible. Since they are possible, we need to look elsewhere for an explanation of the original contrast in (2)-(3). The crucial difference between (3) and (4) seems to be in their focus structure, so an obvious place to start is in the semantics of focus. I will show that independently motivated principles relating to focus can indeed provide an explanation that accounts for both contrasts. But first let me lay out some concrete assumptions about the semantics of adverbial quantifiers and quantificational indefinites.
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2. The Meanings of Temporal Quantifiers I assume adverbial quantifiers like usually are ambiguous between a meaning that will yield quantificational readings of indefinites and a more basic meaning that just quantifies over time. This more basic meaning is needed for sentences like (5). (5)
On Sunday I usually call my mother.
Lexical entries for this basic use are given in (6). (6)
(a)
[[usually]] = [λp . [λq . For most times t s.t. p(t)=1, q(t)=1] ] =1 [λp . [λq . | {t: p(t)=1} ∩ {t: q(t)=1} | is a sufficiently large fraction of |{t:p(t)=1}| ] ]
(b)
[[always]] = [λp . [λq . For all times t s.t. p(t)=1, q(t)=1] ] = [λp . [λq . {t: p(t)=1} ⊆ {t: q(t)=1} ] ]
(c)
[[rarely]] = [λp . [λq . For most times t s.t. p(t)=1, q(t)=0] ] = [λp . [λq . | {t: p(t)=1} ∩ {t: q(t)=1} | is a sufficiently small fraction of |{t:p(t)=1}| ] ]
In other words, temporal quantifiers take two arguments that are properties of times – that is, elements of type (intensions of propositions with respect to time), or, equivalently, sets of times. The first argument corresponds to the restrictor and the second to the nuclear scope. I’m taking times to be intervals, not points; I’ll come back to some issues about quantifying over intervals below. I also assume that the clause I call my mother in (5) has perfective aspect, and more generally that tensed clauses always have either perfective or imperfective aspect in addition to simple tense operators (although I’ll be ignoring tense). Lexical entries for the two aspectual morphemes PERF (perfective) and IMPF (imperfective) are given in (7). Note that these assumptions are for concreteness; my central claims will not depend on the exact details of a theory of aspect and could probably be adapted to a different view. (7)
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(a) (b)
[[PERF]] = [λf . [λt . ∃t’[t’⊆int t and f(t’)=1] ] ] [[IMPF]] = [λf . [λt . ∃t’[t’⊇int t and f(t’)=1] ] ]2 [where ⊆int and ⊇ int represent the sub- and superinterval relations]
Throughout I will use sets and their characteristic functions interchangeably.
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Before aspect is added, then, I assume that propositions are true only of exact time intervals, and generally have neither the subinterval property nor the superinterval property. For example, [[I call my mother]] denotes the set of just those exact intervals that go from the beginning to the end of a single call. Similarly, [[it rains]] denotes the set of intervals that exactly cover times of rainfall, but not proper subintervals of those. Adding perfective aspect yields the set of all superintervals of the original intervals, and adding imperfective aspect yields the set of all subintervals of the original ones. The effect of the aspectual morphemes is represented in (8). (8) Effect of perfective and imperfective aspect (a)
[[p]]
(b)
[[PERF]]([[p]])
(c)
[[IMPF]]([[p]])
These assumptions give the correct meaning for (5), repeated in (9.a), as shown in (9.b). Assume for now that on Sunday denotes just the set of entire Sundays. (9)
(a) (b)
On Sunday I usually call my mother. [[(9.a)]] = [[usually]] ( [[on Sunday]]) ([[PERF]] ( [[I call my mother]]) ) = [[usually]] ( [λt1 . t1 is a Sunday] ) ( [λt2 . ∃t3 [I call my mother at t3 and t3⊆int t2] ) = for most times t s.t. t is Sunday, ∃t’⊆int t s.t. I call my mother at t’ ≈ on most Sundays, I call my mother sometime during the day
There are two things to notice here. First, the contribution of the perfective aspect is crucial, since without it the calls would be required to last all day. Second, each Sunday only counts once, which seems to be correct. (If I happen to call my mother four times some Sunday, that doesn’t get me off the hook for the rest of the month.)
2
I’m ignoring complications relating to the “imperfective paradox.” See, e.g., Landman (1992), Portner (1998), and Parsons (1990) for discussion of how (7.b) might need to be modified.
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3. Maximal Intervals Example (9) was carefully chosen to avoid a problem that comes up in quantification over time. Plausibly the set denoted by [[on Sunday]] includes just those intervals that go from the beginning of the day on a Sunday to the end of that day. So, for example, the interval going from 3:00 pm to 3:30 pm some Sunday doesn’t count as “a Sunday” even though it’s part of a Sunday. In other words, it’s plausible to assume that on Sunday is like a clause without aspect, as illustrated in (8.a). However, we might want to say that on Sunday is like a clause with imperfective aspect, in which case it would include an interval like 3:00-3:30 pm some Sunday. In any case, we need to account for cases where the restrictor is a when-clause that actually has imperfective aspect, as in (10). (I assume that the English progressive –ing is essentially an imperfective marker.) (10)
When it’s raining I always call my mother. 1st argument of always: [[it’s raining]] = [[IMPF]] ( [[it rains]] ) 2nd argument of always: [[PERF]] ( [[I call my mother]] )
I’ve switched to an example with always to make the predictions clearer. Assuming that when has no semantic contribution, if the denotation of it rains without aspect is the set of times pictured in (8.a), then the denotation of [IMPF [it rains] ] will be the set of times pictured in (8.c). The pictures are repeated in (11). (11) Effect of imperfective aspect (a) (b)
[[it rains]] t1
t2
[[IMPF]] ([[it rains]])
The first argument of always in (10) will thus be the set of times illustrated in (11.b), which includes all the subintervals of the original times. This creates a problem, though: look at the two intervals marked as t1 and t2 in (11), where t1 is one of the original intervals and t2 is a subinterval of t1. According to the semantics of always, in order for (10) to be true it must be the case that I call my mother at some subinterval of t1, and also
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at some subinterval of t2.3 That means that if I only called my mother once during t1, and it was at a time that was not a subinterval of t2, then t2 would constitute a falsifying instance for the universal quantification and the sentence would be predicted to be false. Since this is also the case for all the other subintervals of t1, the semantics assumed so far would require not only that I call my mother once during each of the times of rain, but that I call her once during each subinterval of a time of rain. If time is dense, this would require me to make an infinite number of calls, which is clearly impossible; but even if we assumed some level of granularity, it would be predicted that I have to call my mother during multiple overlapping intervals, whereas it’s clear that sentence (10) only requires that I call my mother once during each of the times of rain.4 To capture the meanings of sentences like (10), then, we need to restrict the quantification to the maximal intervals in the restrictor set. If we define Max(p) as the set of maximal p-intervals as in (12), then we just need to modify the lexical entries for temporal adverbs as in (13). (12)
Max(p) = {t: p(t)=1 and ~∃t’[t⊂int t’ and p(t’)=1} [where ⊂int is the proper subinterval relation]
(13) (a)
[[usually]] = [λp . [λq . For most times t s.t. t∈Max(p), q(t)=1] ] = [λp . [λq . | Max(p) ∩ {t: q(t)=1} | is a sufficiently large fraction of |Max(p)| ] ]
(b)
[[always]] = [λp . [λq . For all times t s.t. s.t. t∈Max(p), q(t)=1] ] = [λp . [λq . Max(p) ⊆ {t: q(t)=1} ] ]
(c)
[[rarely]] = [λp . [λq . For most times t s.t. t∈Max(p), q(t)=0] ] = [λp . [λq . | Max(p) ∩ {t: q(t)}=1 | is a sufficiently small fraction of |Max(p)| ] ]
Later I will motivate a more complicated notion than maximal intervals, and this will be revised. However, the result will be the same for examples like (10).
3
Since I assume that I call my mother has perfective aspect, what is really required is that I call my mother at a subinterval of a subinterval of t1, and the same for t2, but since these need not be proper subintervals, this amounts to the same thing. 4 A separate problem comes up with perfective when-clauses, since essentially it’s necessary to reverse the effect of the perfective aspect. There are various ways to work out these details and various difficulties that come up, but these are tangential to the issues at hand.
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4. Deriving Quantificational Readings Let’s look again at sentence (2), repeated in (14). (14)
I usually read a book about slugs. (i) ≈ [On Tuesdays] What I usually do is read a book about slugs. (ii) ≈ When I encounter a book about slugs, I usually read it. = “quantificational reading”
If we use the meaning for usually from (13), we’ll get reading (i), assuming a restrictor argument (e.g., on Tuesdays) is provided by the context. To get reading (ii), we’ll have to do something other than just quantify over times. I’m going to assume an unselective binding approach to adverbial quantification (rather than having usually quantify over situations or something similar). Under this view, there are two possibilities that we might consider to get reading (ii): the first is to have usually simply quantify over individuals instead of times, and the second is to have it quantify over pairs of individuals and times. Percus (1999) gives evidence against treating adverbs like usually as quantifiers over individuals. One example he discusses is (15). (15)
[Context: Ursula is the subject of an experiment where blue-eyed bears walk in front of her one at a time, and she’s supposed to judge whether each bear is intelligent.] Ursula usually knew whether a blue-eyed bear was intelligent. [Percus (1999), (17)]
If each bear only walked out once, then (15) could plausibly be analyzed as containing a quantifier over individuals, since in that case it would just mean that for most of the bears, Ursula knew whether they were intelligent. But judgments change if you consider the possibility that a single bear could walk out more than once. In this kind of scenario, it would be possible for Ursula to know for most bears whether they were intelligent and yet not know for most trials whether the bear in that trial was intelligent. (This would happen if the few bears whose intelligence she was unsure of came out many times while the many bears whose intelligence she was sure of came out few times.) Percus observes that in this kind of scenario, (15) is interpreted as quantifying over trials rather than bears. I will thus follow him in rejecting the option of treating adverbs as quantifying over individuals.
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This leaves me with the second option, that of treating usually as quantifying over pairs of individuals and times. Note that this option can account for Percus’s example, since each trial in the experiment can count as a separate pair of an individual and a time. It’s straightforward to generalize usually so that it takes sets of pairs of individuals and times as its arguments. A lexical entry for usually in this use is given in (16). (16)
[[usually2]] = [λP . [λQ . For most pairs such that t∈Max(P(x)), Q(x)(t)=1] ]
I’ve called this usually2 since this meaning is in addition to that given earlier in (6) and revised in (13). However, from now on the first meaning for usually will mostly be irrelevant, so I will use usually to mean usually2. It’s somewhat less straightforward to explain how an indefinite like a book about slugs can come to be an argument of this quantifier. I will simply assume that it has a meaning (in addition to its normal meaning) in which it denotes a set of pairs of individuals and times. Intuitively speaking, this is the set of pairs such that x is a book about slugs and t is any time whatsoever. This is formalized in (17). (17)
[[a book about slugs]] = [λx . [λt . ∃t’ [x is a book about slugs at t’] ] ] = {: x is a book about slugs at some time t’}
Crucially, the time at which the individual is a book about slugs (t’) is not bound by or in any way linked to the time argument in the lambda term (t), allowing it to be any time at all. To derive the meaning in (17) compositionally, we would presumably have to give a second lexical entry to the indefinite article as in (18). (18)
[[a2]] = [λP . [λx . [λt . ∃t’ [P(x)(t’) = 1] ] ] ] = [λP . {: P(x)(t’) = 1 for some t’} ]
Finally, I assume that I read has the meaning given in (19), which could be achieved by movement of the object or some other means, such as function composition. (19)
[[I read]] = [λx . [λt . I read x at t] ]
I don’t intend (17)-(19) to constitute a serious analysis of quantificational indefinites, but only to provide a shortcut for deriving quantificational readings. Most of my time will be spent on details relating to the quantification itself; thus the question of how best to 8
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explain the phenomenon of quantificational indefinites, difficult and interesting though it may be, is not one that needs to be resolved for my purposes. Given the meanings in (17)-(19), the quantificational reading of (14), I usually read a book about slugs, is predicted to be as shown in (20). (20)
[[I usually read a book about slugs]] = [[usually]] ( [[a book about slugs]]) ([[I read]] ) = 1 iff for most pairs such that t∈Max([λt . ∃t’: x is a book about slugs at t’]), I read x at t.
Given the definition of Max from (12), this is equivalent to (21). (21)
[[I usually2 read a book about slugs]] = 1 iff for most pairs such that (i) ∃t’[x is a book about slugs at t’] and (ii) ~∃t’[t⊂int t’ and ∃t”[x is a book about slugs at t”] ], I read x at t.
The restriction in (ii) of (21) comes from the definition of the “Max” operator. Note that the embedded existential (underlined above) plays no role since it will be satisfied by any pair that satisfies (i). In effect, then, the Max operator prevents the domain of quantification from containing two pairs and where t’ is a proper subinterval of t, in each case removing the pair that has the subinterval. If we assume that the context always provides at least a set of relevant individuals and a relevant time span, then without further restrictions, the domain of quantification will include exactly one pair for each relevant book about slugs – namely, the pair of that book with the entire relevant interval of time. For example, suppose that there are twenty books about slugs that are relevant, and the time relevant to the conversation is just a particular one-year time span. Then sentence (14) is predicted to be true if I read most of those twenty books (however many “most” is) at some point during that year. So far this makes the same predictions as simply quantifying over individuals. However, since the domain of quantification is actually pairs of individuals and times, a rich enough context could restrict the domain to a set of relevant pairs. For instance, look again at Percus’s example from (15), repeated in (22).
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(22)
Ursula usually knew whether a blue-eyed bear was intelligent.
If the context is an experiment where bears walk out one at a time, then there’s a clear set of relevant individual-time pairs, namely, the set of pairs where t is the time of a single trial and x is the bear that walks out during that trial. Since the context already restricts the domain of quantification to these pairs, the restriction in (ii) of (21) just ensures that only the entire time of each trial is paired with its bear, and not any proper subintervals of these times. It doesn’t matter that the times of the trials are proper subintervals of the entire relevant time span, since the pairs consisting of each bear and the entire relevant interval of time are already eliminated from the domain of quantification by the rich context. In Section 6 I will revise the analysis somewhat so that every sentence with a quantificational reading of an indefinite actually contains a restriction of this kind. In the context of (22), then, we allow for the possibility that one bear could walk out twice, and thus be counted in two pairs. For example, if a single bear x1 walked out in the first trial, at time t1, and also in the third trial, at time t3, then both and would be included in the domain of quantification. Since the times of different trials can’t be in a superinterval-subinterval relationship, neither of these pairs are eliminated by the Max operator. Thus it’s correctly predicted that (22) would be false in a situation where Ursula could tell whether most of the bears were intelligent, but the few for which she couldn’t tell happened to be in most of the trials. At this point there’s no explanation for the original contrast between creation and non-creation verbs from (2)-(3). The analysis I’ve given predicts a quantificational reading for I usually write a book about slugs that is exactly parallel to the one predicted for I usually read a book about slugs, shown in (23). (23)
[[I usually write a book about slugs]] = [[usually]] ( [[a book about slugs]]) ([[I write]] ) = 1 iff for most pairs such that (i) ∃t’[x is a book about slugs at t’] and (ii) ~∃t’[t⊂int t’ and ∃t”[x is a book about slugs at t”] ], I write x at t.
Without further contextual restrictions, (23) says that for most relevant books about slugs, I wrote them at some point during the relevant time span. But of course the sentence 10
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doesn’t have this meaning. In the next section I will consider and reject one kind of change that might account for this difference between read and write. Then in Section 6 I will turn to accounting for a different contrast – that between focused and unfocused creation verbs. In Section 7 I will show how my explanation of the focused/unfocused contrast can be extended to also explain the original creation/non-creation contrast.
5. A Second Look at Preexistence Now that we have a concrete semantic analysis to work with, it’s worth taking another look at the idea of a preexistence requirement, to see whether an explanation along the lines of Diesing’s can make sense after all once it’s adapted to these assumptions. It turns out that at least the most obvious ways of adapting Diesing’s explanation still make the wrong prediction about the examples with focused creation verbs from (4). The crucial examples are repeated in (24)-(26). (24)
I usually read a book about slugs. ≈ When I encounter a book about slugs, I usually read it.
(25)
I usually write a book about slugs. ≠ When I encounter a book about slugs, I usually write it / I’m usually the one who wrote it
(26)
I usually [KNIT]FOC a scarf. ≈ When I make a scarf, I usually do it by knitting.
Recall that the meaning I’m assuming for the indefinite article in quantificational readings, repeated in (27), does not link its time argument in any way to the time argument of the predicate – that is, t does not appear inside the value description of the lambda expression (underlined below). (27)
[[a2]] = [λP . [λx . [λt . ∃t’[P(x)(t’) = 1] ] ] ]
The reason for keeping the two time variables independent in this way was so that the meaning of, for example, a book about slugs, would be the set of pairs where x is a book about slugs and t is any time at all. But an obvious question that comes to mind is whether the two time variables could be linked in some way. This would undoubtedly lead to a less suspicious-looking meaning, so the question is just whether it could be 11
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empirically correct. There are many possible ways to do this; I will consider a few that I think are most relevant. First, the most obvious way to link the two variables is to simply identify them with each other, eliminating the existential expression altogether, as in (28). (28)
[[a2]] = [λP . [λx . [λt . P(x)(t) = 1] ] ] = [λP . {: P(x)(t) = 1} ]
When this applies to [[book about slugs]], for example, it will yield the set of pairs such that x is a book about slugs throughout t. Assuming that to be a book about slugs at some time implies existence at that time, this means that x must exist throughout t. Thus this is similar to a preexistence requirement, and in fact it would account for the contrast between read and write in (24)-(25), as I will show. When the meaning of (24) is computed using (28) as the lexical entry for a, the result is (29). (29)
[[I usually2 read a book about slugs]] = [[usually]] ( [[a2]] ([[book about slugs]]) ) ( [[I read]] ) = 1 iff for most pairs such that (i) x is a book about slugs at t and (ii) ~∃t’[t⊂int t’ and x is a book about slugs at t’ ], I read x at t.
The only difference between this meaning and the one derived in (20)-(21) above is that the times that can be paired with each book are also bounded by the lifetime of the book – that is, if a relevant book comes into existence during the relevant time span, then that book can only be paired with intervals that start after the book comes into existence. Without further restriction, then, the domain of quantification will again include exactly one pair for each book about slugs, namely, the pair of that book with the maximal interval within the relevant time span that is also in the lifetime of the book. Then the sentence says that for most such pairs, I read the book at some point during the part of the relevant time span when the book existed. Since books generally can’t be read unless they exist anyway, this will not have any detectable effect on the truth conditions. On the other hand, now consider what happens if we replace read with write. When the meaning of (25) is computed using (29), the result is (30).
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(30)
[[I usually2 write a book about slugs]] = [[usually]] ( [[a2]] ([[book about slugs]]) ) ( [[I write]] ) = 1 iff for most pairs such that (i) x is a book about slugs at t and (ii) ~∃t’[t⊂int t’ and x is a book about slugs at t’ ], I write x at t.
In this case, the restriction to times when the books exist does make a difference. Writing a book involves bringing it into existence, which means that if I write a book x at time t, then x must not exist at the beginning of t. But (i) in (30) eliminates from the domain of quantification any pairs where x doesn’t exist at the beginning of t, and therefore no pair in the domain will satisfy the quantification. Under this view, then, the quantificational reading of (25) is predicted to be odd by virtue of being necessarily false. This explanation is in the spirit of Diesing’s preexistence requirement, and it fails for the same reason: it predicts that quantificational readings should always be impossible with creation verbs. As we see in (26), though, quantificational readings become possible when the creation verb is given contrastive focus. Even if focus contributes additional domain restrictions (and I will take the view that it does), this won’t help, since the problem is that the domain is too small, not too large. Other ways of linking the two time variables in the meaning of the indefinite article also fail in the same way. For example, instead of requiring of each pair that x exist throughout t, we could just require that x exists at an initial subinterval of t, or that x exists at some time before t. Lexical entries for a reflecting these two possibilities are shown in (31) and (32), respectively. (31)
[[a2]] = [λP . [λx . [λt . ∃t’[t’⊆initial t and P(x)(t’) = 1] ] ] = [λP . {: P(x)(t’) = 1 for some initial subinterval t’ of t }] [where < represents temporal precedence and t’⊆initial t iff t’⊆int t and there is no t”⊆t such that t”
(32)
[[a2]] = [λP . [λx . [λt . ∃t’[t’ . {: P(x)(t’) = 1 for some t’ before t} ]
With either of these options, the domain of quantification will be restricted to pairs where x exists at the beginning of t (or, in the case of (32), possibly where x existed but then ceased to exist before t). Since in order to write x at t, x must not exist at the beginning of t, no pair will satisfy the quantification and (25) will again be predicted to 13
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be necessarily false. But again, this will incorrectly rule out a quantificational reading of a creation verb when it’s focused, as in (26). I conclude that an explanation in terms of preexistence still doesn’t work. In the remaining sections I’ll offer one that, I hope, does.
6. Introducing Focus Sensitivity In this section I will show how we can derive the meaning of (26), which contains a focused creation verb, using a principle of quantification that is sensitive to focus. In Section 7 I will show how this can be extended so that it will also account for the original contrast between (unfocused) read and write. The principle I propose is given in (33). (The idea behind this is due to Rooth (1985), and has also been discussed by von Fintel (1994), among others.) (33)
Focus-sensitive restriction on quantification: When quantifying over a domain represented by a set of tuples of variables v (= ), the domain is restricted to values of v such that the focus-alternative set for that value of v contains at least one proposition that is true.
We can now apply this to (26), repeated in (34). (34)
I usually [KNIT]FOC a scarf. ≈ When I make a scarf, I usually do it by knitting.
To see how the principle in (33) applies in this case, let’s first assume that the relevant alternatives to knit are crochet and sew. (It’s also an interesting question why the obvious alternatives that come to mind are other creation verbs, but this relates to more general issues around the selection of alternative sets that are beyond the scope of this paper.) Now imagine a situation where there are just four relevant scarves s1, s2, s3, and s4, and four times t1, t2, t3, and t4. This is an idealization, of course, but it makes it easier to see how the focus-sensitive restriction works. Before (33) applies, the domain of quantification includes all 16 pairs made up of these four scarves and four times. For each of these pairs, an alternative set is constructed that predicates each of the alternatives knit, crochet, and sew to the pair. This is illustrated in (35).
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(35)
Preliminary domain of quantification for (34) with alternative sets: : Alt = { I knit s1 at t1, I crochet s1 at t1, I sew s1 at t1 } : Alt = { I knit s1 at t2, I crochet s1 at t2, I sew s1 at t2 } : Alt = { I knit s1 at t3, I crochet s1 at t3, I sew s1 at t3 } : Alt = { I knit s1 at t4, I crochet s1 at t4, I sew s1 at t4 } : : : :
Alt = { I knit s2 at t1, I crochet s2 at t1, I sew s2 at t1 } Alt = { I knit s2 at t2, I crochet s2 at t2, I sew s2 at t2 } Alt = { I knit s2 at t3, I crochet s2 at t3, I sew s2 at t3 } Alt = { I knit s2 at t4, I crochet s2 at t4, I sew s2 at t4 }
: : : :
Alt = { I knit s3 at t1, I crochet s3 at t1, I sew s3 at t1 } Alt = { I knit s3 at t2, I crochet s3 at t2, I sew s3 at t2 } Alt = { I knit s3 at t3, I crochet s3 at t3, I sew s3 at t3 } Alt = { I knit s3 at t4, I crochet s3 at t4, I sew s3 at t4 }
: : : :
Alt = { I knit s4 at t1, I crochet s4 at t1, I sew s4 at t1 } Alt = { I knit s4 at t2, I crochet s4 at t2, I sew s4 at t2 } Alt = { I knit s4 at t3, I crochet s4 at t3, I sew s4 at t3 } Alt = { I knit s4 at t4, I crochet s4 at t4, I sew s4 at t4 }
Now suppose that the facts are as follows: I knitted s1 during t1, I knitted s2 during t2, I knitted s3 during t3, and I sewed s4 during t4, and I didn’t make any other relevant scarves during the relevant times. The focus-sensitive principle in (33) tells us to check each value of to see if one of the alternatives is true. In (36) below, the true propositions are in bold and underlined. Then any values of for which there is no true alternative are eliminated. These are crossed out in (36). (36)
Applying the focus-sensitive restriction (33): : Alt = { I knit s1 at t1, I crochet s1 at t1, I sew s1 at t1 } Alt = { I knit s1 at t2, I crochet s1 at t2, I sew s1 at t2 } : Alt = { I knit s1 at t3, I crochet s1 at t3, I sew s1 at t3 } : : Alt = { I knit s1 at t4, I crochet s1 at t4, I sew s1 at t4 } : : : :
Alt = { I knit s2 at t1, I crochet s2 at t1, I sew s2 at t1 } Alt = { I knit s2 at t2, I crochet s2 at t2, I sew s2 at t2 } Alt = { I knit s2 at t3, I crochet s2 at t3, I sew s2 at t3 } Alt = { I knit s2 at t4, I crochet s2 at t4, I sew s2 at t4 }
: : : :
Alt = { I knit s3 at t1, I crochet s3 at t1, I sew s3 at t1 } Alt = { I knit s3 at t2, I crochet s3 at t2, I sew s3 at t2 } Alt = { I knit s3 at t3, I crochet s3 at t3, I sew s3 at t3 } Alt = { I knit s3 at t4, I crochet s3 at t4, I sew s3 at t4 }
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: : : :
Alt = { I knit s4 at t1, I crochet s4 at t1, I sew s4 at t1 } Alt = { I knit s4 at t2, I crochet s4 at t2, I sew s4 at t2 } Alt = { I knit s4 at t3, I crochet s4 at t3, I sew s4 at t3 } Alt = { I knit s4 at t4, I crochet s4 at t4, I sew s4 at t4 }
Once the extra pairs are eliminated, we are left with only the four pairs , , , and , as shown in (37). Then the meaning of usually requires that out of the remaining pairs , most are such that I knitted x at t. (37)
The new domain of quantification, with alternative sets: : Alt = { I knit s1 at t1, I crochet s1 at t1, I sew s1 at t1 } : Alt = { I knit s2 at t2, I crochet s2 at t2, I sew s2 at t2 } : Alt = { I knit s3 at t3, I crochet s3 at t3, I sew s3 at t3 } : Alt = { I knit s4 at t4, I crochet s4 at t4, I sew s4 at t4 }
In this case, then, three out of the four pairs in the new domain satisfy the quantification, and so (34) is correctly predicted to be true in the scenario described. Crucially, if the focus-sensitive restriction (33) had not applied, then the domain would have included all 16 original pairs. Since only three of these satisfy the quantification, this would have been too few to satisfy the semantics of usually, and sentence (34) would have been incorrectly predicted to be false. This result generalizes to sentences with contrastive focus on other constituents such as the subject or an adverbial modifier. For example, consider sentence (38), which has contrastive focus on the subject. (38)
[I]foc usually knit a scarf. ≈ when someone knits a scarf, I’m usually the one who does it.
Suppose again that there are four relevant scarves, s1, s2, s3, and s4, and four relevant times t1, t2, t3, and t4. Also suppose that the relevant alternative knitters are Rebecca and Georgia, and that the facts are as follows: I knitted s1 at t1, s2 at t2, and s3 at t3, and Georgia knitted s4 at t4, and Rebecca didn’t knit any scarves. When we apply the focussensitive restriction (33), the result is as shown in (39). (39)
The case of contrastive focus on the subject: : Alt = { I knit s1 at t1, Rebecca knits s1 at t1, Georgia knits s1 at t1 } : Alt = { I knit s1 at t2, Rebecca knits s1 at t2, Georgia knits s1 at t2 } : Alt = { I knit s1 at t3, Rebecca knits s1 at t3, Georgia knits s1 at t3 } : Alt = { I knit s1 at t4, Rebecca knits s1 at t4, Georgia knits s1 at t4 } 16
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: : : :
Alt = { I knit s2 at t1, Rebecca knits s2 at t1, Georgia knits s2 at t1 } Alt = { I knit s2 at t2, Rebecca knits s2 at t2, Georgia knits s2 at t2 } Alt = { I knit s2 at t3, Rebecca knits s2 at t3, Georgia knits s2 at t3 } Alt = { I knit s2 at t4, Rebecca knits s2 at t4, Georgia knits s2 at t4 }
: : : :
Alt = { I knit s3 at t1, Rebecca knits s3 at t1, Georgia knits s3 at t1 } Alt = { I knit s3 at t2, Rebecca knits s3 at t2, Georgia knits s3 at t2 } Alt = { I knit s3 at t3, Rebecca knits s3 at t3, Georgia knits s3 at t3 } Alt = { I knit s3 at t4, Rebecca knits s3 at t4, Georgia knits s3 at t4 }
: : : :
Alt = { I knit s4 at t1, Rebecca knits s4 at t1, Georgia knits s4 at t1 } Alt = { I knit s4 at t2, Rebecca knits s4 at t2, Georgia knits s4 at t2 } Alt = { I knit s4 at t3, Rebecca knits s4 at t3, Georgia knits s4 at t3 } Alt = { I knit s4 at t4, Rebecca knits s4 at t4, Georgia knits s4 at t4 }
In a way exactly parallel to (34), the domain is restricted to the four pairs , , , and , and the sentence is correctly predicted to be true. This can be worked out in a completely parallel way for sentences with contrastive focus on some other constituent such as an adverbial modifier.
7. Extending Focus Sensitivity Given the account for focused creation verbs that I presented in the previous section, we can ask whether the focus-sensitive restriction in (33) can or should have any effect on the original sentences (2)-(3), where there’s no contrastive focus on the verb. The sentences are repeated again in (40)-(41). (40)
I usually read a book about slugs. ≈ When I encounter a book about slugs, I usually read it.
(41)
I usually write a book about slugs. ≠ When I encounter a book about slugs, I usually write it / I’m usually the one who wrote it
The most obvious possibility to consider is that the focus-sensitive restriction (33) simply doesn’t apply when there’s no contrastive focus, since this means there are no alternative sets. However, if we take that route we will be left with no explanation for the contrast between read and write in (40)-(41). I propose, then, that we extend (33) so that it can apply even in cases like (40) and (41). A preliminary version of this is given in (42).
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(42)
Principle of default focus [to be revised]: For the purposes of principle (33), if a sentence S has no overt contrastive focus, it’s taken to have the alternative set {S, NOT S}, where NOT is propositional negation.
Let’s see if (42) can help. Imagine a scenario where there are four relevant books about slugs b1, b2, b3, and b4, and four relevant times t1, t2, t3, and t4. Then the preliminary domain of quantification for (40) would be as shown in (43). (43)
Preliminary domain of quantification for (40) with alternative sets: : Alt = { I read b1 at t1, I don’t read b1 at t1 } : Alt = { I read b1 at t2, I don’t read b1 at t2 } : Alt = { I read b1 at t3, I don’t read b1 at t3 } : Alt = { I read b1 at t4, I don’t read b1 at t4 } : : : :
Alt = { I read b2 at t1, I don’t read b2 at t1 } Alt = { I read b2 at t2, I don’t read b2 at t2 } Alt = { I read b2 at t3, I don’t read b2 at t3 } Alt = { I read b2 at t4, I don’t read b2 at t4 }
: : : :
Alt = { I read b3 at t1, I don’t read b3 at t1 } Alt = { I read b3 at t2, I don’t read b3 at t2 } Alt = { I read b3 at t3, I don’t read b3 at t3 } Alt = { I read b3 at t4, I don’t read b3 at t4 }
: : : :
Alt = { I read b4 at t1, I don’t read b4 at t1 } Alt = { I read b4 at t2, I don’t read b4 at t2 } Alt = { I read b4 at t3, I don’t read b4 at t3 } Alt = { I read b4 at t4, I don’t read b4 at t4 }
However, in this case the focus-sensitive restriction won’t change the domain, because it’s a logical necessity that one of the two alternatives is true in every case. And the situation will be exactly the same for (41), since for each pair , it’s also a logical necessity that one of {I write x at t, I don’t write x at t} will be true, if we’re dealing with simple propositional negation. Therefore a principle of default focus like that in (42) cannot provide an explanation for the contrast between read and write. There is an intuition, though, that it’s easier to talk about the books that you didn’t read than it is to talk about those that you didn’t write. (If you didn’t write it, then unless someone else did, how do you know which book it is?) One way to think of this is that it’s fairly clear what it means to have the opportunity to read a particular book, whether you take the opportunity or not, whereas it’s not so clear what it means to have the
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opportunity to write a book – that is, not just the time, resources, etc. to write a book, but to write a specific book. If you don’t take the opportunity, what book is it that you had the opportunity to write? I think this is what’s behind the intuitive appeal of an explanation involving preexistence. To capture this, I propose the revised principle of default focus in (44). Principle of default focus [final]: For the purposes of principle (33), if a sentence S has no overt contrastive focus, it’s taken to have the alternative set {S, FAIL-TO S}, where FAIL-TO p = NOT p and POSSIBLE p = ~p & ◊p
(44)
The possibility operator in (44) is meant to express something like having the opportunity – so, for example, FAIL-TO [I read A at t1] means that I had the opportunity to read A at time t1 but didn’t. It’s not clear how to make this notion fully precise, but certainly the modal base should be restricted to worlds where all the facts up to the specified point in time are the same as in the actual world. Requirements of a deontic or other nature also need to be included. This is so that, for example, seeing a book about slugs in the window of a closed bookstore will not count as an opportunity to read it, given that smashing the window to get it would violate social norms and potentially lead to unacceptable consequences (arrest, prosecution, committal to a mental institution, etc.). Formally, though, the only crucial aspect of this FAIL-TO operator is that it includes both propositional negation and a possibility modal, assuming some version of Kratzer’s possible-worlds semantics for modals (Kratzer, 1977, 1991). Under the new principle of default focus in (44), it’s no longer logically necessary that one of the alternatives for each pair is true. Specifically, if I had no opportunity to read some book x at some time t (and therefore didn’t read it), then neither of the alternatives {I read x at t, I FAIL-TO read x at t} would be true, and so such a pair would be eliminated from the domain of quantification. For example, suppose again that there are just four relevant books about slugs b1, b2, b3, and b4, and four relevant times t1, t2, t3, and t4. Then the preliminary domain of quantification for (40) would be as shown in (45). (This is just like (43) except that the simple negation has been replaced with FAIL-TO.)
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(45)
Revised preliminary domain of quantification for (40): : Alt = { I read b1 at t1, I FAIL-TO read b1 at t1 } : Alt = { I read b1 at t2, I FAIL-TO read b1 at t2 } : Alt = { I read b1 at t3, I FAIL-TO read b1 at t3 } : Alt = { I read b1 at t4, I FAIL-TO read b1 at t4 } : : : :
Alt = { I read b2 at t1, I FAIL-TO read b2 at t1 } Alt = { I read b2 at t2, I FAIL-TO read b2 at t2 } Alt = { I read b2 at t3, I FAIL-TO read b2 at t3 } Alt = { I read b2 at t4, I FAIL-TO read b2 at t4 }
: : : :
Alt = { I read b3 at t1, I FAIL-TO read b3 at t1 } Alt = { I read b3 at t2, I FAIL-TO read b3 at t2 } Alt = { I read b3 at t3, I FAIL-TO read b3 at t3 } Alt = { I read b3 at t4, I FAIL-TO read b3 at t4 }
: : : :
Alt = { I read b4 at t1, I FAIL-TO read b4 at t1 } Alt = { I read b4 at t2, I FAIL-TO read b4 at t2 } Alt = { I read b4 at t3, I FAIL-TO read b4 at t3 } Alt = { I read b4 at t4, I FAIL-TO read b4 at t4 }
Now suppose the facts were as follows: I had the opportunity to read b1 at t1, b2 at t2, b3 at t3, and b4 at t4. I actually read b1 at t1, b2 at t2, and b3 at t3, and I didn’t read any other relevant books about slugs in the relevant times. In this case when we apply the focussensitive restriction (33) to the new domain of quantification in (45), there will be many pairs for which neither alternative is true. This is illustrated in (46). (46)
Applying the focus-sensitive restriction (33): : Alt = { I read b1 at t1, I FAIL-TO read b1 at t1 } : Alt = { I read b1 at t2, I FAIL-TO read b1 at t2 } : Alt = { I read b1 at t3, I FAIL-TO read b1 at t3 } : Alt = { I read b1 at t4, I FAIL-TO read b1 at t4 } : : : :
Alt = { I read b2 at t1, I FAIL-TO read b2 at t1 } Alt = { I read b2 at t2, I FAIL-TO read b2 at t2 } Alt = { I read b2 at t3, I FAIL-TO read b2 at t3 } Alt = { I read b2 at t4, I FAIL-TO read b2 at t4 }
: : : :
Alt = { I read b3 at t1, I FAIL-TO read b3 at t1 } Alt = { I read b3 at t2, I FAIL-TO read b3 at t2 } Alt = { I read b3 at t3, I FAIL-TO read b3 at t3 } Alt = { I read b3 at t4, I FAIL-TO read b3 at t4 }
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: : : :
Alt = { I read b4 at t1, I FAIL-TO read b4 at t1 } Alt = { I read b4 at t2, I FAIL-TO read b4 at t2 } Alt = { I read b4 at t3, I FAIL-TO read b4 at t3 } Alt = { I read b4 at t4, I FAIL-TO read b4 at t4 }
This means that the domain is restricted to the pairs , , , and . Since three pairs out of the four left over are such that I read x at t, sentence (40) is correctly predicted to be true. Furthermore, this explains why we tend to give (40) paraphrases like “when I encounter a book about slugs, I usually read it.” The encountering part comes from the notion of opportunity inherent in the FAIL-TO operator. Now we have an explanation for the fact that a quantificational reading is not available with an unfocused creation verb as in (41). Given the focus-sensitive restriction in (33) combined with the principle of default focus in (44), in order for a pair of a book and a time to be included in the domain of quantification, it has to be the case that I had the opportunity to write x at t. But in order to talk about having the opportunity to write this particular book independently of having written it, it would need to be sufficiently individuated out of the vast class of imaginable books. Without more context, one of two things would happen. Either no books would count as ones I had the opportunity to write unless I actually wrote them, or else all imaginable books that I could plausibly have written during any of the relevant times would have to count – which is to say that even if I did write a book during some relevant time, any book I might have written instead would have to be included as well (provided at least that it was sufficiently distinct from the one I did write to be called a different individual). In the first case, (41) would be necessarily true, since I must have written any books that I wrote. And in the second case, (41) would be almost necessarily false, since there are always going to be far too many different imaginable books for someone to have written most of them. Of course, the same thing would happen if the adverb in (41) were always instead of usually. If the adverb were a negative one like rarely, then the situations would be switched, with the first case leading to necessary falsity and the second leading to almost necessary truth. In any of these cases, trying to derive a quantificational reading of a sentence like (41) that has an unfocused creation verb will lead to nearnecessary truth or falsity. Assuming that sentences can be ruled out on the basis of that, this explains the original contrast between non-creation verbs like read and creation verbs
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like write. This also explains why putting contrastive focus on a creation verb makes a quantificational reading suddenly available: once a set of salient alternatives to a creation verb is present (such as {knit, crochet, sew}), the default focus principle (44) is no longer applicable, and so the problem of determining what counts as an opportunity to write a particular book does not arise. On the other hand, if we could set up a context where the relevant books that someone had the opportunity to write were sufficiently individuated independently of whether they wrote them, then applying the focus-sensitive restriction (33) along with the principle of default focus (44) would no longer lead to (near-)necessary truth or falsity. In such a context we would expect a quantificational reading to become possible. This is in fact what happens in (47). (47)
[Context: I’m a freelance writer who gets requests from clients to write books, articles, and so on to various specifications.] I usually write a book about slugs. (ii) When I get a request for a book about slugs, I usually take the job.
In this kind of scenario, (47) indeed allows the kind of reading in (ii). This is predicted because in the context given, it’s clear that any time I get a request to write a book, that counts as an opportunity to write a specific book. So we can simply look at the relevant pairs of books and times such that I got a request to write x in t, and see whether I took the job and wrote x.
8. Projections of Sets of Intervals In Section 3 I introduced the Max operator, which takes a set of intervals and yields only the maximal members of that set. This was adequate for sentences with imperfective when-clauses, such as (10), as well as for quantificational readings of indefinites under the analysis developed up through Section 5. However, once the focussensitive restriction (33) and principle of default focus (44) are added to the analysis, a more complicated notion than maximal intervals is needed. This is because in the earlier version of the analysis, the sets of times that the Max operator applied to always had the
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subinterval property, whereas in the revised version this is not necessarily the case. For example, consider sentence (40), repeated once again in (48). (48)
I usually read a book about slugs. ≈ When I encounter a book about slugs, I usually read it.
Again I assume there’s a set of relevant books, but let’s just consider one of them – let’s call it b. Let’s also assume that the context provides a relevant time span; for concreteness, let’s assume that this is the calendar year from January to December (2005 if you want to be really concrete about it). Let’s further suppose that I come into contact with book b only once during the year, when I’m in a bookstore on August 15 from 1:00 to 4:00 in the afternoon. Let’s call the interval when I’m in the store S. Now clearly all the intervals at which I have the opportunity to read b are subintervals of S. But which subintervals? Let’s suppose that b is a relatively short book that would only take, say, 15 minutes to read. Furthermore, let’s suppose that I’m just not the kind of person who would stop and take a break in the middle of reading such a short book, and that I read at a constant rate, so in fact it would take exactly 15 minutes for me to read b. (If you don’t think this is realistic, at least grant that there could be a minimum and a maximum time I could take to read the book, for example, between 10 and 20 minutes.) Crucially, assume that given my dispositions and the length of the book, taking the whole interval of S to read the book is just not a possibility. This means that S itself will not count as an opportunity to read the book, but all the 15-minute subintervals of S will. This is illustrated in (49). (49) Opportunities to read a book
opportunities to read b
Let T be the set of intervals illustrated in (49), i.e., the set of all the 15-minute subintervals of S. Recall that the definition of the Max operator is as in (50). (50)
Max(p) = {t: p(t)=1 and ~∃t’[t⊂int t’ and p(t’)=1}
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If the Max operator applies to the set of intervals pictured in (49) (the set of all 15-minute subintervals of S), it will have no effect, because no member of the set is a subinterval of any other member of the set. Thus each pair consisting of book b and any one of these 15-minute intervals is included in the domain of quantification. Since there’s an infinite number of these intervals, this leads to a problem similar to the one encountered with imperfective when-clauses in Section 3: we have to quantify over an infinitude of overlapping times. If we replaced usually with always in (48), then, in order for the sentence to be true it would have to be the case that I read book b an infinite number of times during S. (Again, even if we assumed some level of granularity, the sentence would still require me to have read book b at multiple overlapping intervals.) Intuitively, though, it’s only necessary that I read b once during all of S. Therefore we need an operator that will take the set of overlapping intervals illustrated in (49) and yield the set containing just S. Intuitively, it should take a set of possibly overlapping intervals and yield only the entire intervals covered by the combination of the original ones. For example, look at (51). (51) Projections of overlapping intervals (a)
(b)
The new operator should take the set of intervals illustrated in (51.a) and yield the set of intervals illustrated in (51.b). I will call this modified set the “projection” of the original set, since the intervals in (51.b) are like the shadows cast by the combination of the intervals in (51.a). An operator that takes any set of intervals T and returns its projection is defined in (52). (52)
For any set of intervals T: Proj(T) = {t: t is an interval and t∈p(∪T) and there is no interval t’ such that t⊂int t’ and t’∈p(∪T)} [where p(A) = the power set of A]
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It’s easier to understand (52) if you think of constructing the projection of T in three steps, as in (53). (53)
For a given set of intervals T: Def: Tu = ∪T = the union of all the intervals t∈T i.e., the set of points of time “covered” by T
(a)
(b)
Def: Tint = {t: t is an interval5 and t∈p(Tu)} = { t: t is an interval and t∈p(∪T) } = the set of intervals that are in the power set of Tu, i.e., the set of intervals containing only points of time in Tu,
(c)
Def: Proj(T) = {t: t∈Tint and there is no t’∈Tint such that t⊂t’} = Max(Tint) = {t: t is an interval and t∈p(∪T) and there is no interval t’ such that t⊂int t’ and t’∈p(∪T)} i.e., the set of maximal intervals that are elements of Tint
Now we can replace the Max operator with this new projection operator in the meaning of usually, as shown in (54). (54)
[[usually2]] = [λP . [λQ . For most pairs such that t∈Proj(P(x)), Q(x)(t)=1] ]
Let’s return to the set of intervals illustrated in (49), shown again in (55). (55) Opportunities to read a book t1
t2 opportunities to read b
In the example discussed, this set represented all the opportunities for me to read a particular book b, and consisted of all the 15-minute subintervals of a larger interval S. The problem before was that the domain of quantification for the sentence I usually read a book about slugs was predicted to include , , and so on for every 15-minute subinterval of S. When the Max operator is replaced with the projection operator, 5
For my purposes, an “interval” is by definition continuous. A so-called “discontinuous interval” under the terminology I’m using is simply a set of points of time that is not an interval.
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however, the domain of quantification will only include one pair with the individual b, namely (assuming I had no opportunities to read b outside of S). What the semantics of usually will then do is check whether I read b during any subinterval of S (the reference to subintervals coming from perfective aspect on read). So if I take any of the opportunities illustrated in (55), this will satisfy the quantification for that pair. Then it will do the same thing for all the other relevant books and my opportunities to read them. There is a technical problem here, however, which is that in order to make this work out I needed to ignore the perfective aspect on read for the purposes of determining the “opportunities” for me to read b, but take it into account in the semantics of usually. This is closely related to the problem of perfectives in when-clauses mentioned in note 4, and it may take some work to sort this out.
9. Conclusions and Further Directions An account using preexistence cannot simultaneously capture both the contrast between creation and non-creation verbs on the one hand [(2)-(3)] and that between focused and unfocused creation verbs on the other [(3)-(4)]. I have proposed an alternative account that captures the basic intuition behind the preexistence explanation while avoiding this disadvantage. The two main ingredients of my account are a focussensitive restriction on domains of quantification and a principle of default focus that pairs focus-less sentences with a strengthened, modalized form of negation (the FAIL-TO operator). Besides accounting for both contrasts in the availability of quantificational readings, this account also helps explain why the quantificational readings that are available are understood the way they are. I would hope, though, that this account could help explain other facts besides these two contrasts in (2)-(4). Diesing (1992) considers a variety of other facts besides those relating to creation verbs in her discussion of quantificational indefinites. For example, she observes that English object extraction and antecedent-contained deletion (ACD) have restrictions on which kind of reading is available. She also shows that, in German, scrambling and a certain kind of extraction show restrictions along similar lines.
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We ought to see if the account I’ve presented here can bring anything to bear on these other phenomena, but I’ll leave that to future work.
References Diesing, Molly, 1992. Indefinites. Linguistic Inquiry Monograph 20. Cambridge, Massachusetts: MIT Press. von Fintel, Kai, 1994. Restrictions on Quantifier Domains. Ph.D. dissertation, University of Massachusetts, Amherst. GLSA Publications. Kratzer, Angelika, 1977. What ‘must’ and ‘can’ must and can mean. Linguistics and Philosophy 1, pp. 337-355. Kratzer, Angelika, 1991. ‘Modality’/ ‘Conditionals.’ In A. von Stechow and D. Wunderlich (eds.), Semantik. Ein internationales Handbuch der zeitgenössischen Forschung. Berlin, 639-659. Landman, Fred, 1992. The progressive. Natural Language Semantics; 1;1: 1-32. Parsons, Terence, 1990. Events in the Semantics of English: A Study in Subatomic Semantics. Cambridge, Massachusetts: MIT Press. Percus, Orin, 1999. A More Definite Article. Quaderni del Dipartimento di Linguistica, 2001, University of Florence. Portner, Paul, 1998. The progressive in modal semantics. Language 74;4: 760-787. Rooth, Mats Edward, 1985. Association with Focus. Ph.D. dissertation, University of Massachusetts, Amherst. GLSA Publications.
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