Kieran Britt Department of Discourse Pragmatic Constraints on Undergraduate Honors Thesis Defended on April 13th, 2020 Thesis Advisor: Professor Laura Michaelis (Department of Linguistics) Honors Council Representative: Professor Jeremy Calder (Department of Linguistics) Outside Reader: Professor Graeme Forbes (Department of Philosophy)

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Discourse Pragmatic Constraints on Quantifier Scope Ambiguity In this thesis, I argue that, in many contexts that appear likely to generate Quantifier Scope Ambiguity (QSA), certain apparently universal discourse pragmatic constraints that are attached to particular syntactic constructions prevent QSA from arising. These discourse pragmatic constraints broadly concern the scopal relations of topical and focal constituents, and manifest at the level of the construction, preventing a sentence with either (a) a particular articulation, or (b) a particular construction, from being ambiguous.

To understand the nature of the problem, consider the following sentences:

(1) Someone talked to everyone at school.1

(2) Everyone at school talked to someone.

What do these sentences mean? I think it is fairly uncontroversial that sentence 1 means something like, “there is a specific person who talked to everyone at school.” This is known as the surface reading, because the scope of the quantifiers matches the word order of the sentence. Represented in the of first-order logic, this would be:2

(1a) (∃x) (Ɐy) Txy

On the hand, in the right , one could interpret sentence 1 as saying, in regimented English, something like, “at least one person, but not necessarily the same person, talked to everyone at school.” This is known as the inverse reading. In first- order logic:

(1b) (Ɐy) (∃x) Txy3

1 Both of these sentences actually exhibit a bracketing , regarding the scope of ‘at school.’ For simplicity, I’ll be ignoring this in this example. 2 Here, I adopt the notation of Forbes 1994. Forbes calls this the some/all reading (Forbes 1994, p. 246.). 3 Forbes calls this the all/some reading (Forbes 1994, p. 246.).

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Sentence 2, on the other hand, seems like it could mean either “Everyone at school talked to at least one person, not necessarily the same one” or “Everyone at school talked to the same specific person” In first-order logic:

(2a) (Ɐx) (∃y) Txy

(2b) (∃y) (Ɐx) Txy

Sentences like those above are not the only class of cases where QSA occurs. On top of sentences like 1 and 2, similar QSA sentences can be generated with a variety of different quantifiers. Quantifier phrases like ‘many people’, ‘most people’, ‘all of the people’, ‘a person’, ‘the person’, ‘three people’, and others4 can be substituted for the quantifiers in sentences 1 and 2, generating (or occasionally not generating) different QSAs. In addition to this, both sentences 1 and 2 can undergo syntactic processes like passivization, which can affect QSAs. QSA can also occur, and interestingly fail to occur, across diathesis alternations in ditransitive sentences. And sentences with multiple quantifiers are not the only ones that can generate QSA (multiple-quantifier ); it can also occur between a quantifier and a operator (quantifier- negation ambiguities), such as in the sentence:

(3) John didn’t eat a cookie.

Which either means, “There is a cookie that John didn’t eat.” or “There are no cookies that John ate.” depending on the context in which the sentence is said, and the prosody with which it is said. There are certainly other contexts where QSA can occur. But the point is that QSA is a surprisingly frequent occurrence, despite not being noticed by most native speakers.

Why are these sentences ambiguous, and why does this ambiguity go generally unnoticed by most speakers? In this paper, I’m going to try to provide a partial answer to these questions by way of answering a related question: why are some putative QSA sentences not ambiguous, despite their syntactic and semantic similarity to the questions above? Ultimately, I will argue that the answer to this question is that certain

4 While my examples here involve persons/people, they obviously can be extended to include all sorts of other nouns, such as ‘man’, ‘woman’, ‘dog’, ‘cat’, ‘chair’, etc.

3 discourse pragmatic constraints—both universal and construction specific—prevent QSA from arising in a wide range of cases. While this won’t explain why these ambiguities arise (assuming this is a well-formed question, which is debatable) or how they are resolved, it will narrow the classes of cases which can be said to genuinely exhibit QSA.

The rest of this work will be structured as follows. Section 1 will discuss some important preliminaries for understanding this work, including the I will adopt, and the theoretical assumptions I will be operating under as I investigate QSA. I will also provide a brief introduction to the discourse pragmatic framework I will be assuming that will do the most work in my analysis. In section 2, I will investigate some of the previous work that has been done which is relevant to QSA, and analyze the cases in which a sentence ought to exhibit QSA, but no QSA occurs. In section 3, I will synthesize these results, providing an account of the discourse pragmatic constraints that prevent QSA. I will summarize my findings and conclude in section 4. In the appendix, I will take a brief look at how my account may be implemented in the formal semantic system provided by event-semantic Type-Logical Grammar. The appendix will be more technical, and is not required for an understanding of the core details of my account.

1. Preliminaries 1.1 Some Notes on the Methodology of this Work Before diving into my analysis of QSA, I must clear up a number of methodological issues. This paper is a work in , and as such, it will not rely overmuch on empirical methods of study. Rather, this work will proceed through analysis of the , , and of English sentences, either of my own creation or that I draw from various sources. The interpretation of these sentences and their grammaticality/felicity will thus rely on my own intuitions as a native speaker of English, as well as the intuitions of the linguists whose data I have drawn from. The rigor in this work will be drawn from the synthesis of the sources from which I draw my data, as well as the mathematical rigor of my implementation of my findings in a formal semantics system.

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The semantic/syntactic framework that will be adopted for this paper is by and large the theoretical framework Neo-Davidsonian event semantics implemented in Type-logical Grammar, an offshoot of that addresses some of the key problems that Montague grammar faced.5 Despite this, real attention will be given to the linguistic findings of both Chomskyan linguists and construction grammarians, and ultimately, it will be argued that discourse pragmatic constraints which affect semantic derivation relevant to QSA exist primarily at the level of construction, rather than at the lexical or syntactic levels. The formal semantics of the examined phenomena will be derived using type-logical grammar into event semantics using the simple theory of types, and the existence of a model-theoretic semantics for this derivation will be presumed. I will provide an overview of the discourse pragmatic theory I will be utilizing in the next section.

In order to keep this paper within a reasonable length, I must sidestep many interesting linguistic and philosophical issues. First, I will be treating ‘a’, ‘the’, and numerals such as ‘two’ or ‘three’ as quantifiers. Second, by and large I will be ignoring the theoretical issues posed by definite descriptions, though certain discourse pragmatic features of definite descriptions will be accounted for. Third, this paper will ignore the interesting and unique QSAs which are generated in intensional contexts.6 Fourth, while I am partial to the analysis of modal and temporal operators in terms of quantification over worlds/times, analogues to QSA with respect to modal and temporal operators will not be addressed here. Fifth, even though QSA is a particular puzzle within the more general issue of quantifier scope, I will not attempt to give a complete analysis of quantifier scope here, and will thus be ignoring certain issues surrounding quantifier scope and bound (the notorious donkey sentences, for example). In doing so, I will be avoiding the analysis of sentences that require Discourse Representation Theory (DRT) or an equivalent to be given formalization.7 Finally, in order to prevent this

5 The account of Type-Logical grammar which I will adopt is, in general, that of Forbes 2017. I will also be adopting some of the more technical apparatus of Forbes 2015. 6 Forbes 2006, pp. 36-51, Pietroski and Hornstein 2002, p. 23-39, and Steedman 2012, p. 50-51, all give examples of these, and discuss them. 7 Steedman 2012 gives this topic a proper treatment, and argues against DRT. Gamut 1994, p. 264-297 gives an overview of DRT and Dynamic Logic.

5 project from ballooning to an unreasonable length, I will be forced to be fairly strict about the classes of sentences (in terms of constructions) that I will investigate.

There is an important distinction, discussed by Pietroski and Hornstein, between syntactic ambiguity and openness to semantic interpretation (Pietroski and Hornstein 2002, p. 1-4). Roughly speaking, ambiguity is a syntactic notion, involving different possible scopal relations of constituents in a sentence. But sentences that admit of no ambiguity can be true on multiple interpretations. Pietroski and Hornstein (2002) argue that sentences which putatively exhibit QSA and are headed by ‘strong determiners’ (each, every, both, etc.), like ‘Everyone pushed a truck’ in fact are not ambiguous, merely open to interpretation. For the sake of this paper, I will remain uncommitted as to the correctness of Pietroski and Hornstein’s analysis, as the correctness of their analysis will ultimately not impact the account of QSA I am giving: if Pietroski and Hornstein are correct, then there is simply another, in this case syntactic, constraint preventing scope inversion in some putative QSA sentences. For the purposes of my analysis, however, I will be taking a very permissive view about which putative QSAs are genuine. I will thus treat these ambiguities as genuine syntactic ambiguities, rather than merely open to interpretation, though if it turns out that Pietroski and Hornstein are correct, my account could be amended without difficulty.

Finally, I should note that I will not attend to the semantics of every possible quantifier phrase—simply because there are too many to give a proper treatment. Rather, I will be focusing my attention on first order definable quantifiers and their English counterparts, though in general my observations should extend to quantifiers which are not definable in first-order logic, such as ‘most’. I will also be exclusively looking at what are called D-quantifiers, rather than A-quantifiers. That is to say, all of the quantifiers I will be investigating are syntactically speaking determiner phrases, even though there are a fair number of non-determiner quantifiers in both English and other , such as ‘always’.8

8 Peters and Westerstahl 2006, pp. 10-13 gives a discussion of this distinction. For a discussion of focus constraints on A-quantifiers that is similar to the view I will be giving, see Herburger 2000.

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1.2 A Brief Introduction to Discourse Pragmatics As my ultimate analysis of QSA will argue that QSA fails to occur when discourse pragmatic constraints prevent scope inversion, it will be necessary to give a brief overview of the discourse pragmatic theory I will be adopting. The account I am going to give is for the most part a synthesis of the accounts of discourse pragmatics given in Lambrecht 1994 and Ward and Prince 1991. I will unfortunately not be able to provide a similar overview of event semantics or type-logical grammar, as providing an overview of those would require a paper in themselves, but my overall analysis of QSA will not require understanding of those particular tools to be understood.9

For my purposes, and following Lambrecht, I will assume that there are two main components of pragmatics: conversational pragmatics, which involves the semantic interpretation of syntactically underdetermined sentences through context and world knowledge using, primarily through Gricean Implicature, and discourse pragmatics, which has to do with the felicity of certain syntactic forms of sentences given the already in the context, and the information that the speaker is intending to convey. Because discourse pragmatic constraints affect the felicity of certain syntactic forms, they thus constrain the permissible interpretations of those forms. This is because, given a domain of discourse, a given syntactic form will only be felicitous to convey certain semantic interpretations: when another interpretation is intended, a different syntactic form ought to be used. Arguably, the correct term for discourse pragmatics is information structure, which Lambrecht defines as follows:

That component of sentence grammar in which … are paired with lexicogrammatical structures in accordance with the mental states of interlocutors who use and interpret these structures as units of information in discourse contexts. (Lambrecht 1994, p. 5).

It should be noted that Lambrecht uses the term ‘’ ambiguously, sometimes meaning ‘proposition’ roughly as it is typically understood in the philosophical tradition,

9 For a very succinct summary of these, see Forbes 2006, pp. 16-35.

7 and sometimes meaning ‘the denotatum of propositions’ (events, states of affairs, etc.), though the former is what is intended here (Lambrecht 1994, p. 53).10

Discourse Pragmatic information involves the speaker’s beliefs about the hearer’s knowledge of the domain of discourse, and can be broadly divided old information and new information. Intuitively, old information is the information conveyed in a discourse or sentence which is assumed by the speaker to be shared by the interlocutors, while new information is what the speaker believes the listener will have to add to the shared background, once uttered by the speaker. Lambrecht defines old information as information that is pragmatically presupposed,11 meaning that the speaker assumes the described events are already known to the listener (Lambrecht 1994, p. 52). New information, by , is information that is pragmatically asserted, meaning that the speaker intends the listener to have a mental representation of the described event as a result of the sentence being uttered (Lambrecht 1994, p. 52). Important to note is that the information that is pragmatically asserted need not all be new to the listener: some asserted information serves only to make the referents of phrases be identifiable to the listener, given what has been presupposed.

Two particularly important discourse pragmatic relations are the topic of a sentence, and the focus of the sentence. The topic of a sentence is, intuitively, the discourse referent that the sentence is about (Lambrecht 1994, p. 118). More precisely, Lambrecht says the following:

A referent is interpreted as the topic of a proposition if in a given discourse the proposition is construed as being about the referent, i.e. as expressing information which is relevant to and which increases the addressee’s knowledge of the referent (Lambrecht 1994, p. 127).12

10 I say ‘roughly’ because Lambrecht, following the traditions of linguistics, seems to view propositions as expressing mental representations of meaning, rather than as abstract objects or sets of possible worlds, as is popular in many philosophical traditions. 11 Lambrecht discusses how pragmatic differs from semantic presupposition in Lambrecht 1994, pp. 61-63. In brief, sentences which all exhibit the same semantic presupposition (require a presupposed proposition in order to have any truth ) may differ in their pragmatic presupposition, which can be marked by focus effects through prosody. 12 I replace Lambrecht’s use of different font to denote technical terms with italics.

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Potential topics thus are the referents of noun phrases and quantified phrases which do refer to some entity or entities; non-referring expressions like ‘no man’ cannot be topics (Lambrecht 1994, p. 156).13 Importantly, the topic of a sentence need not be the first element in a sentence, the subject of a sentence, or the theme of a sentence (Lambrecht 1994, p. 117), and some sentences contain no topic, while others may have multiple topics. Topic expressions must refer to referents that have been pragmatically presupposed, which (as I’ll discuss later) means that topical referents cannot be the focus of a sentence (Lambrecht 1994, pp. 151-156).

There are important restrictions on the acceptability of discourse referents as topics. Lambrecht provides a topic acceptability scale, which categorizes a potential topic referent as more or less acceptable depending on how identifiable the discourse referent is: currently active referents under discussion are the preferred topics, followed by accessible referents which have been previously topical. Unused but mentioned referents, and brand-new ‘anchored’ (known to both speaker and listener) referents are next in line for acceptability, with brand-new unanchored discourse referents being least acceptable (Lambrecht 1994, p. 165). I will be adopting this approach to assess topic felicity, though I will supplement it with an analysis due to Ward and Prince (Ward and Prince 1991). Ward and Prince provide formal constraints on topic acceptability, arguing that felicitous topics are those that stand in a (discourse) salient partial or strict ordering relation to previously mentioned discourse referents: relations such as ‘part of’, ‘subset of’, ‘member of’, and ‘subtype of’ (Ward and Prince 1991, p. 173). The ordering refers to how the previously mentioned discourse referents stand in relation to a topic. For example, if the discourse is about the cars that someone owns, it would be felicitous to mention one’s own car as a topic (an object at the same level in the parthood ordering), or to discuss a part of a previously mentioned car (an object lower in the parthood ordering), or to discuss an overall brand of car (an object higher in the subtype ordering)

13 Lambrecht’s analysis also entails that many uses of quantifier phrases like ‘some dog’ or ‘every dog’ cannot be topical. However, Lambrecht notes that some universally quantified phrases may be topical, “provided that their referents are coextensive with the entire class designated by the NP” (Lambrecht 1994, p. 127) and gives the example, “as for all his friends, they…” (ibid). Additionally, Lambrecht seems to have no qualms with treating phrases like, ‘a boy’ or ‘the children’ as potentially topical, and nothing in his analysis blocks specific existentially quantified noun phrases like ‘some guy wearing a red shirt’ from being topical in certain contexts.

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(Ward and Prince 1991, p. 175). Importantly, possible discourse referents that stand in a relation to previous topics that is not a strict or partial ordering on the domain of discourse are not permissible as topics (Ward and Prince 1991, pp. 175-176).

The other important discourse pragmatic relation for my purposes is Focus. Intuitively, the focus of a sentence is the important new information in the sentence. More precisely, Lambrecht defines focus as, “the semantic component of a pragmatically structured proposition whereby the assertion differs from the proposition.” (Lambrecht 1994, p. 213). In essence, the focus of a sentence is the part of what is asserted that is wholly new, and thus not recoverable from what has been pragmatically presupposed. Unlike topics, all sentences must have a focus (Lambrecht 1994, p. 206, also p. 224), and when nothing in the assertion is presupposed, the focus and the assertion will coincide (Lambrecht 1994, p. 217). The focus of a sentence is usually, though not always, marked by prosodic accent on the focal constituent,14 and the focus of a sentence is always a phrasal constituent; either a predicate, an , or an entire proposition expressed through a sentence/clause (Lambrecht 1994, p. 215).

While I will be arguing that discourse pragmatic constraints on constructions prevent scope inversion which generates QSA, it is important to note that sentences which are semantically/syntactically identical may differ in the discourse pragmatic relations held by sentence constituents. This can be seen through a very common method of demonstrating differences in topic/focus, the question-answer test. A particular sentence may serve to be the answer to multiple questions, but the constituents of the sentence will serve different discourse pragmatic functions in different contexts. Consider the following example, where words written in all-caps are prosodically stressed (adapted from Lambrecht 1994, p. 121):

(4a) (What did the children do next?) The children went to SCHOOL.

(4b) (Who went to school?) The CHILDREN went to school.

14 Thorough discussion of the prosodic marking for various focal accents is out of the scope of this paper, though Lambrecht gives a thorough analysis. One important note, however, is that prosodic marking underdetermines focus at least in cases where the VP of an utterance is accented (See Lambrecht 1994, p. 304), and this underdetermination must be made up for by context.

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(4c) (What happened?) The CHILDREN went to SCHOOL!

Using this example, it is possible to provide three broad discourse pragmatic categories of sentence. 4a is known as a topic-comment sentence, and serves the function of predicating a property over a previously established discourse referent, in this case ‘the children’. In such a sentence, the subject is (usually)15 the topic—subject position is the grammatically unmarked topic articulation—while the focus element will be the verb phrase that is predicated on the topic, namely ‘went to school’. Topic-comment sentences thus exhibit predicate focus, as the predicate is the wholly new information in the sentence.

Example 4b. is what Lambrecht calls an identificational sentence (Lambrecht 1994, p. 122). Identificational sentences serve to establish a relationship between an argument and an as-yet unsaturated proposition (Lambrecht 1994, p. 126). No sentence constituent can properly be called topical in such a sentence, as the topic is the open proposition which the new element saturates, and the new argument (here, the subject of the sentence) is the focal element. Such a sentence thus has argument focus, as whatever argument saturates the open proposition will be focal.

Finally, example 4c. is dubbed by Lambrecht as an event-reporting sentence (Lambrecht 1994, p. 126), and, when the verb is intransitive, falls under the broader category of thetic sentences, which include event-reporting sentences and presentational sentences (Lambrecht 1994, p. 144). These are sentences which seek to assert an event (event reporting) or the existence of an object (presentational). They are felicitous to assert out of the blue, and the hallmark of these sentences is that none of the information conveyed is pragmatically presupposed. Thetic, event reporting, and presentational sentences thus do not have a topic, and the entire sentence can be described as in focus, as the entire sentence is new. Such sentences therefore have sentence focus.

15 Lambrecht adds a caveat to this, which I will not discuss here. See Lambrecht 1994, pp. 122 and 131- 137.

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With this analysis of discourse pragmatics in , we can now discuss the discourse pragmatic constraints which affect QSA, first looking at the sorts of sentences which do not exhibit QSA, despite their syntax.

2. When QSA Does Not Arise: Diathesis Alternations, Specificity Effects, and Topicality and Focus Effects on QSA

In this section, I will discuss linguistic constraints on certain constructions that prevent QSA from arising when it otherwise would. These constructions, sometimes referred to as argument-structure constructions, are closely associated with specific classes of verbs (e.g., transfer verbs like give, send and present), and regulate the morphosyntactic realization of of verbs in the class. For example, the Simple Transitive construction requires that the second argument of a transitive verb be realized as an accusative case direct object. There is often more than one morphosyntactic realization possibility for a given verb class, and in such cases linguists have recognized pairings called alternations or diathesis alternations. The constructions and diathesis alternations that I will consider are the Simple Transitive, and the following trivalent constructions and alternations: The create/transform alternation, the spray/load alternation, and the dative alternation. It will be worth looking at some examples of each of these constructions before going forward.

Simple Transitive

The simplest type of construction that I will be looking at is the simple transitive. This construction characterizes most instances of QSA, in both its multiple-quantifier ambiguity and quantifier-negation ambiguity forms. The following sentences are examples of the simple transitive:

(5) John sees Mary

(6) John sees Mary across the street16

16 This sentence technically exhibits a bracketing paradox: ‘across the street’ could scope over the whole sentence, or merely over the verb phrase. The former case might be meant in a context where the speaker wishes to address that the seeing of Mary by John is done across the street, while in the latter

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Despite the added content in sentence 6, both of these sentences are simple transitive, because both of these sentences contain only a transitive verb, and have the general syntactic structure SVO. More precisely, the syntactic derivations I’ll be using for such sentences are the following:

(7) [John]NP [[sees]v [Mary]N]VP

(8) [John]NP [[sees]v [Mary]N [[across]prep [[the]Det [street]N]DP]PP]VP

The majority of our examples of QSA are examples of simple transitive constructions, e.g.:

(9) Someone guards every door of the palace

(10) John didn’t see a man

Simple transitive constructions may also be passivized, as in the following:

(11) Every door of the palace is guarded by someone

(12) A man wasn’t seen by John

(13) No man was seen by John

Due to the prevalence of transitive verbs, simple transitive constructions account for the majority of QSAs.

Trivalent Constructions

The other kind of constructions that I will be looking at are associated with an array of verb classes that denote three-argument relations. These trivalent constructions include: the create/transform alternation, the spray/load alternation, and the dative alternation. For example, the following sentences illustrate the ditransitive alternation:

case, Mary is across the street from John, and John sees her. I will be adopting the latter reading and ignoring this ambiguity for this example.

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(14) The instructor gave a book to every student. (Oblique goal)

(15) The instructor gave a student every book. (Double object)

As I’ll discuss in the next section, the first of these exhibits QSA, while the second does not. Verb alternations such as these involve a ditransitive verb which may manifest in two different constructions: in the oblique goal construction (so called because, for other manifestations of this construction, the semantic goal argument is in the oblique position, that is, in the outer verb shell), the direct object (‘a book’) is in the inner verb shell. In the double object variant, the object positions flip, and the direct object (or more precisely, the secondary object) is in the outer verb shell.

I’ll give a more thorough discussion of the trivalent constructions in question in the next section, but for now it suffices to recognize that each of these patterns serve to map an ordered three-place semantic relation (e.g., the give relation, with arguments agent, theme and recipient) to a syntactic template that likewise contains three ordered grammatical roles, subject, object, and oblique. The subject is the preverbal noun phrase that controls verb agreement, the object is the immediately postverbal noun phrase that would be assigned accusative case if it were a pronoun, and the oblique is a preposition phrase that follows the object (e.g., to every student). The noun phrase that follows the object in the Double Object construction is sometimes referred to as a secondary object, and I will follow that practice here. It is important to distinguish semantic roles from grammatical roles because, as we will see, a recipient argument that is mapped to the secondary object role via the Double Object construction has different discourse-pragmatic properties from a recipient mapped to the oblique role (via the oblique goal construction). A summary of the syntax-semantics mapping properties of each of the constructions examined here is given in Table 1.

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Alternation Construction Example Thematic Grammatical Roles (in Roles order)

Create/ Transform: Create John made a Agent, Subject, Object, statue from a Theme, Oblique Creation verbs like: slab of marble Source make, bake, knit, sculpt, etc.

Transform John made a Agent, Subject, Object, slab of marble Theme, Goal Oblique into a statue

Spray/Load Applicative John sprayed Agent, Subject, Object, paint onto a Theme, Oblique Cause motion verbs wall Location like: load, spray

Oblique John sprayed a Agent, Subject, Object, Goal wall with paint Location, Oblique Theme

Dative Oblique John gave a Agent, Subject, Object, Goal book to a Theme, Oblique Transfer verbs like: student Recipient give, send, offer

Double John gave a Agent, Subject, Object, Object student a book Recipient, Secondary Theme Object

Table 1. Argument-structure alternation

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In the next sections, I’ll take a look at the data that indicates the discourse pragmatic constraints on QSA which I’ll be discussing, and where this data originates from.

2.1 Basilico’s Analysis of Diathesis Alternations In the paper, “Object Position and Predication Forms” (Basilico 1998), David Basilico provides a rigorous analysis of the syntactic properties of various diathesis alternations, specifically the create/transform constructions, the spray/load constructions, and the dative constructions. Basilico provides a syntactic analysis of these constructions which provides a unified explanation of many of their observed properties, representing these various sentence types syntactically in terms of verb shells. For example, the sentence (Basilico 1998, p. 541):

(16) Mary sent the letter to Jill” can be broken down into not only the subject (Mary) and predicate (sent the letter to Jill), but further into an “inner subject” (the letter) and “inner predicate” (sent to Jill). The inner predicate combines with the inner subject, as follows (Basilico 1998, p. 542):

(17) [the letter]NP[[sent]V[to Jill]PP]V’ to form the predicate ‘sent the letter to Jill’, which combines with ‘Mary’ to form ‘Mary sent the letter to Jill, represented syntactically:

(18) [Mary]NP [[the letter]NP[[sent]V[to Jill]NP]V’]VP

Basilico’s analysis delineates between what he calls “thetic” and “categorical” inner predication. Proponents of the thetic/categorical distinction claim that there is a between a type of predication that asserts the existence of an object, and then applies a predicate to that object (categorical predication, such as in the sentence, “The dog is large”), and a type of predication that merely recognizes some object or of affairs (thetic predication, such as in the sentence, “It’s raining.”) (Basilico 1998, p. 546). Basilico argues that a wide range of systematic syntactic differences can be explained in terms of “thetic” and “categorical” inner predication. For Basilico, “thetic” inner predication occurs when the direct object (the inner subject) is predicated in the

16 inner verb shell (Basilico 1998, p. 543). For example, in the create construction sentence:

(19) The baker baked three dozen cookies from one pound of dough.

The direct object (three dozen cookies) occurs within the inner shell of the verb phrase. By contrast, “categorical” inner predication occurs when the direct object (what I called the ‘oblique’ argument in my discussion above) occurs in the outer verb shell (Basilico 1998, p. 543), such as in the transform construction sentence:

(20) The baker baked one pound of dough into three dozen cookies.

Using this syntactically defined notion of thetic/categorical inner predication, as well as a rigorous Chomskyan analysis of movement constraints involving the sentence constituents, Basilico is able to explain systematic differences in the properties of each type of alternation, ranging from scope-taking properties (Basilico 1998, pp. 551-558), to permissibility in there-existential sentences (Basilico 1998, pp. 561-568), to permissibility of sentence inversion through passivization (Basilico 1998, pp. 568-574). For my purposes here, the differences between the alternates in scope taking properties is of the most importance: Basilico shows, through a myriad of examples, that the categorical variants of these diathesis alternations do not admit of QSA, while the thetic variants do. To see this, consider the following examples, modified from (Basilico 1998, pp, 551-552):17

The Create/Transform Alternation

(21a) The gardener grew a plant from every seed in the package

(21b) The gardener grew a seed into every plant

(21c) The gardener grew every plant from a seed in the package

(21d) The gardener grew every seed into a plant

(22a) The sculptor carved a statue from every slab of marble

17 The a and b variants are from Basilico’s data, while the c and d are my own expansion.

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(22b) The sculptor carved a slab of marble into every statue

(22c) The sculptor carved every statue from a slab of marble

(22d) The sculptor carved every slab of marble into a statue

The Spray/Load Alternation

(23a) The farmer loaded a bale of hay onto every truck

(23b) The farmer loaded a truck with every bale of hay

(23c) The farmer loaded every bale of hay onto a truck

(23d) The farmer loaded every truck with a bale of hay

The Dative Alternation (Oblique Goal/Double Object)

(24a) The instructor gave a book to every student

(24b) The instructor gave a student every book

(24c) The instructor gave every book to a student

(24d) The instructor gave every student a book

In these examples, the a and c variants exhibit “thetic” inner predication, according to Basilico, and correspond to the create/spray/ditransitive constructions. The b and d variants exhibit “categorical” inner predication, and are examples of the transform/load/double object constructions. Basilico claims that the categorical alternants do not allow scope inversion, while the thetic alternants do. This seems to be the correct analysis, and interestingly, is maintained even when the resulting reading is infelicitous given world knowledge. To see this, consider the following examples:

(25a)# The gardener grew a seed into five trees18

(25b)# The gardener grew five seeds into a tree

18 I use the pound , ‘#’, to indicate infelicity.

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In both cases, world knowledge constraints fail to force a more sensible reading. It is very difficult, if not impossible, to interpret 25a as “There were five seeds each grown into a tree.” Rather, 25a must be interpreted as “one seed was grown into five trees”19 despite world knowledge that this is impossible. A similar result occurs for 25b; world knowledge makes the prospect of five seeds becoming a single tree generally infelicitous, but this reading is forced regardless. This is in contrast to standard transitive constructions, where a nonsensical or infelicitous word-order reading will force the inverse reading to be defaulted to. For example:

(26) A soldier is guarding every door of the palace.

I suggest that, in this example, world knowledge makes the adoption of the “multiple guards each guarding a door” reading preferable, despite the word-order indicating the “a single guard guarding the entire palace” reading. A full analysis of this phenomenon is out of the scope of this paper, as it has to do with factors affecting ambiguity resolution, while I am concerned with factors that prevent QSA from arising, but for now it suffices to acknowledge that the constraint on inversion that Basilico has discovered is strong enough to resist attempts to reinterpret the categorical alternates more felicitously when they conflict with world knowledge.

While Basilico’s analysis is extremely robust, it also has its shortcomings, and will not suffice as an explanation of Basilico’s observations for my purposes. Most importantly, the thetic/categorical distinction seems misapplied in the case of inner predication, and with regard to Basilico’s examples. The thetic/categorical distinction, which originates from the philosopher Brentano, traditionally refers to a purportedly logical distinction between judgements that recognize a subject and assert a predicate about that subject (categorical) and judgments that merely recognize some judgement material, without predicating upon any object (Lambrecht 1994, p. 139). Quintessential examples include “it’s raining” and “her father died”, uttered in certain contexts (Lambrecht 1994, pp. 141-142). As Lambrecht argues, theticity is best interpreted as fundamentally discourse pragmatic. Lambrecht observes first that there is no formal

19 The fact that I can use this as a example of the forced reading seems to show that when passivized, the sentence retains its scope rigidity, and in fact may be more rigid than before.

19 marking of theticity unless the sentence in question has a full lexical NP as subject, e.g. “her father died”, in which case, the marking is prosodic, and indicates that the sentence’s subject is not a topic (Lambrecht 1994, pp. 142). Thetic sentences with pronominal subjects are syntactically and semantically indistinguishable from categorical sentences. To see this, consider the thetic sentence, “it’s raining” vs. the categorical sentence, “it’s leaking” (taken from Lambrecht 1994, p. 141). The fundamental difference between these sentences is that the latter is only felicitous to assert when the subject ‘it’ refers to a contextually presupposed topic. To account for this, Lambrecht defines the category of thetic sentences to be those sentences where all the information is wholly new and assertoric: thetic sentences introduce a new element (either event or object) into the discourse without linking said object to a previously established discourse referent (Lambrecht 1994, pp. 144-145). Thetic sentences thus generate a discourse-pragmatic category including intransitive examples of what Lambrecht calls “presentational sentences” and “event-reporting sentences”, as I discussed in section 1.2. All other sentences, for Lambrecht, are categorical.

The problem with Basilico’s examples is that, across the board, neither the sentences nor the inner predicates can be classified as thetic, at least per Lambrecht’s definition. The hallmark of thetic sentences is that, in a thetic sentence, no constituent may be topical, as the entire sentence is focal. But this does not seem to apply either for the sentences as a whole nor for the inner predicates. First, note that all of Basilico’s examples would generally be topic-comment sentences: none of these sentences are intransitive, and even setting this aside, none of Basilico’s examples would be felicitous for a person to utter out of the blue, meaning that none of these examples are thetic overall. As for the inner predicates, only Basilico’s categorical examples would have any possible claim to theticity, because only in the categorical examples are any constituents necessarily non-topical. One way to show this is to point out that, generally speaking, topical NPs are permitted to be replaced by unaccented anaphors. Across all of Basilico’s alternations, any NP can be replaced by an anaphoric expression, with the exception of the oblique/secondary objects in the categorical alternations. Take the following examples:

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(27a) (What did the sculptor make every statue from?) “He made them from a block of marble.”

(27b) (What did the sculptor use the block/blocks of marble for?) “He made every statue from it/them.”

(27c) (What did the sculptor use the block/blocks of marble for?) “He made it/them into every statue.”

(27d)# (What did the sculptor make into every statue?) “He made a block of marble into it/them.”

Only 27d is infelicitous. In such a context, one would instead use 27a to answer the question. I claim that a similar infelicity holds across Basilico’s other categorical examples when an anaphoric expression is inserted into the oblique/secondary object position. If this is correct, then the only constituent which is necessarily non-topical is the oblique/secondary object in Basilico’s categorical alternation, which means that this alternation has the best claim to possible theticity, contra Basilico. So while I will ultimately be arguing that these constructions do elicit discourse pragmatic constraints on their objects which prevent inversion where inversion is prevented, Basilico’s syntactically defined thetic/categorical distinction will thus not work for my purposes, especially because I will not be adopting a Chomskyan account of syntax. Ultimately, I will need a different analysis of Basilico’s extremely robust data.

In place of Basilico’s analysis, I claim that what distinguishes the “thetic” alternates from the “categorical” ones, is that in the “categorical” constructions, the argument encoded as an oblique/secondary object is necessarily non-topical. This is a discourse pragmatic constraint on the constructions in question, and is specific to the constructions. I claim that the necessary non-topicality of these arguments is what prevents the arguments from taking a higher scope position, and that this points toward a more general constraint on all constructions in English: necessarily non-topical elements must take lowest scope.

There is one final question to be answered regarding Basilico’s data. I stated that the oblique/secondary object in the “categorical” alternates is necessarily non-topical—it

21 can never serve as a topic of a sentence. But is it thereby necessarily focal? I argue that it is.20 As I’ve discussed, none of Basilico’s examples can be considered thetic sentences. But one may wonder if such sentences could be identificational: that is, if there is a possible context where someone could ask, say, “who made a block of marble into every statue?” If this were felicitous, then, while ‘every statue’ would not be properly speaking topical, it would be pragmatically presupposed, and thereby not focal. The appropriate answer, if the sentence in question is identificational, is “John made a block of marble into every statue.” But note that, in such a context, answering with a full sentence seems infelicitous; it would be better to respond, “John did”. Even in more natural contexts, such as when someone asks, “who made the statues?”, if one wished to convey that a single block of marble was used to make every statue, one would likely say, “John did. He made them from a single block of marble.” I therefore claim that Basilico’s sentences are not generally speaking felicitous as identificational sentences, nor as thetic sentences. Basilico’s categorical alternates are thus best thought of as topic-comment sentences, and only felicitous to utter when the oblique/secondary object (in this example, ‘every statue’) is focal.

Going forward, and following Basilico, I will assume that the create/spray/double object constructions do not exhibit QSA, because their oblique/secondary objects are necessarily focal. This indicates a general discourse pragmatic constraint, which I will adopt going forward: necessarily focal sentence constituents must take lowest scope: they are scoped over by all other syntactically permissible constituents. I’ll refine this analysis, and elaborate more on it, in section 3.

2.2 Specificity Effects and QSA

In “The Semantics of Specificity” (Enç 1991), Mürvet Enç provides an account of specificity which rejects the then-common supposition among Chomskyan linguists, that an NP is specific when it takes wide-scope over another operator (Enç 1991, p. 1-3). Instead, Enç’s account hypothesizes, following Hintikka, that NPs containing the phrases specific, particular, or certain are always specific (Enç 1991, p. 3-4). Enç cites

20 This same claim is made in Michaelis 2015, p. 26.

22 many examples of cases, in both English and Turkish, where specific NPs take narrow scope over the other operators in a sentence, demonstrating the failure of the specificity-as-wide-scope hypothesis. In its place, Enç seeks to provide an account of specificity which is at its core semantic, and which links up with much of the core literature on the so-called effect. For Enç, definiteness and specificity are defined in terms of relationships between NPs and previously established discourse referents. On Enç’s account, an NP is definite iff the referent of the NP is identical to a previously established discourse referent (Enç 1991, p. 8). An NP is specific iff the referent of the NP stands in the “inclusion” relation to a previously established discourse referent (Enç 1991, p. 7-8). Enç never fully defines “inclusion” but seems to have in mind relations like identity, the subset relation, and counterparthood, as “specificity involves linking objects to the domain of discourse in some manner or other” (Enç 1991, p. 21).

As a result of this analysis, all definite NPs are specific (Enç 1991, p. 9), and all indefinite unspecific NPs must be novel- what in discourse pragmatics is referred to as “new information” (Enç 1991, p. 9) Specific, indefinite NPs need only be distinct from the set of objects already in the domain of discourse (Enç 1991, p. 7). Enç’s analysis also entails that partitives, such as “two of” or “some of” are necessarily specific, and, according to Enç, all quantifiers are specific, though notably, she argues that indefinite articles/definite articles/numerals are not quantifiers, dovetailing from the analysis I am giving here.

While Enç is correct in attempting to go away from a syntactic account of specificity, her account is not strictly speaking semantic, but rather is better thought of as discourse pragmatic. The reason for this is that her analyses do not, even by her own account, treat specificity as in any way truth functional, and the definition of specificity that Enç provides is closer to the new/old information distinction. However, regardless of whether it is semantic or pragmatic, Enç’s analysis is problematic, as it is dangerously close to defining specificity as topicality, does not correctly assess the intuitive nonspecificity of generic NPs in some cases, and has some other difficulties which I won’t go into here. Nevertheless, Enç’s observations about the effects of

23 specificity on scope are quite robust. It is out of the scope of this paper to give a proper definition of specificity, but going forward, I will not be adopting Enç’s definition, though I will assume her key observations hold for whatever the correct account of specificity is.

One may wonder what the relationship is between specificity and definiteness, on the one hand, and topicality and focus, on the other. I claim that neither topicality and specificity, nor focality and nonspecificity, are identical, though they are correlated. First, note that, as most topical expressions must designate referents which the listener can identify, felicitous topical NPs are usually specific (Lambrecht 1994, pp. 77-87).21 Lambrecht equates specificity and cognitive identifiability, and says the following:

a “specific indefinite NP” is one whose referent is identifiable to the speaker but not to the addressee, while a “non-specific indefinite NP” is one whose referent neither the speaker nor the addressee can identify at the time of utterance. This is tantamount to saying that a non-specific indefinite NP is one which may have no referent at all (Lambrecht 1994, p. 81).

However, as Ward and Prince point out, topical NPs can be non-specific, and give the following example (Ward and Prince 1991, p. 169).

(28) A 'course of events' is a function from locations to situation types... A course of events that is defined on just one location we call a ‘state of affairs'.22

In this example, the generic, indefinite NP ‘a course of events’ is topical, but is nonspecific. This suffices to show that topicality and specificity may come apart. It can also easily be shown that focal constituents may or may not be specific: consider the following to examples, where ‘a Scot’ is focal:

(29a) (Who would you prefer to marry, a Scot or an Englishman?) I’d prefer a Scot.

(29b) (Is Jane marrying an Englishman or a Scot?) She’s marrying a Scot.

21 This also follows from his Topic-Acceptability Scale, Lambrecht 1994, p. 165. 22 This is also a key example where Enç’s analysis fails: on Enç’s account, ‘a course of events’ would have to be specific, though it clearly isn’t.

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Definiteness shares a similar relationship to topicality as specificity does. As most definite NPs refer to pragmatically supposed discourse referents, definite NPs are often topics, though need not be. Lambrecht points out that the definite article can often be used to mark generic NPs, which need not be pragmatically presupposed (hence need not be topical), and gives the following example (Lambrecht 1994, p. 83):

(30) She is now studying the whale.

Depending on the context of this sentence’s uttering, different constituents may be focal, though ‘the whale’ is certainly non-topical, despite being definite. So ultimately, it is clear that neither definiteness nor specificity either require or bar topicalization.

Despite the problems with her account, the specificity effects that Enç discusses have important effects on QSA. Perhaps most importantly, Enç claims that nonspecific NP’s always take narrow scope, citing the following examples (Enç 1991, p. 22):

(31) John didn’t buy a coat

(32) Everybody designed a coat

Enç claims that it is impossible to get a reading of either of these sentences where the indefinite NP takes wide scope if the indefinite NP is nonspecific. If the NP is specific, then it is permitted, though not required, to take wide scope. If this is correct, then ‘a coat’ cannot take wide scope in either of these sentences unless the coat in question is already in some “inclusive” relation to some previously mentioned object in the domain of discourse. This seems to be the correct analysis.

Also relevant to QSA is Enç’s claim that universal quantifiers, and perhaps all quantifiers in general (recall that for Enç, indefinite NPs and numerals are not QNPs) are necessarily specific. This does not seem to be the case, though there is a strong correlation between specificity and the use of universal quantifier expressions like ‘every’, simply because most instances of ‘every’ used as a referring expression are topical, and, as I pointed out before, topical NPs are usually specific. Note that other linguists, including Basilico, non-specific uses of the quantifier ‘some’ (Basilico 1998, pp. 581-589). This seems to provide a straightforward counterexample

25 to all quantifiers being necessarily specific. But as a general tendency, Enç’s observation of the correlation between quantifier usage and specificity seems plausible.

Going forward, I will accept Enç’s claim that nonspecific NPs must take narrow scope. I will thus argue that, for discourse pragmatic reasons, putative QSAs whose existentially quantified NPs are non-specific do not exhibit QSA.

2.3 Herburger’s Focal Mapping, the Scope of Topical vs. Focal NPs, and Lambrecht’s Constraint on Topicality and Negation In the literature on topicality, some linguists have posited that topical NPs always take scope over focal NPs.23 While there is a certain amount of strength to this intuition, in part because Topical NPs tend to pattern with both grammatical subjects and with specific NPs, this proposal is problematic. Consider the following example:

(33) Speaker 1: Did the English really design everything in the store?

Speaker 2: No. An Englishman designed every coat. But some of the other clothes are imported from other countries.

In this example, ‘an Englishman’ is both the subject of the sentence, and is topical. Nevertheless, the inverse reading of the sentence is possible (perhaps preferred). If no particular Englishman designed all the coats, then, ‘an Englishman’ must take narrow scope with respect to ‘every coat’ (the focal element) in order to achieve the appropriate reading. I’ll discuss this example further in section 3, but for now it suffices to observe that it is not universally the case that topical NPs scope over focal NPs.

There is, however, another reason that the claim that topical NPs always scope over focal ones has strength, beyond the correlation between topicality, subjecthood, and specificity. In What Counts: Focus and Quantification, Elena Herburger argues that focus (and topicality, though she doesn’t mention it explicitly) impose a particular semantic constraint on the scope of the event quantifier in the event semantic interpretation of English sentences. Herburger argues that “all the nonfocused material

23 This is discussed in Michaelis 2015, pp. 24-26.

26 in the scope of the event quantifier Q also restricts Q” (Herburger 2000, p. 18). This is accomplished, according to Herburger, by way of a process of ‘Focal Mapping’:

Focal Mapping: The nonfocused material in the c-command domain of Q also provides an internal argument for Q (Herburger 2000, p. 43).

Ignoring the Chomskyan syntactic constraints in this definition, the core idea of Herburger is that nonfocused material (that is, pragmatically presupposed sentence constituents) that is within the scope of the event quantifier is in the restriction of the event quantifier. This allows for a straightforward analysis of some of the topicality effects that are under discussion. Consider the following sentence, assuming that ‘Montmartre’ is focal, marked by italics (Herburger 2000, pp. 29-34):

(34) Sascha didn’t visit Montmartre.

Herburger argues that the sentence in example 34 can have three different readings, which she calls the bound, free, structured wide readings. These can be rendered in the semantic representation used in Type-Logical Grammar respectively as the following, ignoring tense:24

(35a) Some[λe.visiting(e) and agent(e)(Sascha)](λe.not(theme(e)(Montmartre))) (Bound)

(36a) Some[λe.not(visiting(e)) and agent(e)(Sascha)](λe.theme(e)(Montmartre)) (Free)

(37a) not[Some[λe.visiting(e) and agent(e)(Sascha)](λe.theme(e)(Montmartre))] (Wide)

In disambiguated English, these would be:

(35b) There was a visiting by Sascha whose theme was not Montmartre. (Bound reading)

24 This notation is an adaptation of the notation used for restricted event quantifiers in Forbes 2015.

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(36b) There was a not-visiting by Sascha whose theme was Montmartre. (Free reading)

(37b) There was not a visiting by Sascha whose theme was Montmartre. (Wide structured reading)

The bound reading, which is preferred in most contexts, expresses that Sascha visited something, just not Montmartre. The free reading, by contrast, expresses that the Sascha’s relationship between him and Montmartre was that of a not-visiting, and would be felicitous, for example, if Sascha saw Montmartre, but didn’t go there.25 The structured wide reading expresses that no visiting occurred, and would be felicitous in the case where Sascha never went anywhere. In all three examples, ‘Sascha’ and ‘visit’ are presupposed, so are in the restriction of the event quantifier, per Herburger’s focal mapping.

If Herburger’s Focal Mapping is taken as a general constraint on the scope of topical and focal sentence constituents, it would help to explain the intuition that topical NPs always scope over focal NPs: Whenever both the topical and focal NPs are within the scope of the event quantifier, this will be true, because the topical NPs, being presupposed, will be in the restriction of the event quantifier, while the focal NPs will not.

One area where this is particularly important with respect to QSA is quantifier- negation ambiguities. First, note, following Lambrecht, that because topical NPs are in a sense, “taken for granted”, they prefer not to be within the scope of negation (Lambrecht 1994, pp. 152-154). Consider the following examples adapted from (Lambrecht 1994, p. 153) (all-caps marks prosodic stress):

(38a). (What didn’t the children do next?) The children didn’t go to SCHOOL.

(38b). (Who didn’t go to school?) The CHILDREN didn’t go to school.

25 Arguably, contra Herburger, the free reading is not an available reading of ‘Sascha didn’t visit Montmartre’, but would rather be the preferred reading of ‘Sascha didn’t visit Montmartre’ (perhaps he lives there). I set this issue aside in this paper.

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(38c). (What happened?) The CHILDREN didn’t go to SCHOOL!

Only the topic-comment variant (38a) has any topical NPs, but intuitively, since ‘the children’ is topical in this variant (as well as being the subject), 38a is only amenable to a reading where ‘the children’ takes wide scope over the negation operator. Additionally, typical quantifier-negation QSAs also appear to follow Lambrecht’s pattern. Consider the following:

(39) As everyone came to the surprise party, they hid under the tables. John didn’t see everyone as he came in.

(40) As John scanned the battlefield, a man rose from the shadows. John didn’t see the man.

I claim that these sentences strongly prefer to be interpreted with ‘everyone’ and ‘the man’, respectively, scoping over negation. This points toward a more general constraint, that topical NPs must scope over negation. Herburger’s analysis, at least in most of the examples that have been considered so far, is compatible with this proposed constraint. However, there is a type of context where the pattern appears to break down. This is the context in which a mistaken presupposition is corrected. An example of this is the wide reading of example 34, represented in 37a and 37b. As can be clearly seen, because the negation is intended to scope over the event quantifier (because no visiting occurred), it necessarily scopes over topical NPs in its restriction, including ‘Sascha’. But another sort of correction also breaks the pattern. Consider the following:

(41) Speaker 1: I heard Sascha went to Montmartre.

Speaker 2: No. Sascha didn’t visit Montmartre. John did.

In this example, Sascha is topical, and his visit to Montmartre is presupposed. The most plausible focal element in this sentence is ‘didn’t’. According to Herburger, when the focal element is the negation itself, the reading that occurs is what Herburger calls the “unstructured wide reading” (Herburger 2000, p. 33). In the unstructured wide reading, ‘not’ takes scope over the event quantifier, as in the structured wide reading, but the

29 event quantifier does not adopt the type of a restricted quantifier. This would be the following:

(42) Sascha didn’t visit Montmartre => not((some)[λe.visiting(e) and agent(e)(Sascha) and theme(e)(Montmartre)])

The key difference between the structured wide and unstructured wide readings is that, in the unstructured wide reading, the effects of focal mapping do not come into play. This means that any scopal constraints that would otherwise be imposed by focal mapping would not occur.

The takeaway is two-fold. First, Herburger’s focal mapping does seem to be empirically supported, and helps explain some of the otherwise recognized scopal relations between topical and focal NPs. I will thus be adopting focal mapping as a discourse pragmatic constraint on quantifier scope. Second, Herburger’s focal mapping helps provide an explanation for Lambrecht’s observation that topical NPs cannot scope below negation, though provides a caveat. Given the discussion above, I think Lambrecht rather has observed the following, albeit weak, constraint on quantifier scope: topical NPs, and their event-semantic representations, may not be in the immediate scope of negation.26 These two constraints help explain how, in some cases, discourse pragmatics prevents quantifier-negation ambiguities from arising. Specifically, quantifier-negation ambiguities where the QNP is focal, and the sentence is not a correction, will exhibit no QSA: the topical NPs will scope over negation. I’ll adopt both Herburger and Lambrecht’s (revised) constraints going forward.

3. The Discourse Pragmatic Constraints on QSA We are now in a position to provide a proper account of the discourse pragmatic constraints on QSA. QSA is affected by discourse pragmatic constraints on two different levels: 1) an ordered set of universal constraints on the scopal relations of sentence constituents which satisfy certain discourse pragmatic functions, and 2) a set of construction-specific constraints on the discourse pragmatic functions of arguments

26 Given the framework of type-logical grammar, this may be more precisely stated as, ‘the subatomic event semantic functions that scope over topical NPs may not be immediately scoped by negation’.

30 within a given construction.27 When combined, we can give an explanation of how discourse pragmatic constraints affect QSA. People’s linguistic knowledge contains knowledge of constructions, and per 2, which arguments in a given construction may be topical or focal. In a given discourse, a speaker will attempt to convey the meanings that they wish by applying these constructions, while being attentive to the information structure of the discourse. The constraints on information structure of particular constructions, which are conventional parts of the language, dictate which constructions may be used, given what the speaker wishes to convey and the discourse that has already occurred. When a speaker utters a sentence with a potential QSA, in many cases, the discourse pragmatic constraints on scope (per 1) prevent the QSA from arising in the given context. These discourse pragmatic constraints, of course, are not isolated from syntactic and semantic constraints. Syntactic barriers to scope taking, such as scope islands produced by relative clauses, as well as lexical semantic effects, such as the strong preference of ‘each’ to take a distributive reading as part of its semantics (Brasoveanu and Dotlačil 2015), will interact with the constraints I am positing. Discourse pragmatics, syntax, and semantics all work together to convey meaning.

It is worth noting that, while the “universal” constraints I am giving apply to the whole language, they arise in a distinctly more “bottom-up” than “top-down” way. As languages evolve, will dictate what discourse-pragmatically structured arguments may go in which positions in given constructions. When enough of these arise following the same trends, this produces a universal for the language. Causally speaking, then, the conventions of the language dictate the universals that exist, even though, in terms of explanation, the universals in some sense come first, and are applied through the given constructions.

The universal constraints in question are those that have been developed and discussed throughout section 2. They can be presented as follows, though it should be noted that this list is not intended to be exhaustive of every possible discourse

27 It is worth noting that not all constructions have such constraints, and that the discourse pragmatic constraints I give only apply to those constructions which do.

31 pragmatic constraint on scope—it merely presents those I have observed throughout this paper:

1. Necessarily focal sentence constituents in a given construction must take lowest possible scope. 2. Nonspecific NPs must take lowest scope. 3. Within the scope of an event quantifier, topicalized NPs take scope over focal NPs, unless a negation element is focal (focal mapping). 4. Topical discourse referents can’t immediately scope below a negation operator.

S. For all discourse pragmatic constraints, ‘lowest scope’ is evaluated with respect to the syntactically available scope options.

The order of these constraints is not accidental: I claim that, when these constraints conflict, higher-ordered constraints take precedence. Additionally, constraint S is a constraint on the application of the other constraints. It will be worth looking at each of these constraints, and both defending them and giving examples of how they affect QSA, each in turn.

First, constraint 1, which was initially discussed in the context of explaining Basilico’s discussion of ditransitive alternations, deserves some elaboration. Recall that Basilico provided an explanation of the different scope-taking capabilities of objects in various ditransitive alternations in terms of syntactically defined “categorical” and “thetic” inner predication. In sentences like the following:

(43) The instructor gave a book to every student (oblique goal “thetic” predication)

(44) The instructor gave a student every book (double object “categorical” predication) the “categorical” alternate (44) does not permit the secondary object (‘every book’) to take scope over the object (‘a student’), while the “thetic” alternate (43) permits both scopal readings, and is thus ambiguous. In section 2.1, I argued against Basilico’s

32 explanation of this, and argued that the key difference between these constructions, as well as Basilico’s other alternates, is that the oblique/secondary object in the “categorical” alternates is necessarily focal, where in the “thetic” alternates, it is permitted to be either topical or focal depending on context. That the oblique/secondary objects in the “categorical” alternates must be focal is a construction specific constraint on discourse functions of construction arguments, but that this constraint prevents the categorical alternates from exhibiting scope inversion points toward a more general constraint on the scope of necessarily focal arguments. If I’m correct, this constraint ought to hold more generally for other constructions which have necessarily focal arguments.

My claim, however, deserves some defense. One may wonder if there are any other equally good explanations for the phenomena I’m citing. In “Constructions License Verb Frames” (Michaelis 2015), Laura Michaelis discusses Basilico’s alternates (Michaelis 2015, pp. 24-28). Michaelis observes, quite rightly, that the fact that Basilico’s categorical alternates may not adopt the inverse reading is not adequately explained either by the quantifier scope hierarchy proposed by some linguists, or by the thesis that topical NPs must take wide scope over focal NPs (Michaelis 2015, p. 25). Michaelis in particular points to the following example, labelled (60) in her paper (Michaelis 2015, p. 25):

(45)# An acorn grew into every oak

In this example, ‘an acorn’ is the theme, while ‘every oak’ is the goal argument. Michaelis observes the following, as I have:

the transformation pattern constrains its locative argument in a way that the creation pattern does not. The creation pattern allows its locative argument (i.e., the source argument) to be either topic or focus… The transformation pattern, by contrast, is pragmatically constrained. Its locative argument (i.e., its goal argument) is necessarily interpreted as focal (Michaelis 2015, p. 26).

From this, Michaelis concludes that whatever causes inversion to be barred in the transformation construction must be specific to the transformation construction

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(Michaelis 2015, p. 25). However, Michaelis argues that the reason inversion does not occur is the following:

As a topic, the theme argument of the transformation pattern cannot readily be interpreted as nonspecific… Because it must be interpreted as denoting a specific entity, an existentially quantified theme argument in the transformation pattern cannot take narrow scope relative to a universally quantified goal argument. This leads to the nonsensical reading in (60), in which an acorn denotes a single acorn (Michaelis 2015, pp. 26-27).

This explanation, however, is problematic. First, it isn’t, in general, the case that topical, specific, existentially quantified theme arguments must take wide scope over universally quantified goal arguments. Consider the following examples:

(46) After signing them and writing a personal message, the author gave a particular book to every fan.

(47) After sorting the hay into different bales for their respective buyers, the farmer loaded a particular bale of hay onto every truck.

The phrases ‘a particular book’ and ‘a particular bale of hay’ require, following Enç, that the theme arguments be specific.28 However, 46 prefers a reading where ‘every fan’ (the recipient argument, which takes the position of a goal argument in this construction) takes wide scope: the author would surely want to give each book to the person he made his autograph out to.29 Similarly, 47 prefers a reading where the farmer designated each bale of hay to go onto the appropriate truck. Therefore, even if ‘a particular bale of hay’ is both specific and topical, the universally quantified goal argument (every truck) may take wide scope in alternations which allow for scope inversion. So while Michaelis is certainly correct that the transformation construction prevents its goal argument from taking scope over its theme, topicality induced

28 Arguably, given the topicality of the themes in both of these examples (formally marked by the use of the unstressed pronoun ‘them’ in the first example, and merely by context in the second), the word ‘particular’ is superfluous: the NPs in question would have been specific without it. I include it simply to ensure specificity. 29 One confounding variable with respect to this example is the fact that ‘a book’ is particularly vulnerable to a type-token ambiguity. On a type reading, ‘a particular book’ does take wide scope. I have tried to elicit a token reading, where, if ‘a particular book’ were to take wide scope, this would mean that the fans would have to share the signed book, and the use of ‘them’ would be misplaced.

34 specificity can’t be the reason for this. I claim that the necessary focality of the goal argument in the transformation construction is the reason it must take narrow scope, as, in neither of my examples, is the goal argument necessarily focal (though it may be focal in context).

Another concern one may have about my explanation, is that one may wonder if other constructions which have necessarily focal elements also force those elements to take lowest scope (within the syntactically permitted scopal options). Existential there constructions, like in the sentence, ‘there’s a man outside’, require the subject NP (‘a man’) to be focal (Lambrecht 1994, p. 170).30 And it appears that, in existential there constructions which contain multiple quantifiers, the subject NP does take lowest scope. Consider the following sentences:

(48) There’s a man with every woman at this party.

(49) There’s a strong woman behind every great man.

(50) There’s a solution for every problem.

In all of these examples, the NP directly following ‘there’ is necessarily focal, and takes lowest scope. This is despite the fact that, generally speaking, prepositional phrases seem to be subordinate to the NPs they modify. There is, however, a difficulty to be overcome. Consider the following:

(51) There’s a dog chasing every cat in the neighborhood.

(52) There’s a truck loaded with every bale of hay.

51 is ambiguous between either referencing a single dog, or many dogs who are chasing the cats in the neighborhood. This is despite, ‘a dog’ being necessarily focal. What explains this ambiguity, if necessarily focal elements must take lowest scope? The

30 There are, however, reasons to contest this. As Graeme Forbes has pointed out to me, the following example seems to violate Lambrecht’s constraint: A: Is that a cat I see out there? B: There's a cat in the garden, but aren't you looking across the street? While the example is debatable on the grounds that, in this context, ‘there’ may not be a use of an existential-there construction, but rather a deictic-there construction, if this is overcome, this example demonstrates that the subject NP’s in existential-there constructions are not necessarily focal. However, if this is the case, then the problematic cases I pose in what follows do not threaten my account.

35 first thing to say is that, with ‘a dog’ being the subject of this sentence, there is a conflict between its necessary focality from being the object of an existential-there construction, and it being topical as subject of the sentence: subjects are unmarked topics in transitive sentences (Lambrecht 1994, pp. 131-137). So one possible explanation is that, when such a conflict arises between topic and focus at the level of syntax, all bets are off: the topical role of ‘a dog’ as subject of the sentence neutralizes the scopal constraint composed by the argument otherwise being required to be focal in the construction. This explanation nicely handles 52 as well. In 52, both ‘a truck’ and ‘every bale of hay’ are necessarily focal, the first thanks to the existential-there construction, the second thanks to constraints on the load construction. But, while ‘every bale of hay’ is uncontested, ‘a truck’, as subject of the sentence, is in conflict with the general topicality requirement of subjects. This leads to ‘every bale of hay’ taking narrow scope, without difficulty.31

Constraint 2 was discussed in section 2.2, and was noted by Enç. It can be seen in sentences such as the following:

(53) John didn’t buy a coat

(54) An Englishman designed every coat

When ‘a coat’ or ‘an Englishman’ are viewed as nonspecific, these NPs must take lowest scope in the sentence. These observations seem very robust, and are independent of whether one accepts Enç’s account of specificity.

Importantly, and as I discussed in section 2.2, this constraint on specificity does not reduce to a constraint on topicality or focus, though topical NPs are usually specific, and focal NPs are often nonspecific. One can see this in sentences where a nonspecific NP is topical, for example in example 33, reprinted below:

(33) Speaker 1: Did the English really make everything in the store?

31 There is a further complexity regarding existential there constructions: some existential there constructions seem to focus an event, rather than an object. This is discussed in Basilico 1998, pp. 561- 568. As each example I give focuses an object, I will not go into this here.

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Speaker 2: No. An Englishman designed every coat. But some of the other clothes are imported from other countries.

In this example, ‘an Englishman’ is topical, yet nonspecific. But nevertheless, it takes lowest scope in the sentence.

How does this square with Herburger style focal mapping? (What follows will be significantly more technical than previous discussion, but the technicality can be safely ignored for those who are not familiar with event semantics or Type-Logical Grammar.) According to Herburger, the topical NP ought to be in the restriction of the event quantifier, so if ‘every coat’ is scoped by the event quantifier, there appears at first glance to be a problem, as the semantics for ‘an Englishman designed every coat’ with ‘an Englishman’ as topical, might be:32

(33a) an Englishman designed every coat => some[λe.designing(e) and (a(Englishman))λy.agent(e)(y)](λe.(every(coat))λx.[theme(e)(x)]) : S

In the sentence above, ‘an Englishman’ is in the restriction of the event quantifier, while the focal ‘every coat’ is within its scope, following Herburger. If this were the correct translation, then it would violate constraint 2. But there are multiple problems with this reading as a translation for the sentence above. First, it doesn’t express the desired reading, as ‘an Englishman’ takes scope over ‘every coat’, contradicting the nonspecificity of the sentence. But there is a second problem which may give a clue as to how to solve the issue at hand: both quantifier phrases are within the scope of the event quantifier. To see the problem, it will be useful to compare the following two sentences, setting aside Herburger’s focal mapping for the moment.

(33b) an Englishman designed every coat => (some)[λe.designing(e) and every(coat)[λx.theme(e)(x) and a(Englishman)λy.agent(e)(y)]] : S

(33c) an Englishman designed every coat => every(coat)λx.[(some)[λe.designing(e) and theme(e)(x) and a(Englishman)λy.agent(e)(y)]] : S

32 I ignore tense markers in this formulation.

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In 33b, all objectual quantifiers are within the scope of the event quantifier, so a plausible English disambiguation might be, ‘some event occurred that was a designing of every coat by an Englishman’. But this is very clearly not what we want, even though it satisfies constraint 2; plausibly, the designing of every coat was not a single event, and if it were, we would wish to express this by a sentence which highlights that the designing was done all at once by a group, perhaps ‘our team of Englishmen designed every coat’. 33c, however, is what we are after, and can be translated as ‘every coat was such that the designing of it was by an Englishman’. This does not imply that the designing was a single event. When Herburger’s focal mapping is applied on 33c, we get:

(33d) an Englishman designed every coat => (every(coat))λx.[some[λe.designing(e) and (a(Englishman))λy.agent(e)(y)](λe.theme(e)(x))] : S

Which satisfies both constraint 2 and constraint 3. The question becomes, can we plausibly argue that this is the reading that is derived when ‘an Englishman’ is nonspecific? I believe we can. First, note that adopting Herburger’s thesis does not force us to assert that every objectual quantifier is scoped over by the event quantifier: Herburger herself states her thesis as (emphasis mine), “All the nonfocused material in the scope of the event quantifier Q also restricts Q” (Herburger 2000, p. 18). And we must be able to derive 33c for it to be plausible that we can derive 33d, because if we can’t derive 33c, we wouldn’t be able to express the proper meaning of nonspecific sentences in event semantics at all, as I have argued. Therefore, so long as it is plausible that the nonspecific reading can actually be conveyed, applying Herburger’s thesis to this reading should pose no issue.

Finally, constraints 3 and 4 have a further difficulty that I did not discuss in section 2.3. In section 2.3, I noted that sentences where the negation operator is focused seem to, according to Herburger, produce the “wide unstructured reading”, effectively nullifying the effects of focal mapping that would otherwise occur. One may wonder however, if this is the right analysis for the example I gave. Consider example 41, which I gave in section 2.3, reprinted below:

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(41) Speaker 1: I heard Sascha went to Montmartre.

Speaker 2: No. Sascha didn’t visit Montmartre. John did.

This was rendered as the unstructured wide reading, repeated here:

(42) not((some)[λe.visiting(e) and agent(e)(Sascha) and theme(e)(Montmartre)])

But one may wonder if the correct focal element in this sentence is not ‘didn’t’, but rather ‘Sascha’. The resulting rendition of this sentence in TLG would thus not have ‘didn’t’ scoping over the event quantifier, but rather, exclusively over ‘Sascha’, producing the following, setting aside focal-mapping:

(55) (some)[λe.visiting(e) and not(agent(e)(Sascha)) and theme(e)(Montmartre)]

This says that a visiting of Montmartre occurred, but that visiting’s agent is not Sascha, which is potentially a better candidate for the correct translation of 41 than the unstructured wide reading. This appears to cause problems for my account, for two reasons. First, it isn’t clear how to apply focal mapping, as every NP is presupposed, so would have to be in the restriction of the quantifier. Second, if this is the correct translation, we have a potential violation of constraint 4: a presupposed, possibly topical element is immediately scoped over by negation. How can these difficulties be overcome?

To respond, it’s worth pointing out that both:

(56) Sascha didn’t visit Montmartre. John did. and

(57) Sascha didn’t visit Montmartre. John did. are appropriate responses in context, but have different purposes. With the focus (marked through prosodic accentuation) on ‘didn’t’, as in 56, the purpose of the sentence seems to be primarily to contradict the previous speaker. Given this “metalinguistic” use of negation, ‘didn’t’ ought to scope over the entire sentence, as the

39 assertion of an event of visiting by Sascha of Montmartre is being denied. The “wide unstructured reading”, rendered in 42, thus seems to be the correct reading. 57, however, is more felicitous when the speaker does not wish to deny an event of visiting, but just that Sascha was the visitor. 57 is thus analogous to an identificational sentence which seeks to answer a question like, “who didn’t go to Montmartre?” Prior to focal mapping, 55 does seem to be the correct representation of 57.

57 is problematic, because, while prosodically, ‘Sascha’ does seem to be marked as focal, in the context of a correction, ‘Sascha’ is also presupposed. However, this may not be unacceptable. Note that, because the presupposition was incorrect in the sentence, ‘I heard Sascha went to Montmartre’, the speaker of 57 would plausibly have to categorize both ‘Sascha’ and ‘didn’t’ as new information to their interlocutor. This, coupled with the formal prosodic marking on ‘Sascha’, allows ‘Sascha’ to plausibly be considered focal in the context of 57. And if this is correct, then this paves the way for focal mapping to be applied. Applying focal mapping to 55, and treating ‘Sascha’ as focal, would yield the following representation in TLG:

(58) some[λe.visiting(e) and theme(e)(Montmartre)] (λe.not(agent(e)(Sascha)))

58 correctly represents Sascha as focal, and has ‘didn’t’ scoping directly over ‘Sascha’, as is required to get the correct reading. So regardless of the intonation and intended focus of example 41, Herburger’s focal mapping (constraint 3) can be plausibly applied. And since 57 is being treated as essentially equivalent to an identificational sentence, no NP in the sentence is properly speaking topical, so constraint 4 is not violated. This allows my account to resolve the problems posed by example 41.

4. Conclusion In this paper, I have argued that, in many cases, QSAs that seem like they ought to arise do not in fact arise, because of discourse pragmatic constraints which manifest at the level of construction. I argue that the following universal (with respect to English) constraints prevent QSA in a wide variety of cases, ranging from the transform, load, and dative double object constructions, to sentences with non-specific NPs, to

40 quantifier-negation ambiguities involving topical NPs, and to the tendency for topical NPs to scope over focal ones:

1. Necessarily focal sentence constituents in a given construction must take lowest possible scope. 2. Nonspecific NPs must take lowest scope. 3. Within the scope of an event quantifier, topicalized NPs take scope over focal NPs, unless a negation element is focal (focal mapping). 4. Topical discourse referents can’t immediately scope below a negation operator.

S. For all discourse pragmatic constraints, ‘lowest scope’ is evaluated with respect to the syntactically available scope options.

These constraints manifest at the level of construction, in context. The relevant discourse pragmatic concepts are known either because they are marked formally through syntax and prosody, or known through context. These constraints do not exist in isolation, but rather interact with the syntactic and lexical semantic constraints on quantifier scope as well. If this analysis is correct, then the class of genuine QSAs is smaller than usually thought, and putative QSAs must be evaluated in the context of information structure for it to be established that they are genuine.

Appendix: Some Notes on Integrating My Analysis into TLG

While it is outside the scope of this paper to give a thorough account of the formal semantics of QSA in light of my previous discussion, there are some worthwhile remarks to be given. Thus far, I have argued for a fundamentally discourse pragmatic account of why QSA often fails to occur, due to a set of constraints that either affect the syntax of sentences, or directly affect their semantic derivation. The set of discourse pragmatic constraints I provided in section 3, I claim, explain why QSA often does not arise: the discourse pragmatic structure of uttered constructions in context prevents the permissibility of one of the otherwise syntactically available readings.

Two questions are pressing regarding the incorporation of my account in event semantic Type-Logical Grammar:

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1. How can knowledge of constructions be incorporated into TLG? 2. How can we derive the correct readings in light of Herburger’s Focal Mapping?

Regarding 1, note that, according to the account I am presenting, knowledge of both discourse pragmatic structure, as well as knowledge of constructions and their discourse pragmatic constraints, is part and parcel of linguistic competency. Topicality and focus are marked formally through either syntactic constraints or prosody, and, through the course of a discourse, interlocutors will have access to the discourse referents that have been presupposed, and will have beliefs about the knowledge of other participants. Speakers thus have all the information required to convey whatever semantic meaning is intended through a given sentence, and listeners, being able to see the entire construction once uttered (and know in advance once the verb is uttered what constructions are possible), as well as being able to recognize the prosodic marking of the sentence and remember what came before in the discourse, should have no difficulty retrieving the correct semantic derivation, provided that the sentence is genuinely unambiguous in light of this information. But as this information is a significant improvement from the mere knowledge of syntax of semantics, it is no mystery that such information prevents QSA from arising in context in many cases.

In terms of representing this knowledge in TLG, a few considerations must be kept in mind. To my knowledge, TLG does not have any mechanism for representing constructions directly. Any construction-based knowledge must be encoded through the lexicon in terms of a) variation in semantic type, b) variation in the particular lexical entry for a given word, or c) variation in syntactic category of a given phrase. While philosophically unsatisfying, the simplest way to represent constructions is to permit separate lexical entries for verbs which give rise to different constructions, coupled with obligatory or permissible prepositional phrase constituents built into the lexical entry for the verb, where appropriate. For example, to differentiate between the oblique goal and double object constructions, we would need to postulate two separate lexical entries

42 which differ in syntactic category and in semantic representation, as in the following (setting aside focal mapping for the time being, and ignoring tense):33

(59) John gave a book to every child => (every(child))[λy.(a(book))λx.[some(λe.[giving(e) and agent(e)(John) and theme(e)(x) and recipient(e)(y)])]] : S

(60) John gave every child a book => (every(child))[λy.(a(book))λx.[some(λe.[giving(e) and agent(e)(John) and theme(e)(x) and recipient(e)(y)])]] : S

As sentences, the semantic representations of the two examples above are identical. The first expresses the preferred, inverse reading of the oblique goal construction, while the second exemplifies the only permissible reading of the double object construction.34 Where these differ, however, is in the categories for the lexical entries for the verb, ‘to give’, which perhaps could be rendered as follows:

(61) gave (oblique goal) => λx.λy.λz.λe.[giving(e) and agent(e)(z) and

theme(e)(x) and recipient(e)(y)] : ((NP\S)/NPdat)/NP

(62) gave (double object) => λx.λy.λz.λe.[giving(e) and agent(e)(z) and theme(e)(x) and recipient(e)(y)] : ((NP\S)/NP)/NP

These differ in their syntactic category: the oblique goal variant looks left for an NP (the theme), then looks left for a dative NP of the form ‘to x’ (the recipient), before finally looking right to find another NP (the agent). The double object variant, by contrast, first looks left to find an NP (the recipient), then looks left to find another NP (the theme), before looking right to find a final NP (the agent). Further differentiation of these constructions in the lexical entry could be provided by further subcategorizing the type of NP which the double object version may permit as recipients. This is done through

33 The account of event semantics and TLG that I adopt in this discussion is that of Forbes 2017, pp. 60- 70. 34 While this expression is the only permissible reading for the double object construction, TLG as it stands offers no mechanism to prevent the overgeneration of the impossible reading. More work will need to be done to integrate measures to prevent this.

43 the implementation of thematic roles, following Parsons (1995),35 which allows for further construction specification if the NPs which are accepted at various points in the derivation are restricted by thematic role, e.g. agent, theme, or recipient. The implementation of thematic roles also paves the way for handling optional arguments, though I won’t launch into discussion of this here. Further work must be done to provide a more thorough account of implementing the effects of constructions in TLG, and to provide an account which avoids representing constructions through lexical ambiguity. Further work will also be required to represent the effects of necessary focality of construction constituents in TLG, though I will suggest that, as necessary focality manifests itself as a discourse pragmatic constraint on syntax, the correct approach may be analogous to the approach for representing scope islands in TLG.36

Regarding question 2, the difficulty is in describing how knowledge of presupposed material is to be represented in TLG, and how it integrates with the possibilities for the unstructured semantics of a given expression. Focal mapping, at its core, involves pulling the presupposed sentence constituents that otherwise would be in the scope of the event quantifier into its restriction. This involves changing the semantic type of the event quantifier to that of a restricted quantifier, and providing a process to insert the presupposed elements. Interlocutor knowledge of which elements are presupposed, or of the possibilities for the unstructured semantics, is not problematic, as Graeme Forbes points out:

There is no mystery about the successful interpreter’s knowledge of which constituents are focused and which are background, since the question-answer contexts, or intonation, provide exactly that information. So expressions can be marked as focus or background without circularly assuming the interpretation of the statement they are part of (Forbes 2015, pp. 135-136).

35 See Parsons 1995 for discussion of thematic roles, and how their implementation can assist with representing optional sentence arguments. See Forbes 2015, pp. 124-129 for discussion of implementation of this idea in TLG. 36 This is discussed in Forbes 2017, p. 53. The core idea is to postulate “semantically inert ‘bracket categories” (Forbes 2017, p. 53) which block the mechanism for representing discontinuity in TLG. If my suggestion is correct, necessarily focal sentence constituents may also be subject to semantically inert bracket categories, built into the lexical entry of the appropriate verb.

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The interlocutors have access to both the semantics of each phrase, as well as knowledge of which elements are topical or presupposed, and which are focused. This allows the speaker to choose the appropriate unstructured semantics of the sentence they are trying to convey prior to the application of focal mapping, and allows the hearer to correctly interpret the modified semantics in light of the available information. Importantly though, both the speaker and listener have access to the options for the unstructured semantics, and the speaker knows what they wish to convey in light of the information structure of the discourse, so we can plausibly apply focal mapping at the appropriate steps in the derivation, while permitting elements that are outside of the scope of the event quantifier to remain so (since they are so in the unstructured semantics).

One serious point of difficulty arises when we consider the position of objectual quantifiers with respect to the event quantifier. Consider the following sentence:

(63) John chased three children

Prior to focal mapping, this sentence has two readings, corresponding to whether the objectual quantifier scopes over the event quantifier, or vice-versa:

(64) John chased three children => three(children)λx.[(some)λe.[chasing(e) and agent(e)(John) and theme(e)(x)]]

(65) John chased three children => (some)λe.[chasing(e) and agent(e)(John) and three(children)λx.[theme(e)(x)]]

The first of these expressions entails that there were three chasings of one child each by John. The second, however, expresses that a single chasing of three children together occurred, by John. So the second would be preferable if John chased the three children all at once. Only sentences like the second are eligible to have their quantifier scope modified by focal mapping, as focal mapping will never impact objectual quantifiers which scope over the event quantifier. Deriving 64 is extremely straightforward in TLG. 65, however, is significantly harder. The difficulty is in inserting the QNP into the scope of the event quantifier, as the usual method for inserting

45 quantifiers will always force them to take scope over everything that has been thus far derived. In order to do this, we need to provide a spot for the QNP in the lexical entry for the verb. How do we do this while allowing verbs to univocally accept NPs and QNPs, which have different syntactic types? The simplest way is to decree that the lexical entries for verbs have slots for QNPs, and to provide a way of type-lifting NPs to fit the appropriate slots. So the lexical entry for ‘chased’ will go from:

(66) chased => λx.λy.λe.(chasing(e) and agent(e)(x) and theme(e)(y)) : (NP\S)/NP to:

(67) chased => λe.λP.λQ.(chasing(e) and Pλx.(agent(e)(x)) and Qλy.(theme(e)(y)) : ((S↑NP)↓S)\S)/((S↑NP)↓S)

Where ‘P’ and ‘Q’ are QNPs, and the change in syntactic category reflects the fact that ‘chased’ now searches for QNPs, rather than NPs. This allows us to derive either 64 or 65, thus paving the way for applying Herburger’s focal mapping. 64 is derived in roughly the usual way. 65 is derived by first doing away with the lambda operator over events with a syntactically inert event pronoun (perhaps analogous in English to a silent ‘it is so’),37 then applying the objectual quantifiers (which replace ‘P’ and ‘Q’, respectively), which will insert in the appropriate places, then finally lambda abstracting over events, and applying the event quantifier.

The next difficult question is about how focal mapping is to be applied. While I can’t go into detail about the exact steps of derivation here, the issue is that focal mapping pulls elements from the scope of the event quantifier into its restriction, which has truth-functional effects: focal mapping rules out possibilities for the unstructured semantics to only those that are compatible with the focal-mapped versions, and sentences whose presupposed elements contain a negation operator will force that operator to only range over the presupposed elements in the event quantifier’s

37 The facts that a) the event pronoun is syntactically inert and b) the event pronoun lacks a plausible English equivalent may cast doubt on this approach. More work will need to be done in the future to either justify this method, or to provide a more appropriate procedure.

46 restriction, once focal mapping is applied.38 Applying focal mapping to 64 and 65 yields different results. Consider the following representations of 64, where focused expressions are italicized.

(64a) John chased three children => three(children)λx.[some(λe.agent(e)(John))[λe.chasing(e) and theme(e)(x)]]

(64b) John chased three children => three(children)λx.[some(λe.agent(e)(John) and chasing(e))[λe.theme(e)(x)]]

(64c) John chased three children => three(children)λx.[some(λe.chasing(e) and theme(e)(x))[λe.agent(e)(John)]

The focal-mapped expressions of 65 are slightly different.

(65a) John chased three children => some(λe.agent(e)(John))[λe.chasing(e) and three(children)λx.[theme(e)(x)]]

(65b) John chased three children => some(λe.chasing(e) and agent(e)(John))[λe.three(children)λx.[theme(e)(x)]]

(65c) John chased three children => some(λe.chasing(e) and three(children)λx.[theme(e)(x)]) [λe.agent(e)(John)]

So how do we arrive at these representations? A simple way to apply focal mapping would be to first derive the constituents that are to be within the restriction of the event quantifier (which are known by the interlocutors since they have access to both the information structure and the candidate unstructured semantics without focal mapping), then derive the elements within the scope of the event quantifier, and finally, those sentence constituents which scope over the event quantifier. This would allow us to apply focal mapping at the end, pulling the presupposed sentence constituents into the scope of the event quantifier without any truth functional effects, as we would already have derived an unstructured semantics which is ordered in such a way as to be

38 As I have seen no natural language examples where a negation in the presupposition is also intended to range over both presupposed and focal elements, it may that this sort of expression is never expressed in English. If so, then for every focal-mapped semantic representation, there should be a truth-functionally equivalent unstructured representation of the same sentence. 47 unaffected by focal mapping. The obvious problem with this, of course, is that such a procedure would render focal mapping truth-functionally superficial, as the unstructured semantics would contain all the information regarding the quantifier scope that focal mapping was supposed to provide. Focal mapping isn’t entirely pointless, however, as it can still be argued that the unstructured semantics that gets selected is that which would facilitate the correct focal mapping: the sentence, in light of its information structure in context, is an event-semantic representation with focal mapping applied, so the fact that we must derive an unstructured semantics which facilitates focal mapping to get to this final representation is not circular. But it would certainly be better to provide a way to derive the presupposed sentence constituents in the restriction of the event quantifier without recourse to a competing derivation with all of the same truth- functional properties. Additionally, the procedure outlined above may not work universally if there are expressions that have a negation operator within the scope of the event quantifier which ranges over both presupposed and focal sentence constituents. More work needs to be done to give a thorough account of how focal mapping can be implemented, and how the aforementioned difficulties can be avoided.

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Gamut, LTF. (1991). Logic, Language, and Meaning, Vol. 2: and Logical Grammar. Chicago: University of Chicago Press. Herburger, Elena. (2000). What Counts: Focus and Quantification. Cambridge (Mass.): MIT Press. Lambrecht, Knud. (1994). Information Structure and Sentence Form. Cambridge: Cambridge University Press. Michaelis, Laura. (2015). “Constructions License Verb Frames.” In Mikko Höglund, Paul Rickman, Juhani Rudanko, and Jukka Havu (eds.). Perspectives on Complementation: Structure, Variation, and Boundaries. London: Palgrave Macmillan. 7-33. Parsons, Terrence. (1995). “Thematic Relations and Arguments.” Linguistic Inquiry 26: 635-662. Peters, Stanley, and Westerståhl, Dag. (2006). Quantifiers in Language and Logic. Oxford: Oxford University Press USA – OSO. Pietroski, Paul and Hornstein, Norbert. (2002). “Does Every Sentence Like This Exhibit a Scope Ambiguity?” In Wolfram Hinzen & Hans Rott (eds.). Belief and Meaning: Essays at the Interface. Deutsche Bibliothek der Wissenschaften. 43-72. Retrieved as Open Access Version from http://www.terpconnect.umd.edu/~pietro/research/papers/AMBIG.pdf (page number: 1-32). Steedman, Mark. (2012). Taking Scope: the natural semantics of quantifiers. Cambridge (Mass.): MIT Press. Ward, Gregory and Prince, Ellen. (1991). On the Topicalization of Indefinite NPs. Journal of Pragmatics 16: 167-177.

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