Alternatives in semantics – Alternatives are generated in the semantics, and are reckoned with January 21, 2015 grammatically. That is, the grammar’s the sort of thing that manipulates alternatives. This is where we’ll focus our energies. 1 Alternatives in semantics and pragmatics 2 Basics • This course: the role of alternatives in the semantics of indefinites, ques- 2.1 A toy alternative semantics for indefinites tions, and (to a lesser extent) focus. • Three parts: lexical entries lifted into sets, new semantics for functional • Alternatives: roughly, things a speaker might have said, but didn’t. application, non-singleton-set semantics for certain items. • Simple example: from I only drink PERRIER, you infer that I don’t drink • Normal semantics, assuming the functor is on the left and ignoring index- any of the salient alternatives to Perrier. From I only DRINK Perrier, you sensitivity (Heim & Kratzer 1998): infer that I don’t do any of the salient alternatives to drinking with Perrier ~XY = ~X(~Y ) (say, bathing with it). • Empirical phenomena where alternatives have been argued to be relevant: • Lifting into an alternative semantics, in the standard way (Hamblin 1973; Rooth 1985, 1992). Meanings of type α systematically replaced with – Indefinites, indeterminates, FCIs, and disjunction (broadly, “indefinite- meanings of type α ! t, and a new semantics for binary composition: ness”). The sine qua non of indefiniteness is the invocation of alternative possibilities. ~XY = fx(y) : x 2 ~X ^ y 2 ~Y g – Questions: interrogatives denote sets of alternative propositions from • Trivial example: which answers are drawn. – Focus: see above. Focused expressions invoke alternatives, which ~Bill left = f f (x) : x 2 fbg ^ f 2 fleftgg interact with focus-sensitive expressions (e.g. certain adverbs). = fleft(b)g – Implicature: utterances generally trigger inferences that logically • Alternative generators: constituents that denote non-singleton sets. stronger relevant alternatives are unassertable. – Transderivational economy: the grammar makes reference to alternative ~a linguist = fx : ling(x)g utterances. = ling • Several ways for alternatives to matter for linguistics: • Exploiting this meaning, here’s a less trivial example: – Alternatives feature in our pragmatic lives, but have no role to play in ~a linguist left = f f (x) : x 2 ling ^ f 2 fleftgg the semantics proper à la (neo-)Grice. = fleft(x) : ling(x)g – Alternatives get generated in the semantics, and are accordingly dealt with semantically. But the necessary adjustments are confined to the • Predicate modification can be lifted in a similar way: lexicon. Nothing about the grammar’s basic workings needs to change (cf. Karttunen 1977). ~XY = fx \ y : x 2 ~X ^ y 2 ~Y g 1 • More generally, for two-place function f , a point-wise version f 0 can • Alternative semantics gives a natural way to derive these sets. Suppose be defined, as follows (i.e. previously we instantiated f as functional who is an alternative-generator: application): ~who = fx : human(x)g f 0(X)(Y ) B f f (x)(y) : x 2 X ^ y 2 Y g • Therefore: • Predicate abstraction? We don’t mention assignment functions in the ~who left = fleft(x) : human(x)g previous versions (for simplicity). Is there a simple abstraction rule, along the lines of application/modification? Turns out, the answer is negative • (Strictly speaking these meanings aren’t correct: they ignore index- (Rooth 1985; Shan 2004; Romero & Novel 2013; Charlow 2014). sensitivity—in particular, sensitivity to a world or circumstance of evalua- tion; that is, which humans are we talking about? But they’re here to whet • In a sense, this isn’t so surprising. Abstraction is non-compositional in our intuitions for what’s to come.) Heim & Kratzer 1998, and so the binary-compositional strategy shouldn’t be expected to work. Still, it comes as a bit of a shock that there is no rule • Operators that manipulate/discharge alternatives (weakly exhaustive): of predicate abstraction consistent with standard treatments of binding. ~knows Q B fλx: λw: 8p 2 ~Q: p(w) ) Belw (x; p)g • Taming alternatives: syncategorematic closure operators. Because alterna- tive expansion is just baked into how the grammar works as a default, rules • Focus: e.g. I only drink PERRIER. The semantics of the focus-sensitive ad- that tame alternatives will need to be specified syncategorematically, i.e. in verb only interacts with the alternatives triggered by the focused PERRIER. terms of the grammar per se. • Alternative semantics for focus: meanings are bidimensional. Expressions ~9 S B f9p: p 2 ~S ^ pg are associated with a normal value, and a focus value. Standard way this is implemented, following Rooth 1985, 1992, is with a pair of interpretation • Example: functions, ~· and ~·f . The former of these works like Heim & Kratzer ~9 [a linguist left] = f9x: ling(x) ^ left(x)g 1998. The latter is alternative-friendly functional application. • More on syncategorematicity: try to specify the semantics of some inde- ~johnf = fx j x 2 Alt ~Johng pendently of its NP. Actually cannot be done! Of course, there are ways around this, though they require complicating the syntax and/or semantics • Only (again, stated syncategorematically!): (see e.g. Rooth & Dong 2011). ~only VP B λx: λw: fP : P 2 ~VPf ^ P(x)(w)g = f~VPg 2.2 Other sources of alternatives • So, coupled with the semantics for focused expressions, only has the effect • Questions: standard line is that the meaning of a question Q is the set of of indirectly quantifying over the focused element(s) in its sister. possible answers to Q (with “possible answer” construed differently in different theories), associated one way or another with some speech-act-y force that instructs the addressee to choose an answer from among the set 3 Consequences of alternatives (Hamblin 1958, 1973; Karttunen 1977; a.o.): 3.1 Islands ~who left = λp: 9x: human(x) ^ p = left(x) • Alternatives expand up to the point where they meet an alternative- = fleft(x) : human(x)g squashing operator. Thus, alternative semantics implies a sort of pseudo- 2 scope mechanism, i.e. one where the semantic effects of alternative genera- • Alternative semantics for questions works similarly: tors can be felt at positions far above their scope position at LF. ~who read what = fread(x; y) : human(x) ^ thing(y)g ~every philosopher met a linguist = f8x: phil(x) ) met(x; y) : ling(y)g • ...As does focus. E.g. for I only introduced BILL to SUE, alternative seman- • Applying 9-closure to this alternative set gives a set whose single member tics readily derives the reading that quantifies over pairs of introducees: is the familiar inverse-scope truth condition that we associate with every philosopher met a linguist. ~introduced billf to suef = fλx: intro(x; y; z) : y 2 ~billff ^z 2 ~sueff g • Happily, island-insensitivity seems to be a hallmark of the things we’ve • Is unselectivity desirable? Dissociable from island-insensitivity, if not? cast in terms of alternative semantics: Some cases to consider: • Indefinites: If ha relative of mine diesi, I’ll inherit a house. (Disjunction: Rooth & Partee 1982) (2) a. If ha lawyer visits a relative of minei, I’ll inherit a house. b. Who knows hwho read whati? • Questions (e.g. Huang 1982; Nishigauchi 1990; Dayal 1996; Reinhart 1997; c. A: John only introduced me to sue . Shimoyama 2006): f B: He also only [introduced mef to suef]. (1) a. Which ling will be offended if hwe invite which phili? • Eep! These cases are uniformly problematic for alternative semantics. How, b. Who knows hwho read whati? in any case, could one alternative generator scope out of the island, and the c. Japanese: Taro-wa hdare-ga kita-karai kaerimasita ka? other not? (Lit. ‘Taro left because who came?’) d. Chinese: Ni xihuan hshei xie dei shu? • And keep in mind: alternative semantics lacks a workable treatment of (Lit. ‘you like the book that who wrote?’) binding. Can we get all the good and none of the bad, or is it a package deal? • Focus: I’ll only go if hjohnf goesi. 4 Scopal treatments 3.2 Unselectivity (and its discontents) • Two indefinites: • Scopal semantics for indefinites: ~a philosopher met a linguist = fmet(x; y) : phil(x) ^ ling(y)g ~a linguist = λP: 9x: ling(x) ^ P(x) • Closure obligatorily forecloses both sources of alternatives: • LF for every philosopher met a linguist: f9x: 9y: phil(x) ^ ling(y) ^ met(x; y)g ~[[a linguist] [1 [every philosopher] met t1]] = 9y: ling(y) ^ 8x: phil(x) ) met(x; y) • That is, the following selective closures are both un-obtainable: • Scopal treatment of (association with) focus (cf. Krifka 1991, 2006): f9x: phil(x) ^ met(x; y) : ling(y)g f9y: ling(y) ^ met(x; y) : phil(x)g ~only = λP: λx: fy : P(y)g = fxg 3 • LF for Mary only met JOHN: • The second: discourse referents (Karttunen 1976). Processing a sentence with a proper name transitions you into a state with a discourse referent for john [only [1 Mary met t ]] ~ f 1 John. E.g., assuming John left: • Scopal semantics for questions (cf. Karttunen 1977; Dayal 1996; Heim ~John left = λs: fs + jg 2000): ~who = ~someone = λP: 9x: human(x) ^ P(x) (As for ‘s + x’, it doesn’t matter what it is. Think of it as an arbitrary way to make x available qua dref in the state s.) • Proto-question formation (cf. Partee 1986’s ident-shifter) • How to fold in indefinites? What does it mean for an indefinite to make a f g ~C◦ B λp: p = λp: λq: p = q discourse referent? • Gives the following LF: • The standard solution relies on nondeterminism (e.g. Heim 1982; Bar- wise 1987; Groenendijk & Stokhof 1991; Dekker 1994; Muskens 1996; 1 [who [2 [C t ][t left]] = λp: who (λx: p = left(x)) ~ ◦ 1 2 ~ Brasoveanu 2007).