Week 12: Introduction to Possible World Semantics Seminar: The Syntax-Semantics Interface M. Louie February Introduction

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1 Week 12: Introduction to Possible World Semantics Seminar: The Syntax-Semantics Interface M. Louie February 2017 These components often form part of the functional clausal spine: grammatical aspect 1. quantifies over the event variable 1 Introduction Whenever you are discussing events or individuals that might or do not exist in the actual world, you need a modal component in the semantics Linguistic elements that (often) have modal components modals (eg., might, must, have to, can, able to,...) grammatical aspect (eg., impf, perf,...) attitude predicates (eg, think, want, hope, introduces the RT 3. locates the τ(e) wrt the RT 4. yields a predicate of times 1 tense maps from AspP (type i, s, t ),. to a proposition (type s, t ), by (V1) quantifying over the RT, and locating RT wrt. UT (V2) satisfying the λt (RT) argument, as a time (type i) TP s, t. A predicate of worlds (i.e., a proposition) adverbs (eg., maybe, possibly, doubt, definitely,...) kinds... T subject T AspP i, s, t. A predicate of times 1.1 REVIEW: Temporal Displacement grammatical aspect and tense encode temporal displacement Asp vp l, s, t. A predicate of events grammatical aspect locates the VP event with respect to a RT e/ e v tense locates the reference time with respect to the UT agent v VP e, l, s, t. A predicate of individuals eg., Yesterday, She had (already) left. V PAST RT UT PERF ET RT ET Yesterday/RT UT theme; object The above shows a case where grammatical aspect and tense are functional heads, but in some languages, these may behave like modifiers 1 correlating to the set of times that would make the proposition true in w 1

2 Last week we also introduced a new compositional rule: Pro-forms and Traces Rule (Heim & Kratzer 1998) If α is a pro-form or trace, i is an index, and g is an assignment function, then α i g = g(i) This rule interprets the meaning of lexical elements with indices (eg., pronouns, pro-vps, traces, and under some analyses, tenses) 2 Modals 2.1 Empirical Observations about Modals Observation 1: The presence of modals affects truth- and use-conditions: (3) a. Snape might be evil. b. Snape must be evil. c. Snape is evil CONTEXT 1 (1) Voldemort has returned. = [-s pres.3sg have -en perf Voldemort return] Voldemort has returned g = (where g(3) = t 0 ) TP λw. e[return(e) exp(v, e) e m w τ(e) pres 3 ] Someone was jinxing Harry s broom during the quidditch match. Hermione saw Snape maintaining eye-contact on Harry the whole time, and when she set fire to Snape s cloak (accidentally knocking Professor Quirrell over at the same time), the jinxing stopped. T AspP λt.λw. e[return(e) exp(v, e) e m w τ(e) t]. Hermione saying:. (3a) T,. (3b) F (#). (3c) F (#) -s pres Asp vp λe.λw.return(e) exp(v, e) e m w have -en PERF [ v exp [Voldemort return] VP ] Today: Modal Displacement (2) a. Voldemort might have returned. b. Voldemort must have returned. c. Dumbledore believes (that) Voldemort has returned. d. Cornelius Fudge thinks (that) Harry is a liar. e. Cornelius Fudge wants Harry to be a liar. f. If Voldemort has returned, Harry s life will be in danger. CONTEXT 2 Harry knew that Snape has the Dark Mark, and had been working as a doubleagent for Voldemort and Dumbledore, but he was not sure where Snape s loyalties really lie. Until Harry saw Snape kill Dumbledore and then escape from Hogwarts (not realizing Snape had promised Dumbledore that he would kill him, to save Draco).. Harry saying:. (3a) T (#). (3b) T,. (3c) F, The difference between (3a, b, c) is often described in terms of strength (3a) is the weakest claim - it has the weakest truth-conditions (3b) is a stronger claim - it has stronger truth-conditions (3c) is the strongest claim - it has the strongest truth-conditions 2

3 This is a matter of theoretical debate, eg., von Fintel & Gillies 2010: must (3b) is equally as strong a claim as non-modal (3a) The difference is evidential; must in (3b) requires that the speaker came to their conclusion via indirect inference. (4) Context: I m looking out the window, and I can see that it s raining (von Fintel & Gillies 2010) a. It s raining b. #It must be raining c. #It might be raining (5) Context: I m sitting in an office, with no windows, about to leave. A colleague comes into the office, with wet hair, carrying a wet umbrella. I think: a. It must be raining b. #It might be raining (7) Draco must/has to be a Death Eater... a....because Harry saw the Dark Mark on his arm, and only Death Eater s have Dark Marks. epistemic b....because Voldemort has taken over the Wizarding World, making it illegal for purebloods to not be Death Eaters. deontic The inference in (7a) is an inference based on the knowledge/evidence available (7b) is based on a system of rules CONTEXT There is a condemned building that is falling apart. The city government has blocked it off, making it illegal for anyone to go inside. We re searching for a murderer on the loose. The tracking dogs have traced him to the condemned building (8) The murderer must be in the condemned building. T, under an epistemic interpretation. F, under a deontic interpretation (6) The ball is in Box A, B or C. It s not in Box A. It s not in Box C.. So it must be in Box C. (von Fintel & Gillies 2010) Observation 2: Modal claims express inferences - i.e., claims about states of affairs that haven t been directly observed, reached via reasoning Observation 3: Modals can be ambiguous about the type of premises used as the basis for reasoning (this is called modal flavour) (9) You can run the entire length of Vancouver s seawall. a....b/c the seawall is a public space with a pedestrian path deontic b....b/c you have two legs and are healthy enough to run 22 km ability If you 1 g = g(1) = Meagan, then (9) is (test for ambiguity) TRUE on the deontic reading FALSE on the ability reading : ( 3

4 2.2 Theoretical Approaches to Modals Empirical Properties of Modals (10) a. might = λw.λp s, t. w [ACC EPIST (w, w ) P(w)] b. must = λw.λp s, t. w [ACC EPIST (w, w ) P(w)] 1. Modal claims express inferences 2. Modal claims differ in strength 3. Modal claims are ambiguous about the source of reasoning (flavour) Basically, the accessibility relation provides a set of possible worlds, eg., the worlds compatible with the rules in w the worlds compatible with x s evidence in w... and then says that Traditional and contemporary approaches to modals treat them as. quantifiers over possible worlds Traditional Modal Logic In traditional modal logic, modals have two components: 1. Quantificational Force w, w 2. Domain of Quantification ACC(w,w ) The type of quantifier ( / ) is meant to capture differences in strength Different types of accessibility relations (ACC epist, ACC deon, ACC abil ) provide the domain of quantification (i.e., the set of possible worlds) This is meant to capture the differences in flavour An accessibility relation takes two world arguments (w, w ), yielding 1 iff one of these worlds ( w ), or all of these worlds ( w ) are P-worlds Some Empirical Problems 1. The traditional modal approach predicts a stronger claim about truth-conditions than must-claims seem to, because. w [ACC epist (w,w ) P(w )]. =. P(w) a 2. What about modals like should? This seems weaker than must but stronger than might. But we don t have an intermediate quantifier... (weak necessity modals) 3. The Good Samaritan Paradox b a Because w is compatible with all of your knowledge in w. b I m not going to discuss this here. You can ask me about if if you want (or read about it in Kratzer 1991), but I m pretty sure you guys don t want to go into the details. w is compatible with the rules in w ACC deon w is compatible with the evidence in w ACC epist (or more traditionally, the subject s knowledge in w) How can we modify the traditional model to address these problems? w is compatible with the subject s abilities in w ACC abil... 4

5 2.2.2 The Standard Model Kratzer 1977, 1981, 1989, 2012 Accessiblity relation, ACC, divided into two functions 1. The modal base (MB), and 2. The ordering source (OS) The modal base is used to provide a set of possible worlds, eg.,. a circumstantial modal base (based on facts of w at t). an epistemic modal base, (based on evidence available in w at t). The ordering source is used to order/rank those worlds in terms of how. likely (os stereotypical ), or. rule-abiding (os deontic ), or. goal-fulfilling (os teleological ), or. desirable (os bouletic ), etc., they are In the traditional modal logic approach: w is contained in the set of worlds that the modal quantifies over this is why must-p entails p (contrary to our intuitions) In Kratzer s approach, w might be one of the worlds that is lower-ranked by the OS this means it may not be included in the worlds that the modal quantifies over So while must-p is compatible with p, it doesn t entail p Kratzer s approach thus avoids the problematic prediction that must claims are stronger than non-modal claims 2 Kratzer formalizes the MB and OS as functions that access contextually salient sets of propositions (12) He might have stolen the sculpture CONTEXT Watching through the museum s security feed, I recognize a famous art Figure 1: Kratzer s Modal Base and Ordering Source The quantifier then quantifies over the highest-ranked worlds thief idling in the room holding The Dying Gaul. The video blanks out, then returns, and although everything looks the same, I suspect the sculpture is a fake (11) a. Snape must be evil. w [ w f epist (w) stereo evil(s,w )] In all of the worlds compatible with the evidence in w, that are highest ranked by a stereotypical ordering source, Snape is evil. b. Snape is evil. evil(s,w) a. MB = {I saw a famous art thief in the room holding The Dying Gaul, The video on the security feed blanked out for a moment, When the security feed turned back it still looked like The Dying Gaul was there,...} b. OS = {Security cameras don t blank out for no reason, Art thieves 2 The introduction of the OS is also crucial in accounting for the Samaritan Paradox. 5

6 often hack security cameras so that when they blank out they can switch masterworks with forgeries,...} Because you are making a universal claim about a smaller set of worlds, you are making a less-strong claim The worlds that satisfy more of the propositions in the ordering source are the ones that are higher-ranked Weak Necessity Q: What about weak necessity? eg., should? 3 The incorporation of the ordering by the OS allows Kratzer to define a notion of better possibility 4 Kratzer 1991 proposes that a weak necessity claim is true iff. p is a better possibility than p in w (wrt. the MB and OS) von Fintel & Iatridou 2008:. Weak necessity claims involve multiple ordering sources, i.e.,. A primary ordering source, and. A secondary ordering source von Fintel & Iatridou 2008 observe that weak necessity is crosslinguistically expressed in similar ways, usually involving a modal (usually a strong future modal), and counterfactual marking 5. The CF marking introduces the additional ordering source The secondary ordering source ranks the (already ranked and reduced) possible worlds and reduces them further 3 There are many, many, many analyses for weak necessity. This is barely scraping the surface. 4 This is another thing we probably don t need to get into in an introductory handout. 5 Often conveyed with past tense marking, or dedicated counterfactual morphology. (13) Context: I want to transfer my driver s license a. You have to provide two pieces of ID b. You should provide two pieces of ID and a small bribe (14) Context: We re discussing requirements for final papers a. You have to have five academic sources in your references b. You should have more than five academic sources in your references 3 Attitude Predicates 3.1 Empirical Observations about Attitude Predicates Observation 1a: Attitude predicates can select for a proposition (semantically) and clauses (syntactically); some also take NP/ complements (15) Attitude Predicates Selecting for CP or IP a. Dumbledore believes (that) Voldemort has returned. b. Harry discovered (that) Tom Riddle was Voldemort. c. Cornelius Fudge thinks (that) Harry is a liar. d. Cornelius Fudge doubts (that) Harry is telling the truth. e. Cornelius Fudge wants Harry to be a liar. 6

7 (16) Attitude Predicates Selecting for a. *Dumbledore believes Voldermort s return. 6 b. Harry discovered Tom Riddle s identity. c. *Cornelius Fudge thinks Harry s story d. Cornelius Fudge doubts Harry s story. e. WormTail wants Voldemort s return. Observation 1b: Different attitude predicates select for clauses with different types of morphosyntactic properties, eg., English finite/infinitival clauses (15) Romance indicative/subjunctive clauses (18) Realis/Irrealis... (17) Spanish Attitude Predicates I (Villalta 2008) a. Victoria Victoria cree believes que that pro hará make:fut.ind.3sg buen good tiempo weather Victoria believes the weather will be good. indicative b. Victoria Victoria quiere wants que that Marcela Marcela venga come:pres.subj.3sg al to-the picnic picnic Victoria wants Marcela to come to the picnic. subjunctive Sometimes an attitude predicate can select for different types of embedded clauses; this often correlates with a difference in interpretation 6 An NP complement is ok if you add in: Dumbledore believes in NP (18) Embedded Clause Type and Interpretation (Villalta 2008) a. Sentir with an embedded subjunctive pro siento sentir que that pro te you hayan have:past.subj.3sg hecho done daño pain I am sorry that they have hurt you. b. Sentir with an embedded indicative pro siento sentir que that pro va go:fut.ind.3sg a to haber there-be un a problema problem I have the impression that there is going to be a problem. Observation 2: Different attitude predicates have different entailments/presuppositions with respect to the truth of the embedded proposition (i.e., veridical vs non-veridical and factive vs non-factive) veridical attitude predicates entail p factive attitude predicates presuppose p (Von Fintel & Heim 2011) (19) a. Dumbledore knows (that) Voldemort has returned,. # but Voldemort hasn t returned. b. Lucius Malfoy is glad (that) Voldemort has returned,. # but Voldemort hasn t returned. c. Harry discovered (that) Tom Riddle was Voldemort,. # but Tom Riddle wasn t Voldemort. d. Cornelius Fudge thinks (that) Harry is a liar.. but Harry isn t a liar. e. Cornelius Fudge wants Harry to be a liar.. but Harry isn t a liar. 7

8 (20) Negation Test for Presuppositions a. Dumbledore doesn t knows (that) Voldemort has returned,. # but/and Voldemort hasn t returned. b. Harry didn t discover (that) Tom Riddle was Voldemort,. because Tom Riddle wasn t Voldemort. c. Lucius Malfoy isn t glad (that) Voldemort has returned,. # but Voldemort hasn t returned Observation 3: Presuppositions contained in the embedded proposition sometimes project; but sometimes they don t (Karttunen 1973). i.e., some attitude predicates are plugs - presuppositions are blocked (don t project). verbs of saying, performatives, holes - presuppositions pass through (project). factives, aspectual verbs like stop, etc. filters - some pass, some are blocked 7 (21) Possessive Existential Presuppositions a. Patrick knows we broke his cello. # but he doesn t have a cello hole b. Patrick is sad we broke his cello. # but he never had a cello hole c. Patrick believes/thinks we broke his cello. but he never had a cello (he s delusional) plug d. Patrick claims/says we broke his cello. but he never had a cello (he s a liar) plug 7 Karttunen 1973 lists conditional constructions and disjunctive constructions (i.e., not attitude predicates) as examples of filters. Observation 4: The referent of a within the embedded clause can be interpreted referentially, or non-referentially. (Quine 1956) CONTEXT Ralph sees a man sneaking around in the dark and concludes that he is a spy. This man is actually Ortcutt, the mayor, who Ralph believes would never be involved in espionage (22) Ralph believes that man is a spy.. T, under a non-referential reading (de re). F, under a referential reading (de dicto) CONTEXT Rita is in love with her boyfriend, Dexter. She doesn t know that he s a serial killer. (23) Rita wants to marry a serial killer.. F, under a non-referential reading (de re). T, under a referential reading (de dicto) Some Empirical Properties of Attitude Predicates 1. Attitude predicates select for propositions/clauses;. the morphosyntactic properties of the clauses can vary 2. Some attitude predicates entail the truth of their complement;. sometimes this entailment is a presupposition. (veridicality and factivity distinctions) 3. Presuppositions within the embedded proposition are non-uniform with respect to their projection (holes and plugs) 4. The de re/de dicto distinction 8

9 3.2 Theoretical Approaches to Attitude Predicates Hintikka 1975: The Traditional Approach Hintikka 1975 : Universal quantifiers over possible worlds. - different attitude predicates have different accessibility relations acc dox (x,w) yields worlds compatible with x s beliefs in w. (doxastic accessibility relation) acc epist (x,w) small yields worlds compatible with x s knowledge in w. (epistemic accessibility relation) acc boul (x,w) yields worlds compatible with x s desires in w. (bouletic accessibility relation) (24) a. believe w,g = λp s, t.λx.[ w [acc dox (w, w, x) p(w )]] b. know w,g = λp s, t.λx.[ w [acc epist (w, w, x) p(w )]] c. want w,g = λp s, t.λx.[ w [acc boul w, w, x) p(w )]] acc epist is a reflexive accessibility relation - w is always one of the worlds, w, that is compatible with x s knowledge in w acc dox and acc boul are not reflexive - it is not guaranteed that w is one of the worlds compatible with - x s beliefs in w - x s desires in w Attitude predicates with a reflexive acc are factive. (because claims about w are also claims about w) The de re/de dicto reading can be viewed as a quantifier scope ambiguity (25) Rita wants to marry a serial killer a. x[serial-killer(x, w) [ w [acc boul (w, w, r) marry(r, x, w )]]] T b. [ w [acc boul (w, w, r) x[serial-killer(x, w ) marry(r, x, w )]]] F VP [ w [acc boul (w, w, r i ) x[s-killer(x, w ) marry(t i, x, w )]]] V λx.[ w [acc dox (w, w, x) evil(s, w )]] V CP λw.evil(s, w) λp s, t.λx.[ w [acc dox (w, w, x) p(w )]] believe C that IP Snape is evil Rita i λy.[ w [acc boul (w, w, y) x[s-killer(x, w ) marry(t i, x, w )]]] V V CP λw. x[s-killer(x, w) marry(t i, x, w)] λp s, t.λy.[ w [acc boul (w, w, y) p(w )]] want C IP All of the worlds, w, compatible with x s beliefs in w,. are worlds where Snape is evil. Whether attitude predicates are factive or non-factive depends on the accessibility relation: PRO i marry a serial killer The referential reading requires a compositional rule to deal with quantifier raising called predicate abstraction 8 8 This compositional rule is also used to formalize the semantics of relative clauses. 9

10 When a quantifier raises, it triggers predicate abstraction This applies to propositions that have elements with indexes It replaces the individual with the index with a variable, eg., x, and adds a lambda abstractor λx to the formula CONTEXT Heim doesn t want to teach on Mondays or Fridays. She would really rather not teach at all, but her job requires that she teach a regular courseload on M/W/F or on T/Th This yields a function from individuals to truth-values (type e, t ) The raised quantifier can then / bind that newly created variable Because the quantifier is outside of the scope of the attitude predicate, it is interpreted with respect to w, not w VP y.[s-killer(y, w) [ w [acc boul (w, w, r i ) marry(t i, y, w )]]] (26) I want to teach Tuesdays and Thursdays next semester T Heim 1992: Desire predicates like want assert that. the embedded proposition is preferable to relevant alternatives 9 VP λy.[ w [acc boul (w, w, r i ) marry(t i, y, w )]] (27) x wants p is true in w iff for every w acc dox (x,w): every p-world maximally similar to w is more desirable to x a serial killer j j VP [ w [acc boul (w, w, r i ) marry(t i, t j, w )]] than any non-p worlds maximally similar to w V λx.[ w [acc boul (w, w, x) marry(t i, t j, w )]] want = λp s, t.λx.[ w [acc dox (w, w, x) Sim w (p)< x,w Sim w ( p)]] Rita i V λp s, t.λx.[ w [acc boul (w, w, x) p(w )]] CP λw.marry(t i, t j, w) Sim w (p) is a selection function;. it yields the set of p-worlds maximally similar to w want C IP < x,w ranks worlds in terms of desirability to x in w PRO i marry t j (where if w < x,w w. then w is preferable to w ) Heim 1992: Preference-Based Attitude Predicates Heim 1992: This approach to attitude predicates make the wrong predictions for cases like (26) Hintikka 1975: (26) T iff all of Heim s desire worlds are worlds where she teaches Tuesdays and Thursdays But her desire worlds include worlds where she doesn t teach at all! Villalta 2008 argues that the subjunctive/indicative distinction in Spanish correlates to this sort of gradability - comparing alternatives p and p. (although not necessarily ordered by desirabiltiy) gradable (p vs p) - select for subjunctive complements non-gradable - select for indicative complements 9 Heim 1992 s analysis is actually (famously) framed in a dynamic semantic framework, where meaning is not formalized as truth-conditions, but rather as context-change potentials. 10

11 References von Fintel, Kai. & Anthony S. Gillies Must... stay... strong! Natural Language Semantics 18(4) von Fintel, Kai & Sabine Iatridou How to say ought in foreign: The composition of weak necessity modals. In Time and Modality, Springer. Quine, Willard V Quantifiers and propositional attitudes. the Journal of Philosophy 53(5) Villalta, Elisabeth Mood and gradability: an investigation of the subjunctive mood in spanish. Linguistics and Philosophy 31(4) Von Fintel, Kai & Irene Heim Intensional semantics. ms., Massachusetts Institute of Technology. Heim, Irene Presupposition projection and the semantics of attitude verbs. Journal of semantics 9(3) Heim, Irene & Angelika Kratzer Semantics in generative grammar Blackwell Textbooks in Linguistics. Blackwell Oxford. Hintikka, Jaakko Semantics for Propositional Attitudes. In Models for Modalities, Springer. Karttunen, Lauri Presuppositions of Compound Sentences. Linguistic Inquiry Kratzer, Angelika What must and can Must and Can Mean. Linguistics and Philosophy 1(3) Kratzer, Angelika Partition and Revision: The Semantics of Counterfactuals. Journal of Philosophical Logic Kratzer, Angelika An Investigation into the Lumps of Thought. Linguistics and Philosophy 87: Kratzer, Angelika Modality. In A. von Stechow & D. Wunderlich (eds.), Semantics: an international handbook of contemporary research, Berlin, Germany: de Gruyter. Kratzer, Angelika Modals and Conditionals: New and Revised Perspectives. Oxford Univ Press. 11