Modals and conditionals Kai von Fintel (MIT) CSSL17 July 1014, - - PowerPoint PPT Presentation

Modals and conditionals

Kai von Fintel (MIT) CSSL17 — July 10–14, 2017

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This intermediate level course introduces the semantics of modals and conditionals and provides a guide to current research in the area.

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http://kvf.me/crete

includes links to these slides, readings, and Slack channel

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How to participate:

• listen & think
• ask questions (in class, on Slack)
• consider other languages
• stay in touch

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• 0. Introduction
• 1. Modals
• 2. Conditionals
• 3. Interactions
• 4. Ask me anything
• 5. X

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• 0. Introduction

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(1) A former meerkat expert at London Zoo has been ordered to pay compensation to a monkey handler she attacked with a wine glass in a love spat over a llama-keeper.

[Associated Press, Oct. 14, 2015]

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The sentence “A former meerkat expert at London Zoo has been ordered to pay compensation to a monkey handler she attacked with a wine glass in a love spat over a llama-keeper.” is true if (and only if) a former meerkat expert at London Zoo has been ordered to pay compensation to a monkey handler she attacked with a wine glass in a love spat over a llama-keeper.

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Meanings of sentences

• describe the world
• distinguish between ways the world may be, matching

some of them, not matching others

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“Ways the world may be” = possible worlds

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• Assertions make claims about what the world is like.
• Questions ask what the world is like.
• Commands order changes in what the world is like.

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There are many ways the world may be.

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Language is a precision instrument to distinguish between many possible ways the world may be.

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Our job as semanticists: Reverse engineer this precision instrument.

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Meanings come about through a combination of

• individual elements of meaning
• the hierarchical syntactic structure they occur in
• principles of meaning composition
• inferences about the situation an expression is used in
• …

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Two (or three) kinds of elements of meaning:

• content words (chair, love, ponder, incandescent, …)
• “function”/logical words (the, most, and, if, might, …)
• and maybe: structural configurations.

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Oh, those big little words!

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After cataloguing various ‘improper’ senses of only, Ockham remarks that These are the senses, then, in which the exclusive expression can be taken improperly. And perhaps there are still other senses in which it can be taken

• improperly. But since they are not as widely used as

the ones we have dealt with, I will leave them to the specialists. “A glorious picture indeed: monasteries crammed to the spires with specialists on only, laboring away on the fine points of the semantics of exclusive propositions. Those were the days!” (Larry Horn)

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So, with the throttling hands of death at strife, Ground he at grammar; Still, thro’ the rattle, parts of speech were rife: While he could stammer He settled οτι’s business — let it be! — Properly based ουν — Gave us the doctrine of the enclitic δε, Dead from the waist down. Robert Browning: “A Grammarian’s Funeral”

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… in this chapter we shall consider the word “the” in the singular, and in the next chapter we shall consider the word “the” in the plural. It may be thought excessive to devote two chapters to one word, but to the philosophical mathematician it is a word of very great importances: like Browning’s grammarian with the enclitic δε, I would give the doctrine of this word if I were “dead from the waist down” and not merely in prison. Bertrand Russell: “Introduction to Mathematical Philosophy”

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The word “if”, just two tiny letters Says so much for something so small The biggest little word in existence; Never answers, just questions us all If regrets were gold, I’d be rich as a queen If teardrops were diamonds, how my face would gleam If I’d loved you better, I wouldn’t be lonely If only, if only, if only Dolly Parton: “If only”

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If

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(2) If it had rained, I would have used an umbrella.

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• the if-clause sets up a hypothetical scenario
• the consequent is used to characterize the scenario

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The world as it would have been like if it had rained is a world where I used an umbrella.

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if p takes us to the world that is just like the actual world in all respects other than that p is true (and whatever is needed to make p true) the consequent q is then used to describe the world that if p took us to

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1.3 Variably Strict Conditionals

(A) VACUOUS TRUTH (B) NON-VACUOUS TRUTH (C) FALSITY- - OPPOSITE TRUE

(D) FALSITY - - OPPOSITE FALSE

FIGURE 3

(3) If Caesar had fought the Korean War, he would have used catapults. vs. (4) If Caesar had fought the Korean War, he would have used nuclear weapons.

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http://youtube.com/watch?v=0lpY0Kt4bn8

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(5) If kangaroos had no tails, they would topple over.

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What use are claims about other possible worlds?

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(6) If there was an earthquake tomorrow, this house would collapse.

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(6) If there was an earthquake tomorrow, this house would collapse. In a world just like ours (where the house is built the same way, the same laws of physics apply, …) but where there is an earthquake, this house collapses.

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Initial insights: the semantics for conditionals/modals

• needs to be context-dependent
• needs to be subject to contextual indeterminacy
• needs to anchor the claim to the actual world

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A bit about the framework

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• Heim & Kratzer 1998
• von Fintel & Heim 2017

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• Each expression has a semantic value (extension) relative

to a possible world (evaluation world): [ [α] ]w

• Each expression has an intension, a function from worlds

to its extension relative to that world: λw. [ [α] ]w

• The extension of a complex expression is calculated

compositionally from the extensions/intensions of its immediate constituents.

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An utterance of a sentence φ in a world w is true iff [ [φ] ]w = 1.

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The context set of a conversation is the set of worlds that are still candidates for being the world the conversation is happening in. Asserting a sentence φ is a proposal to eliminate any world w from the context set such that [ [φ] ]w = 0.

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Modals, finally

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must, have to, should, ought to, may, might, can, could, need

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Two dimensions of modal meaning:

• modal force (necessity … possibility)
• modal flavor (epistemic, deontic, …)

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(7) It has to be raining. (8) Visitors have to leave by six pm. (9) You have to go to bed in ten minutes. (10) I have to sneeze. (11) To get home in time, you have to take a taxi.

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• Modals are quantifiers over possible worlds.
• Which possible worlds they quantify over constitutes their

flavor.

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• Force = quantificational strength (universal … existential)
• Flavor = type of anchoring

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The general schema: M [f(w)] (φ) M the quantificational relation between two sets of possible worlds f(w) a set of possible worlds assigned by flavor f to the evaluation world w φ the prejacent proposition, a set of worlds where φ is true

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(12) It has to be raining. M universal quantification (subset relation) f(w) the set of worlds compatible with the evidence in w φ the set of worlds where it is raining ⇝ the evidence in w entails that it is raining

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(13) Iris can have one cookie after dinner. M existential quantification (compatibility relation) f(w) the set of worlds that satisfy the parental wishes in w φ the set of worlds where Iris has one cookie after dinner ⇝ the parental wishes in w allow Iris to have one cookie after dinner

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From syntax to interpretation:

• how does the modal get a prejacent proposition to work
• n?
• where does the flavor f(w) come from?

Lots of implementation options. But core insight is important.

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Modals and conditionals — Day Two

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Reminder

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http://youtube.com/watch?v=0lpY0Kt4bn8

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Initial insights: the semantics for conditionals/modals

• needs to be context-dependent
• needs to be subject to contextual indeterminacy
• needs to anchor the claim to the actual world

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The general schema for modals: M [f(w)] (φ) M the quantificational relation between two sets of possible worlds f(w) a set of possible worlds assigned by flavor f to the evaluation world w φ the prejacent proposition, a set of worlds where φ is true

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Simple flavors:

• epistemic (worlds compatible with the evidence)
• deontic (worlds that satisfy the rules)

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Complex flavors

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(14) Howard forgot to return his library book. He has to pay a $5 fine. complex flavor: the actual world circumstances + what the rules are

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essentially complex:

• not just the circumstances: Howard may be a scofflaw who

never pays fines

• not just the rules: Howard would not have failed to return

the book

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insight: flavors can be complex implementation: lots of options

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Famously, Kratzer relativized the semantics of modals to two parameters:

• modal base (core flavor)
• ordering source (comparing worlds in the modal base)

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Iteration

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(15) Cosette might have to be home by midnight. One modal embedded under the other:

• epistemic might
• deontic have to

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might f1(w) [ λw′. have to f2(w′) Cosette be home by midnight ] ⇝ the evidence leaves open that Cosette is required to be home by midnight

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More on strength

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• there are many kinds of quantifiers over individuals

(including cardinals, proportional, …)

• modals show less variety

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Weak necessity: (16) I don’t have to work on this tonight but I should.

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von Fintel & Iatridou 2008:

• weak necessity modals are necessity modals with an

additional narrowing of their domain

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Rubinstein 2014:

• must/have to are sensitive to non-negotiable priorities
• nly
• should/ought to are sensitive to further priorities

(i.e. negotiable)

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Rullmann, Matthewson & Davis 2008:

• narrowing of domain can make necessity modals as weak

as possibility modals

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Deal 2011:

• when a language doesn’t have a necessity modal, the

possibility modal can fill the void

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von Fintel & Gillies 2010 vs. Lassiter 2016: Is epistemic must weaker than the bare prejacent?

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(17) It must be raining. vs. (18) It’s raining.

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• 2. If (again)

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(19) If Rosa left before 6am, she got there in time.

• epistemic flavor
• worlds compatible with the evidence + where Rosa left

before 6am

• all of those worlds are worlds where she got there in time

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Just like modals:

• quantificational force (universal)
• modal flavor (epistemic)
• anchoring to actual world (actual evidence)

plus: restriction to worlds where the antecedent is true

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Obvious idea: if is a modal operator

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if [f(w)] (p) (q)

• the antecedent p
• the modal flavor function f(w)
• the consequent q

true iff ∀w′ ∈ p ∩ f(w): q(w′) = 1.

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An alternative (closer to what we said in the intro):

• if p is a plural definite description of the p-worlds of a

certain flavor

• the consequent is claimed to be true in those worlds

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if [f(w)] (p) = the plurality of worlds that contains the p-worlds in f(w)

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What happens when we combine the if p-plurality of worlds with the consequent proposition?

• the consequent is a function from individual worlds to

truth-values

• it can’t be directly applied to a plurality of worlds

The same thing happens in the case of pluralities of individuals!

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(20) The students laughed.

• the students denotes a plurality of individuals (made up
• f all and only the students)
• laughed is a predicate of single individuals

The combination needs to be mediated.

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The students * laughed The *-operator “pluralizes” a predicate. The resulting plural predicate is true of a plurality iff the original predicate is true

• f every atom making up the plurality.

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if p, * q true iff q is true of every world in the plurality of worlds denoted by if p (or more precisely, if f(w) p).

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Conditionals as plural definite descriptions:

• Schlenker 2004

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Xs and Os

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(21) If Rose scored, we won. (22) If Rose had scored, we would have won. Sometimes: indicative vs. subjunctive Sometimes: indicative vs. counterfactual

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(21) If Rose scored, we won. (22) If Rose had scored, we would have won. Sometimes: indicative vs. subjunctive Sometimes: indicative vs. counterfactual

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Not always subjunctive: (23) If Rose had scored, we would have won.

English has no subjunctive

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Not always counterfactual: (24) a. If he had taken arsenic, he would be showing exactly these symptoms.

Anderson 1957

b. If she brought pie, we would eat it rightaway.

future less vivid (FLV)

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Again, not counterfactual: (25) The murderer used an ice-pick. But, if the butler had done it, he wouldn’t have used an ice-pick. So the murderer must have been someone else.

Stalnaker 1975

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We need neutral terminology. O-marking: ordinary, open, “indicative” conditionals X-marking: the extra marking on counterfactuals, FLVs, etc.

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• What meaning does X-marking contribute?
• How does it achieve the meaning it contributes?

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Iatridou 2000: X-marked conditionals quantify over a domain

• f worlds that excludes the actual world.

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But Mackay 2015: (26) a. If Jones had taken arsenic, things wouldn’t be quite as they actually are. b. If Jones had taken arsenic, everything would be exactly as it actually is.

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Modus ponens: (27) A: If Heather had left before 9am, she would have made it to the meeting. B: Well, you’re wrong. She did leave before 9 and still didn’t make it.

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For all conditionals: the domain of quantification must include antecedent worlds. The meaning of O-marking:

• The domain of quantification is entirely within the context

set. The meaning of X-marking:

• The domain of quantification is not entirely within the

context set.

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• von Fintel 1998: X-marking triggers non-inclusion

presupposition

• Leahy 2017: X-marking has no meaning, triggers

counterfactuality implicature when in competition with O-marking

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How do O/X-marking have the meaning they do? As Iatridou 2000 showed, X-marking is complex:

• an extra layer of past, not obviously temporal
• often a future morpheme (in the consequent)
• often a “fake” aspect, not obviously temporal
• often subjunctive mood

We don’t understand much yet how these interact. Most work has been done on the role of past tense.

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For now: if O(f(w) p)(q) signals that f(w) ∩ p ⊆ cs if X(f(w) p)(q) signals that f(w) ∩ p ̸⊆ cs

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Ordering in conditional semantics

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(Failure of?) Strengthening the Antecedent: (28) a. If Sophie had gone to the parade, she would have seen Pedro. b. If Sophie had gone to the parade and and been stuck behind a tall person, she would have seen Pedro.

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Sobel Sequence: (29) If Sophie had gone to the parade, she would have seen Pedro; but if she had gone to the parade and and been stuck behind a tall person, she would not have seen Pedro.

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Lewis: “our problem is not a conflict between counterfactuals in different contexts, but rather between counterfactuals in a single context. It is for this reason that I put my examples in the form of a single run-on sentence, with the counterfactuals

• f different stages conjoined by semicolons and but.”

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Lewis: “It is still open to say that counterfactuals are vague strict conditionals based on similarity, and that the vagueness is resolved-the strictness is fixed-by very local context: the antecedent itself.That is not altogether wrong, but it is

• defeatist. It consigns to the wastebasket of contextually

resolved vagueness something much more amenable to systematic analysis than most of the rest of the mess in that wastebasket.”

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Edgington: “a piece of masonry falls from the cornice of a building, narrowly missing a worker. The foreman says: (30) If you had been standing a foot to the left, you would have been killed; but if you had (also) been wearing your hard hat, you would have been alright.

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Edgington: “the building foreman’s remarks above […] constitute a single, pointful piece of discourse”

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Reverse Sobel: (31) #If Sophie had gone to the parade and been stuck behind a tall person, she would not have seen Pedro; but if she had gone to the parade, she would have seen Pedro.

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(32) a: If Sophie had gone to the parade, she would have seen Pedro; but if she had gone to the parade and and been stuck behind a tall person, she would not have seen Pedro. b: But then she wouldn’t necessarily have seen Pedro, right?

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• von Fintel 2001
• Gillies 2007
• Moss 2012
• Holst 2013
• Klecha 2014
• Dohrn 2017
• K. Lewis 2017

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Modals and conditionals — Day Three

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Reminders and Clarifications

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The general schema for modals: M [f(w)] (φ) M the quantificational relation between two sets of possible worlds f(w) a set of possible worlds assigned by flavor f to the evaluation world w φ the prejacent proposition, a set of worlds where φ is true

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Complex flavors: (33) Howard has to pay a fine. quantifies over worlds

• where the same things happened as in the evaluation

world

• and that afterwards are as good as possible according to

the rules

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If we want to stick to our simple semantics, with its flavor function (from evaluation worlds to sets of worlds quantified

• ver), we have to locate the complexity in the pragmatics of

determining a salient value to the context-dependent flavor.

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Alternatively, we can complicate the semantics. This is what Kratzer did.

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• In full generality, Kratzer assumes two contextually

supplied parameters.

• They are both functions from evaluation worlds to sets of

propositions.

• One is employed as the modal base, to determine for

each evaluation world a set of worlds (= the intersection

• f the propositions assigned to the evaluation world)
• The other is employed as the ordering source, to

determine for each evaluation a preference ordering of worlds (the more propositions in the set of propositions assigned to the evaluation world are true in a world, the better that world)

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One can imagine systems of intermediate complexity. For example, one could sue something of the same type as our simple flavor as the modal base:

• a function from worlds to sets of worlds (≈ modal

base/accessibility function) And then, a second ordering parameter:

• a function from worlds to ordering relations (function

from worlds to ordered pairs of worlds, ≈ ordering source)

• or a function from worlds to subset selection functions

These are mathematically slightly less complex. You’ll find such setups in some of my papers and lecture notes.

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Pedagogically and strategically, I like to start with the simplest plausible system and complicate things only if and when needed.

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Two proposals for conditionals:

• 1. if as a necessity modal

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if [f(w)] (p) (q)

• the antecedent p
• the modal flavor function f(w)
• the consequent q

true iff ∀w′ ∈ p ∩ f(w): q(w′) = 1.

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Two proposals for conditionals:

• 1. if as a necessity modal
• 2. if as a (plural) definite description operator

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if f(w) (p) = the plurality of worlds that contains the p-worlds in f(w) if f(w) (p), ∗q true iff q is true of every world in the plurality of worlds denoted by if f(w) (p)

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• 3. Interactions

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Semantics is a lab science in several ways. The most crucial way is that we learn a lot about our objects of study when we put them together and see how they react to each other.

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Modal sentences, conditional sentences, and their sentential constituents (the prejacent of modals, the antecedent and consequent of conditionals) are all the same type (propositions, functions from worlds to truth-values). So, we expect them to freely mix-and-match, embed in each

• ther.

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Modal sentences in the antecedent of conditionals

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No problem: (34) If Howard has to pay a heavy fine, he will be broke. (35) If one can get to that beach by bike, Iris did just that.

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Epistemic modals in the antecedent? Lots of people think not. For example, Papafragou 2006: (36) a. ?If Max must be lonely, his wife will be worried. b. ?If Max may be lonely, his wife will be worried.

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Conditionals signal that the antecedent is “iffy”. An epistemic modal statement can only be “iffy”, if the speaker is not certain about what “the evidence” is. That can only be if “the evidence” is not the evidence that the speaker has full access to.

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(37) If there have to be two reds, your next move is obvious. (38) If John might have cancer [the doctors haven’t told us], he will have to see an expert in Boston.

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Modal sentences in the consequent of conditionals

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(39) If jaywalking is illegal here, then that guy has to pay a fine.

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A scenario devised by Sarah Moss: We’re trying to figure out what the roommate arrangements between Caspar and Chris are. We have concluded that one of them vacuums on Saturdays and the other cooks on Sundays. (40) If Caspar vacuums on Saturday, then Chris has to cook

• n Sunday.

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An example due to Zsofia Zvolenszky: (41) If Britanny drinks Coke, she must drink Coke. If we saw Britanny drink Coke, we would conclude that she’s contractually required to drink Coke.

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(42) If Howard returns his book late, he has to pay a fine.

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Modals in both components of a conditional: (43) If Cosette has to be home by midnight, she ought to think about leaving now.

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So far, so good

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Modals and conditionals — Day Four

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Our friends Jacy and Macy have been driving in the Massachusetts hinterlands, inexplicably without iPhones or GPS, and are relying entirely on an old-fashioned map. They’ve just passed through a little town with an iconic New England church and are looking on the map to try to figure out where they are. They have concluded that they are either on Route 117 or on Route 62. There are two plausible candidate towns on Route 117 (Maynard and Stow) and just one on Route 62 (Clinton).

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They are on Rte 62 (and don’t know it) or on Rte 117 (and don’t know it). They are in Maynard, Stow, or Clinton (and don’t know it).

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It’s true when they say: (44) We might be in Maynard. since there are worlds compatible with their evidence where they are in Maynard.

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It’s true when they say: (45) If we’re on Route 62, we’re in Clinton. Because of the three towns that they know they might be in,

• nly Clinton is on Rte 62.

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Our semantics for conditionals (either the modal analysis or the plural description analysis) has the conditional take us to worlds that are (i) in f(w), here in the set of worlds compatible with their evidence and (ii) are antecedent worlds. Among the worlds compatible with their evidence, all p-worlds (worlds where they are in Rte 62) are worlds where they are in Clinton.

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Problem cases (46) a. If we’re on Route 117, we might be in Stow.

True

b. If we’re on Route 117, we might be in Clinton.

False

c. If we’re on Route 62, we must be in Clinton.

True

These cannot be explained in our framework!

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Take (47) If we’re on Route 62, we must be in Clinton. The conditional takes us to those worlds that are (i) compatible with their evidence, with what they know (which includes their knowledge that they don’t know in which of the three towns they are) and (ii) where they are on Rte 62. In all of those worlds, they are in Clinton, but in none of them do they know or have any additional evidence that they are in Clinton.

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Some of the ways out:

• 1. The Restrictor Theory
• 2. A non-epistemic analysis of epistemic modals
• 3. A meaning for conditionals where “if p” means “if we

learn p” [… surely more, we’re desperate after all]

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We’ll leave the idea that epistemic modals are not epistemic

• aside. It’s been pursued:
• Yalcin 2007 (“Epistemic modals”, Mind)
• Gillies 2010 (“Iffiness”, S&P)

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We’ll also leave the idea aside that “if p” doesn’t mean “if p” but “if we learn p”. It’s been pursued (in a related context):

• von Fintel 2012 (“The best we can (expect to) get?

Challenges to the classic semantics for deontic modals”)

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The Restrictor Theory

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Kratzer 1986: the history of the conditional is the story of a syntactic mistake. There is no two-place if …then connective in the logical forms of natural languages. If-clauses are devices for restricting the domains of various operators.

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Kratzer’s Thesis If-clauses are devices for restricting the domains of various

• perators.

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(48) If we’re on Route 62, we must be in Clinton. must [f(w) ∩ p] (we be in Clinton) The only thing the if-clause is doing is restricting the flavor argument of must. There’s no additional modal operator contributed by if.

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What now about the modal-less conditional? (49) If we’re on Route 62, we are in Clinton. If if is a device for restricting the domains of operators, where is the operator being restricted here?

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Two options:

• if ambiguous between modal operator and restrictor

readings

• if always a restrictor, “bare” conditionals have covert

modals Kratzer: covert modals

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Some questions:

• 1. Can the restrictor theory cover all the cases that

previously we viewed as involving nested modality (conditional on top of a modal)?

• 2. Can we finally decide whether we can have a theory with a

simple flavor function, or do we need the Kratzerian two-parameter theory?

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(50) If Howard returned his book late, he has to pay a fine.

165

Earlier, this seemed unremarkable:

• we don’t know if Howard returned his book late
• but in the worlds compatible with our evidence where he

did, the rules are such that in such a circumstance they require a fine How does the restrictor theory deal with this case?

166

Assume the simple flavor view: The consequent modal has a flavor argument f(w) and the if p-clause is used to restrict that to the p worlds in f(w). λw. M [f(w) ∩ p] (q)

167

In our case (Howard has to pay a fine), f(w) is a complex flavor (combining the actual circumstances and what the rules say about those circumstances)

168

Imagine that unbeknownst to us Howard did return his book

• n time.

169

Now, we say (51) If Howard returned his book late, he has to pay a fine. It seems we’re saying something true (even though in actual fact, he returned his book on time).

170

The simple view does not get that right. λw. M [f(w) ∩ p] (q)

• f(w) contains only worlds where the circumstances are like

in the actual world, including that Howard returned his book on time, and in none of those does he pay a fine

• if f(w) contained all the best worlds compatible with our

evidence (we don’t know whether he returned the book on time), the best worlds will still be worlds where he did return the book on time and doesn’t pay a fine

• in either case, when we intersect that set with the

proposition that he returned the book late, we get the empty set

171

• ⇒ under the restrictor theory the simple view is wrong:

complex flavors need a complex representation.

• the restrictive if-clause restricts only the modal base

(which has to be epistemic in our case)

• the ordering happens on top of that

λw. M (O(w)[M(w) ∩ p]) (q)

172

A problem

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Zvolenszky’s example again: (52) If Britanny drinks Coke, she has to drink Coke. If the if-clause restricts the modal base to worlds where Britanny drinks Coke, then it is trivially true that the best worlds among those are worlds where she drinks Coke.

174

The way out for the restrictor theory

175

In the restrictor theory, conditionals with modals in the consequent are in principle structurally ambiguous:

• if restricts the overt modal
• if restricts a covert modal that takes the overt modal as

its argument.

176

(53) If Britanny drinks Coke, she has to drink Coke. ≈ (54) If Britanny drinks Coke, she must have to drink Coke.

177

Once we recognize the availability of nested structures (covert modal restricted by if + overt modal embedded in the consequent), we see that the restrictor theory can mimic our previous theory in all cases where it was successful.

178

(55) If jaywalking is illegal here, then that guy has to pay a fine. (56) If Cosette has to be home by midnight, she ought to think about leaving now.

179

Anette Frank 1997: “There are in fact no truly deontically modalized if-conditionals. Instead, we assume conditionals with a deontic modal operator in the consequent clause to be analyzed throughout in terms of an implicit or explicit epistemically (or circumstantially) based modal operator. The deontic modal adverb is then to be analyzed within the scope

• f the ‘higher’ epistemic modal operator.”

180

We have to revisit our earlier conclusion that the simple flavor view is not compatible with the restrictor theory.

181

(57) If Howard returned his book late, he has to pay a fine. This can be analyzed as a nested structure with a simple flavor analysis.

182

What would it take to show that we need a non-nested complex representation of a conditional with a complex-flavor modal in the consequent?

183

Add to our Massachusetts scenario, that there are two Route 62 possibilities, one is Clinton (which is much more likely) and the other, quite unlikely, is Berlin. (58) If we’re on Rte 62, we ought to be in Clinton.

184

Epistemic modals provide the strongest arguments for both the restrictor theory and the complex analysis of complex flavors.

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What could be next if we had more time together:

• anankastic conditionals (another case for nested

structures)

• adverbs of quantification and the restrictor theory
• the non-epistemic analysis of epistemic modals
• information-sensitive deontic modals (the “Miners

Paradox”)

• the “indicative”/“subjunctive” distinction in modals &

conditionals

• the cross-linguistics of weak necessity

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Ask me anything

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Bonus section: The referential view

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Is the restrictor theory compatible with the idea that if-clauses are definite descriptions of pluralities of worlds?

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Simple case: if f(w) (p), * q No covert modal needed. The work is distributed between the f(w) flavor argument of if and the star-operator.

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Nested reading: if f(w) (p), * λw’. M f’(w’) q

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But what about the one-modal restricted reading (like the examples with our lost friends)? That must be analyzed without the star-operator. But how?

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if f(w) (p), λP M P q

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End of Bonus section

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