Rutgers Job Talk

<h2 class="title">How Presuppositions and Scalar Implicatures Interact</h2>

(joint work with Benjamin Spector)

### Yasutada Sudo (UCL)

Rutgers University

13 February, 2017

---

# Presupposition

<p><ex>Alice is <pr>unaware</pr> that I'm Japanese.</ex></p>

presupposition: I'm Japanese

<p><ex>Ben, <pr>too</pr>, is guilty.</ex></p>

presupposition: Another (salient) person is guilty

<p><ex>Cate <pr>forgot</pr> to call Daniel.</ex></p>

presupposition: Cate was supposed to call Daniel

---

# Scalar Implicature (SI)

<p><ex><si>Some</si> of my students smoke</ex></p>

SI: ¬(<b>all</b> of my students smoke)

<p><ex>Alice <si>or</si> Becky smokes</ex></p>

SI: ¬(Alice <b>and</b> Becky smoke)

<p><ex>Chris knows <si>a few</si> Japanese words</ex></p>

SI: ¬(Crhis knows <b>many</b> Japanese words)

---

# Presupposition + SI

What happens if you put these together?

<p><ex>Alice is <pr>unaware</pr> that <si>some</si> of my students smoke</ex></p>

Many theories of presupposition and many theories of SI.

But their interactions are not well understood.

---

# Outline

1. <b>Puzzle</b>: presupposed ignorance

2. Preliminary account

3. <b>Main topic</b>: How presuppositions and SIs interact

<div class="shaded">
  <b>Main claim</b>: Two scalar strengthening mechanisms are at play
    <ol type="I">
      <li>Presupposed Ignorance Principle</li>
      <div style="height:12pt;"></div>
      <li>Exhaustivity operator (Exh) as a presupposition hole</li>
    </ol>
</div>

---

# Presupposed Ignorance

---

# Standard analysis of <pr>too</pr>

<div class="shaded">
<p style="margin-top: -2pt; margin-bottom: 6pt;"><ex>Alice, <pr>too</pr>, smokes</ex></p>

<table class="indented">
    <tr><td style="text-align: right;">asserts:</td><td style="padding-left: 1em;">Alice smokes</td></tr>
    <tr><td>presupposes:</td><td  style="padding-left: 1em;">Another individual (antecedent) smokes</td></tr>
  </table>

</div>

This explains the following contrast.

<p><ex>Ben went to Harvard. Alice, <pr>too</pr>, went to Harvard.</ex></p>

<p><ex>Ben went to Harvard.</ex> #<ex>Alice, <pr>too</pr>, went to Yale.</ex></p>

---

# Puzzle

But then why is the following bad?

<p><ex>Ben went to Harvard.</ex><br />
  #<ex>Alice, <pr>too</pr>, went to Harvard or Yale.</ex></p>

If Ben went to Harvard, he went to Harvard or Yale, so the presupposition of <ex><pr>too</pr></ex> should be satisfied!

<div style="height:12pt;"></div>
--

<p>Intuitively the presuppositional inference is stronger: we must be ignorant as to whether Ben went to Harvard or Yale.</p>

<p><ex>Ben went to Harvard or Yale.</ex><br />
<ex>Alice, <pr>too</pr>, went to Harvard or Yale.</ex></p>

---

# Analysis

This sentence has additional inferences that require something to be not common ground (CG).

We call such inferences **presupposed ignorance inferences**.

<div class="shaded">
<p style="margin-top: -2pt; margin-bottom: 6pt;"><ex>Alice, <pr>too</pr>, went to Harvard or Yale</ex></p>

<table class="indented">
    <tr><td style="text-align: right;">asserts:</td><td style="padding-left: 1em;">Alice went to Harvard or Yale</td></tr>
    <tr><td style="text-align: right;">presupposes:</td><td  style="padding-left: 1em;">Antecedent went to Harvard or Yale</td></tr>
    <tr style="height: 12pt;"></tr>
    <tr><td style="text-align: right;"><b>presupposed</b></td><td  style="padding-left: 1em;">¬CG(Antecedent went to Harvard)</td></tr>
    <tr><td style="text-align: right;"><b>ignorance</b></td><td  style="padding-left: 1em;">¬CG(Antecedent went to Yale)</td></tr>
  </table>

</div>

---

# Some more data

Presupposed ignorance inferences are triggered in other presuppositional contexts too.

<p class="indented"><ex>Alice went to Yale.</ex><br />
#<ex>Ben is <pr>unaware</pr> that she went to Harvard or Yale.</ex></p>

<p>Generally, items that give rise to ignorance inferences in simple sentences give rise to presupposed ignorance inferences in presuppositional contexts.</p>

<p class="indented">
<ex>Alice has three children.</ex><br />#<ex>Ben, <pr>too</pr>, has <strong>at least two</strong> children.</ex>
</p>

<p class="indented">
<ex>Alice has three children.</ex><br />
#<ex>Ben is <pr>unaware</pr> that she has <strong>at least two</strong> children.</ex>
</p>

---

# Some more data (cont.)

Items that do not give rise to ignorance inferences robustly do not give rise to presupposed ignorance inferences robustly either.

<p><ex>Ben went to Harvard.</ex><br />
  <ex>Alice, <pr>too</pr>, went to <strong>an</strong> Ivy League college.</ex></p>

<p>
<ex>Alice has three children.</ex><br />
<ex>Ben, <pr>too</pr>, has <strong>more than one</strong> child.</ex>
</p>

---

# Presupposed Ignorance Principle

---

# A Preliminary Account

To derive presupposed ignorance inferences, we postulate a principle:

<div class="shaded">
<p style="margin-top: -4pt;"><strong>Presupposed Ignorance Principle (PIP)</strong>:<br />
  φ<sub>p</sub> is infelicitous in context c if there is an alternative ψ<sub>q</sub> s.t.
<ol type="a" style="margin-bottom: 0pt; margin-top: -6pt;">
  <li>q is stronger than p; and</li>
  <li>q is part of the common ground in c, CG<sub>c</sub>(q)</li>
</ol>
</p>
</div>

---

# Example

<p>φ: <ex>Alice, <pr>too</pr>, went to Harvard or Yale</ex></p>

The 'Sauerland altenatives' for disjunction:

- <ex>Alice, <pr>too</pr>, went to Harvard</ex>

- <ex>Alice, <pr>too</pr>, went to Yale</ex>

- <ex>Alice, <pr>too</pr>, went to Harvard and Yale</ex>

Assuming antecedent = Ben, PIP predicts φ to be # if:

- CG(Ben went to Harvard); or
- CG(Ben went to Yale); or
- CG(Ben went to Harvard and Yale)

---

# Section summary

**Presupposed Ignorance Principle (PIP)** derives presupposed ignorance inferences.

<div class="indented">
<p>φ: <ex>Alice, <pr>too</pr>, went to Harvard or Yale</ex></p>
<ul>
  <li>¬CG(Ben went to Harvard); or</li>
  <li>¬CG(Ben went to Yale); or</li>
  <li>¬CG(Ben went to Harvard and Yale)</li>
</div>

Further question: Does PIP follow from a more general principle?

(I believe PIP should replace <i>Maximize Presupposition!</i>)

---

# How Presuppositions and SIs Interact

---

# Presuppositions and SIs

We want to understand how presuppositions and SIs interact:

<p><ex>Alice is <pr>(un)aware</pr> that <si>some</si> of my students smoke.</ex></p>

- <ex><pr>aware</pr></ex> is <strong>Strawson-U(pward)E(ntailing)</strong>. Its presupposition and assertive meaning are both positive.
- <ex><pr>unaware</pr></ex> is <strong>Strawson-D(ownward)E(ntailing)</strong>. It has a positive presupposition and a negative assertive meaning.

<p>PIP explains Gajewski & Sharvit's (2012) observation about Strawson-DE environments.</p>
<p>PIP cannot explain Strawson-UE environments, for which we will postulate a different mechanism, Exh.</p>

---

# G&S's observation

<div class="shaded">
<b>Gajewski & Sharvit's observation</b>: when a scalar item occurs in a Strawson-DE context, only the presupposition is strengthened.
</div>

<p><ex>Alice is <pr>unaware</pr> that <si>some</si> of my students smoke.</ex></p>

<table class="indented">
  <tr><td style="text-align: right;">asserts:</td><td style="padding-left: 1em;">¬(A believes that some of my students smoke)</td></tr>
  <tr><td>presupposes:</td><td  style="padding-left: 1em;">some <si>but not all</si> of my students smoke</td></tr>
</table>

It is # if it is commonly known that all of my students smoke.

(G&S makes some theoretical claims based on this observation, but we think they are not entirely justifiable)

---

# PIP applied to G&S's observation

<p>φ: <ex>Alice is <pr>unaware</pr> that <si>some</si> of my students smoke.</ex></p>

Alternative with a stronger presupposition:<br />
<p>ψ: <ex>Alice is <pr>unaware</pr> that <si>all</si> of my students smoke.</ex></p>

PIP says: φ is # if the presupposition of ψ is common ground, CG(all of my students smoke).

∴ A felicitous use of φ requires ¬CG(all of my students smoke).

---

# Epistemic Step

You might feel that the inference should be

<div class="indented">
CG(<si>¬</si>all of my students smoke)
</div>

rather than

<div class="indented">
<si>¬</si>CG(all of my students smoke).
</div>

We could derive this stronger inference with Chemla's (2008) pragmatic reasoning ('epistemic step for anti-presuppositions').

We will not go into details today.

---

# Strawson-UE Contexts

So PIP explains G&S's observation about Strawson-DE contexts.

But it fails to account for Strawson-UE contexts.

<p>φ: <ex>Alice is <pr>aware</pr> that <si>some</si> of my students smoke.</ex></p>

Alternative with a stronger preuspposition:<br />
<p>ψ: <ex>Alice is <pr>aware</pr> that <si>all</si> of my students smoke.</ex></p>

Then PIP derives: ¬CG(all of my students smoke)

But φ can be used in contexts where CG(all of my students smoke) (unlike its negative counterpart).

---

# Strawson-UE vs. -DE

Strawson-UE:
<p class = "indented"><ex>Alice is (only) <pr>aware</pr> that <si>some</si> languages have pronouns.</ex></p>

Strawson-DE:
<p class = "indented">#<ex>Alice is (only) <pr>unaware</pr> that <si>some</si> languages have pronouns.</ex></p>

The latter realy requires that not all languages have pronouns.

Notice also that <ex>only</ex> can be added to the former but not to the latter.

---

# Summary So Far

We need PIP to account for presupposed ignorance.

<div class="shaded">
<p style="margin-top: -4pt;"><strong>Presupposed Ignorance Principle (PIP)</strong>:<br />
  φ<sub>p</sub> is infelicitous in context c if there is an alternative ψ<sub>q</sub> s.t.
<ol type="a" style="margin-bottom: -4pt; margin-top: -6pt;">
  <li>q is stronger than p; and</li>
  <li>q is part of the common ground in c, CG<sub>c</sub>(q)</li>
</ol>
</p>
</div>

PIP accounts for scalar inferences triggered in Strawson-DE environments (G&S's observation).

But it fails to explain Strawing-UE environments.

---

# SIs with Presuppositions

---

# Mechanism of SI Computation

A scalar item in a Strawson-UE environment triggers an SI.

<p><ex>Alice is <pr>aware</pr> that <si>most</si> languages have pronouns.</ex></p>

SI: ¬(Alice is aware that <b>all</b> languages have pronouns)

Let us assume that a phonologically null operator (<ex>Exh</ex>) is responsible for SIs.

(We could adopt a more pragmatic approach to SIs for most of our data)

---

# Exh

Standard definition of <ex>Exh</ex> <span class="small">(Groenendijk & Stokhof 1984, Chierchia 2006, Chierchia, Fox & Spector, Fox 2007, van Rooij & Schulz 2004, Spector 2007)</span>:</p>

Excl(ψ,φ) = 'ψ is excludable given φ'. We adopt Fox's (2007) notion of <b>Innocent Exclusion</b>.

φ: <ex><si>Some</si> of my students smoke</ex>
<span style="margin-left: 1em;">ψ: <ex><si>All</si> of my students smoke</ex></span>

⟦<ex>Exh(<si>some</si> of my students smoke)</ex>⟧<sup>w</sup> = 1 iff<br>
some of my students smoke in w and not all of my students smoke in w

---

# Exh as a presupposition hole

What if φ and ψ have presuppositions?

<p><ex>Exh</ex> is a <b>presupposition hole</b> wrt negated alternatives:</p>

'<ex>Exh</ex> φ' is # if the presupposition of φ is not satisfied, or there's an excludable alternative ψ whose presupposition is not satisfied.

This is a natural extension of <ex>Exh</ex>, because it is a kind of negation.

---

# Example

<p>Exh(φ):<br /><ex style="margin-left: 12pt;">Exh(Alice is <pr>aware</pr> that <si>most</si> of my students smoke)</ex></p>

Exludable alternative ψ:<br /><ex style="margin-left: 12pt;">Alice is <pr>aware</pr> that <si>all</si> of my students smoke</ex>

- Exh(φ) presupposes that what φ and ψ presuppose: <br />
all of my students smoke.

- Exh(φ) asserts φ and ¬ψ:<br />Alice is aware that <b>most</b> of my students smoke but is not aware that <b>all</b> of my students smoke.

---

# PIP and Exh

What about PIP? How does it interact with <ex>Exh</ex>?

PIP has no effect here, provided that it applies <b>after</b> <ex>Exh</ex>.

Both of the following presuppose that all of my students smoke, so there's no presuppositionally stronger alternative.

<p><ex>Exh(Alice is <pr>aware</pr> that <si>most</si> of my students smoke)</ex></p>

<p><ex>Exh(Alice is <pr>aware</pr> that <si>all</si> of my students smoke)</ex></p>

---

# PIP and Exh

In some cases PIP and <ex>Exh</ex> both give rise to inferences.

<p>Exh(φ):<br /><ex>Exh(Alice is <pr>unaware</pr> that <si>most</si> of my students smoke)</ex></p>

<p>ψ:<br /><ex>Alice is <pr>unaware</pr> that <si>some</si> of my students smoke</ex></p>

<p>Exh(ψ'):<br /><ex>Exh(Alice is <pr>unaware</pr> that <si>all</si> of my students smoke)</ex></p>

<div class="indented">
  <p>SI: Alice is aware that <si>some</si> of my students smoke</p>

<p>Presupposition: (Some and) most of my students smoke</p>

<p>Presupposed ignorance: ¬CG(all of my students smoke)</p>
</div>

---

# Summary

A scalar item gives rise to a scalar inference via one of two mechanisms:
<ol>
  <li><strong>Presupposed Ignorance Principle</strong><br />
    The presupposition of a presuppositionally stronger alternative must not be satisfied.
  </li>
  <li><ex>Exh</ex><br />
    The presupposition of an excludable alternative must be satisfied.</li>
</ol>

PIP explains G&S's observation.

<p><ex>Exh</ex> explains examples with SIs.</p>

---

# Ambiguity

Strawson-UE examples are actually ambiguous.

<p><ex>Alice is <pr>aware</pr> that <si>most</si> of my students are Chinese.</ex></p>

This is usable in two types of contexts:
<div class="indented">
  <p>Situation 1: All my students are Chinese.</p>
  <p>Situation 2: Most but not all of my students are Chinese.</p>
</div>

<p><ex>Exh</ex> derives the reading most natural in Situation 1.</p>

<p>The other reading is derived by PIP without <ex>Exh</ex>.</p>

---

# Ambiguity (cont.)

<p><ex>Exh(Alice is <pr>aware</pr> that <si>most</si> of my students are Chinese)</ex></p>
  <table class="indented">
    <tr><td>presupposes:</td><td style="padding-left: 1em;">All my students are Chinese</td></tr>
    <tr><td>asserts:</td><td style="padding-left: 1em;">Alice is aware that most of them are Chinese but is not aware that all of them are.</td></tr>
    <tr><td>PI:</td><td style="padding-left: 1em;">---</td></tr>
  </table>

<p><ex>Alice is <pr>aware</pr> that <si>most</si> of my students are Chinese</ex></p>
<table class="indented">
  <tr><td>presupposes:</td><td style="padding-left: 1em;">most of my students are Chinese</td></tr>
  <tr><td>asserts:</td><td style="padding-left: 1em;">Alice is aware that most of them are Chinese.</td></tr>
  <tr><td>PI:</td><td style="padding-left: 1em;">¬CG(all of my students are Chinese)</td></tr>
</table>

<p style="border: 1px solid gray; padding-left: 1em;">A scalar item must result in scalar strengthening via either of the mechanisms whenever possible.</p>

---

# Stress and 'Only'

A stress on a scalar item correlates with the presence of <ex>Exh</ex>.
<p><ex>Alice is <pr>aware</pr> that <si>MOST</si> of my students are Chinese.</ex></p>

Cf. <ex>only</ex>:

<p><ex>Alice is only <pr>aware</pr> that <si>MOST</si> of my students smoke</ex></p>
<table class="indented">
  <tr><td style="text-align: right;">asserts:</td><td style="padding-left: 1em;">¬(A is aware that all of my students smoke)</td></tr>
  <tr><td>presupposes:</td><td  style="padding-left: 1em;"><si>all</si> of my students smoke</td></tr>
</table>

We analyze <ex>only</ex> as a presupposition hole wrt negated alternatives as well.

---

# Vacuity and Monotonicity

One nice consequence is that we account for the infelicity of the following example with an auxiliary assumption: vacuous uses of <ex>Exh</ex> are infelicitous.

<p>#<ex>Alice is (only) unaware that <si>SOME</si> of my students smoke</ex></p>

The stress here indicates the use of <ex>Exh</ex>, but it is vacuous, because it has no exludable alternative.

Similarly:

<p>#<ex>Alice is (only) aware that <si>ALL</si> of my students smoke</ex></p>

---

# Summary (again)

PIP explains G&S's observation about strengthened presuppositions.

<p><ex>Exh</ex> explains examples with SIs.</p>

---

# Loose Ends

---

# Presupposed Ignorance with SI

<p><ex>Alice speaks French (and not German).</ex><br />
  #<ex>Ben, <pr>too</pr>, speaks French <si>or</si> German.</ex></p>

<p><ex>Alice speaks French or German.</ex><br />
  <sup>ok</sup><ex>Ben, <pr>too</pr>, speaks French <si>or</si> German.</ex></p>

SI: Ben does not speak both French and German.

<b>Wrong analysis</b> (<ex>Exh</ex> > <ex><pr>too</pr></ex>): because <ex>Exh</ex> is a presupposition hole, it will inherit the presupposition of the negated conjunctive alternative and presuppose that Alice speaks both.

<p><ex>Alice speaks French and German.</ex><br />
  #<ex>Ben, <pr>too</pr>, speaks French <si>or</si> German.</ex></p>

---

# Presupposed Ignorance with SI (cont.)

If <ex><pr>too</pr></ex> takes scope below <ex>Exh</ex>, it'll work:

φ: <ex><pr>too</pr>(Exh(Ben speaks French <si>or</si> German))</ex>

<p>
Alternatives:<br />
<ex style="margin-left:1em;"><pr>too</pr>(Exh(Ben speaks French))</ex><br />
<ex style="margin-left:1em;"><pr>too</pr>(Exh(Ben speaks German))</ex><br />
<ex style="margin-left:1em;"><pr>too</pr>(Exh(Ben speaks French and German))</ex>
</p>

PIP generates the following inferences:

<p style="margin-left:1em;">
¬CG(Alice speaks French)<br />
¬CG(Alice speaks German)<br />
¬CG(Alice speaks French and German)
</p>

---

# Presupposed Ignorance with SI (cont.)

Remaining question: Why must <ex>Exh</ex> take scope below <ex><pr>too</pr></ex>?

It might be because of association. <ex>Exh</ex> > <ex><pr>too</pr></ex> requires a nested dependency.

*<ex><span style="border: 3px solid red; padding: 0.5ex;">Exh</span> ( <span style="border: 3px solid green; padding: 0.5ex;">JOHN</span> <pr>too</pr> speaks French <si>OR</si> German )</ex>

<p><ex><span style="border: 3px solid green; padding: 0.5ex;">JOHN</span> <pr>too</pr> <span style="border: 3px solid red; padding: 0.5ex;">Exh</span>  (speaks French <si>OR</si> German)</ex></p>

<div style="height:12pt;"></div>
--

<p>But other scalar items are fine with nested dependency.</p>

<p><ex>Alice read all of the books. Ben, <pr>too</pr>, read <si>most</si> of them.</ex></p>

---

# Existential Presuppositions

PIP predicts too strong an inference when applied to an existential presupposition.

<p class="indented"><ex><pr>Everyone</pr> who did <si>most</si> of the homework got an A.</ex></p>

PIP predicts: ¬(CG some did <si>all</si> of the homework)

But the sentence can be felicitously used in a context where it's known that some did all of the homework.

A similar problem arises with:
<p class="indented"><ex>Alice is <pr>unaware</pr> that there are students who did <si>some</si> of the homework.</ex></p>

---

# Existential Presuppositions (cont.)

It appears that existential quantifiers in alternatives are generally interpreted as pronouns (Geuts 2009, Sudo 2016).

<b>Proposal</b>: the presupposed ignorance inference is about the same group of people.

<p class="indented"><ex><pr>Everyone</pr> who did <si>most</si> of the homework got an A.</ex></p>
<div class="indented">
  <p>Presupposition: some people X did most (or all) of the homework</p>
  <p>Presupposed ignorance: ¬CG(X did all of the homework)</p>
</div>

See Sudo (2016) for a concrete implementation in dynamic semantics.

---

# Non-Monotonic Presuppositions

<p><ex><pr>Discover</pr></ex> has a non-monotonic presupposition.</p>

<p><ex>Mary <pr>discovered</pr> that John lost his job.</ex></p>

Presupposition: John lost his job and Mary didn't know it.

PIP predicts no inference, because the presupposition of the alternative is independent.

But this seems to be a bad prediction:

<p># <ex>Mary <pr>discovered</pr> that most languages have pronouns.</ex></p>

---

# Non-Monotonic Presuppositions

We could change PIP to be about presuppositionally <b>non-weaker</b> alternatives, rather than presuppositionally stronger alternatives.

But then we overgenerate for the following.

<p><ex>Mary <pr>discovered</pr> that all languages have pronouns.</ex></p>

Due to the alternative with <ex>some</ex>, we derive the inference:

¬CG(Mary did not know that some languages have pronouns)

But this seems to be too strong, because the sentence is usable even if Mary knew nothing about languages.

---

# Selected References

Chierchia, Fox & Spector (2012) Scalar implicature as a grammatical phenomenon. In <i>Semantics: International Handbook of Natural Language Meaning</i>, pp. 2297-2331.

Gajewski & Sharvit (2012) In defense of grammatical approach to local implicatures. <i>Natural Language Semantics</i>, 20(1): 31-57.

Spector & Sudo (2017) Presupposed ignorance and exhaustification: how scalar implicatures and presuppositions interact. <i>Linguistics and Philosophy</i>, 40(5): 473-517.

Sudo (2016) The existential problem of scalar implciatures and anaphora across alternatives. In <i>EISS 11</i>, pp. 225-224.