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# A New Semantics for Classifiers<br />(in Japanese)

<h2 style="margin-top: 2em;">
  Yasutada Sudo <img src="ucl.png" style="height:1em;margin-left:0em;vertical-align:text-top;" />
</h2>

23 May, 2019<br />
Bar Ilan University

---

# Classifier Languages

**(Obligatory) classifier languages**, e.g. Japanese, Korean, Mandarin, Thai, Vietnamese, etc.

1. Nouns resist direct modification by numerals.
<div class="wrapper">
  <div class="gword">
    <p class="target">一*(<strong>輪</strong>)の</p>
    <p class="target">ichi-*(<strong>rin</strong>)-no</p>
    <p class="gloss">one-*(CL)-GEN</p>
  </div>
  <div class="gword">
    <p class="target">花</p>
    <p class="target">hana</p>
    <p class="gloss">flower</p>
  </div>
  <div class="gword" style="width:4em;">
  </div>
  <div class="gword">
    <p class="target">五輪の</p>
    <p class="target">go-rin-no</p>
    <p class="gloss">five-*(CL)-GEN</p>
  </div>
  <div class="gword">
    <p class="target"><strong>花</strong></p>
    <p class="target"><strong>hana</strong></p>
    <p class="gloss">flower</p>
  </div>
</div>
2. No obligatory number marking on nouns.
3. Bare nouns can receive kind readings.

---

# Why Classifiers?

<p style="margin-bottom: 3em;">
Why are classifiers required in <strong>(obligatory) classifier languages</strong> like Japanese?
</p>

- <b>Classical answer</b>: because nouns in these languages are all mass and uncountable

- <b>My answer</b>: because numerals in these languages are exclusively singular terms and cannot function as nominal modifiers

---

# Outline

<ol>
 <li style="margin: 30pt 0;">Countability of nouns and a semantic view of classifiers</li>
 <li style="margin: 30pt 0;">The Number Asymmetry Hypothesis and a syntactic view of classifiers</li>
 <li style="margin: 30pt 0;">A new look at numerals and classifiers</li>
 <li style="margin: 30pt 0;">Appendix: Details of the analysis</li>
</ol>

---

# 1. The Countability Hypothesis

---

# Mass/Count: Morphosyntax

English nouns are either **mass** or **count**.

Morpho-syntactic criteria:
1. Direct modification by numerals → Count
2. Pluralization → Count
3. Modifier selection:
  - <ex>much, little</ex> → Mass
  - <ex>many, few</ex> → Count
4. Mass nouns can appear bare, count nouns cannot.

---

# Mass/Count: Semantics

<table style="width:80%;margin:auto;">
  <tr>
    <th style="width:50%;">Mass</th>
    <th>Count</th>
  </tr>
  <tr>
    <td>blood</td>
    <td>book</td>
  </tr>
  <tr>
    <td>gold</td>
    <td>city</td>
  </tr>
  <tr>
    <td>oil</td>
    <td>car</td>
  </tr>
  <tr>
    <td>sweat</td>
    <td>umbrella</td>
  </tr>
</table>

Mass/count has semantic effects <span class="small">(Quine 1960, Link 1983, Gordon 1985, Wisniewski, Imai & Casey 1996)</span>. Roughly:
<div class="shaded">
  Count nouns describe concrete and countable objects;<br />
  Mass nouns describe uncountable stuff/substances.
</div>

---
# Flexible Nouns

However, the physical properties of the object(s) being described don't uniquely determine mass/count.

**Flexible nouns** can be used as either mass or count <span class="small">(Gillon 1992, 1999, Barner & Snedeker 2005, Bale & Barner 2009, Pelletier 2014)</span>:
e.g. <ex>stone</ex>, <ex>paper</ex>, <ex>rope</ex></i>

The same object(s) can be described by either.
--
<img src="paper.gif" style="width:37%;margin-right: 1em;margin-top:1ex;display:block;float:right;">
<p class="indented">
<ex>There is a lot of paper.</ex><br />
<ex>There is a lot of papers.</ex>
</p>

---

# The Countability Hypothesis

A semantic/pragmatic theory of mass/count <span class="small">(Borer 2005, Chierchia 1998a,b,2010, Krifka 1995,2008, Landman 2011, Link 1983, Scontras 2013,2014)</span>:
<div class="shaded">
  <ul>
    <li>Count nouns have <strong>countable denotations</strong>.</li>
    <li>Mass nouns have <strong>uncountable denotations</strong>.</li>
  </ul>
</div>

Numerals, pluralization, and <ex>many</ex>/<ex>few</ex> require countable nouns.

Flexible nouns like <ex>paper</ex> can sometimes have countable denotations, but not always.

Mass/count may have semantic effects.

---
# Barner & Snedeker's Comparative Task

---

# Classifier Languages

The Countability Hypothesis offers an appealing account of classifiers in **(obligatory) classifier languages**.

<b>Classifier languages</b>:

---
# Classifiers under the Countability Hyp.

<div class="shaded">
<b>All nouns in classifier languages have uncountable denotations</b>
<span class="small">(Bunt 1985, Krifka 1995,2008 Chierchia 1998a,b, Borer 2005, Scontras 2013,2014).</span>
</div>

Semantic explanation for the obligatory use of classifiers: Classifiers turn uncountable denotations into countable denotations.

Their semantic functions are akin to measure phrases like <ex>glasses</ex> and <ex>pieces</ex> in English:
<div class="indented">
  <p><ex>three *(<strong>glasses</strong> of) milk</ex><br />
  <ex>five *(<strong>pieces</strong> of) information</ex></p>
</div>

---

# Interim Summary

**The Countability Hypothesis**
- Count nouns have countable denotations.
- Mass nouns have uncountable denotations.

<b>Semantic explanation for mass/count</b>: Numerals and modifiers like <ex>many</ex> require countable denotations, and are incompatible with mass nouns.

<b>Semantic view of classifiers</b>: All nouns in obligatory classifier languages have uncountable denotations. Classifiers turn uncountable denotations into countable denotations.

---

# 2. The Number Asymmetry Hypothesis

---

# Problems of the Countability Hypothesis

Two problems of the Countability Hypothesis
<ol>
  <li style="margin: 36pt 0;"><strong>Object mass nouns</strong> are mass nouns that have countable denotations.</li>
  <li style="margin: 36pt 0;">Certain modifiers in Japanese require no classifiers but still give rise to count-based readings.</li>
</ol>

---

# Challenge 1: Object Mass Nouns

**Object mass nouns** describe countable entities but are mass <span class="small"> (Gillon 1992, Chierchia 1998a, Barner & Snedeker 2005)</span>.

<table style="width:80%;margin:auto;">
  <tr>
    <th style="width:50%;">Object Mass</th>
    <th>Count</th>
  </tr>
  <tr>
    <td>furniture</td>
    <td>chair, desk</td>
  </tr>
  <tr>
    <td>silverware</td>
    <td>fork, knife</td>
  </tr>
  <tr>
    <td>mail</td>
    <td>letter</td>
  </tr>
  <tr>
    <td>luggage</td>
    <td>suitcase</td>
  </tr>
  <tr>
    <td>foliage</td>
    <td>leaf</td>
  </tr>
  <tr>
    <td>toast</td>
    <td>sandwich</td>
  </tr>
  <tr>
    <td>kin</td>
    <td>relative</td>
  </tr>
  <tr>
    <td>rice</td>
    <td>lentil</td>
  </tr>
</table>

---

# Barner & Snedeker on Object Mass Nouns

Barner & Snedeker's (2005) comparative task show that object mass nouns have countable denotations.

---

# Challenge 2: Counting Modifiers in Japanese

<img src="i&b-results.jpeg" style="width:55%;display:block;float:right;">
Certain modifiers require no classifiers, but receive count-based readings.

Inagaki & Barner's (2009) comparative test:

<div class="wrapper">
  <div class="gword">
    <p class="target-small">どちらの</p>
    <p class="target-small">dochira-no</p>
    <p class="gloss-small">which-GEN</p>
  </div>
  <div class="gword">
    <p class="target-small">人が</p>
    <p class="target-small">hito-ga</p>
    <p class="gloss-small">person-NOM</p>
  </div>
</div>
<div class="wrapper">
  <div class="gword">
    <p class="target-small">より多くの</p>
    <p class="target-small">yori-ooku-no</p>
    <p class="gloss-small">more-many-GEN</p>
  </div>
  <div class="gword">
    <p class="target-small"><span style="color:rgb(249, 38, 114);">靴/辛子/家具</span>を</p>
    <p class="target-small"><span style="color:rgb(249, 38, 114);">kutsu/karashi/kagu</span>-o</p>
    <p class="gloss-small">shoes/mustard/furniture-ACC</p>
  </div>
  <div class="gword">
    <p class="target-small">持っている?</p>
    <p class="target-small">motteiru?</p>
    <p class="gloss-small">have</p>
  </div>
</div>
<div class="trans">'Which person has more shoes/mustard/furniture?'</div>

---

# Counting Modifiers in Japanese (cont.)

Proportional expressions (e.g. <ex>hotondo ほとんど</ex> 'most') show the same point.

<div style="margin-left: 2em;">
<div class="wrapper">
  <div class="gword">
    <p class="target-small">ほとんどの</p>
    <p class="target-small">hotondo-no</p>
    <p class="gloss-small">most-GEN</p>
  </div>
  <div class="gword">
    <p class="target-small">カバンが</p>
    <p class="target-small">kaban-ga</p>
    <p class="gloss-small">bag-NOM</p>
  </div>
  <div class="gword">
    <p class="target-small">赤い</p>
    <p class="target-small">akai</p>
    <p class="gloss-small">red</p>
  </div>
</div>
<div class="trans">
  'Most bags are read'
</div>
</div>

<img src="bags.png" style="width:55%;display:block;float:right;margin-top: -1em;">
The most natural interpretation of this sentence is count-based.

---

# More Data: Context and Object Mass

Some argue that object mass nouns and count nouns should have different semantic representations <span class="small">(Chierchia 1998a,b; contra Bale & Barner 2009)</span>.

In particular, unlike count nouns, object mass nouns don't seem to force count-based readings in comparative tasks <span class="small">(Rothstein 2017)</span>.

---

# Preliminary Data: Design

<span class="small">(joint work with Nathan Klinedinst; thanks to Xiaomeng Zhang for help with images)</span>

<div style="width: 95%; margin: 0 auto; border: 2px groove black; padding: 0em 1em; padding-bottom: 1em;">
  <p>Context: Two passengers are checking in at the airport.</p>
  <div style="width: 85%; margin: 0 auto;">
  <p><b>Which passenger has more luggage?</b></p>

</div>

---

# Preliminary Data: Design

<span class="small">(joint work with Nathan Klinedinst; thanks to Xiaomeng Zhang for help with images)</span>

<div style="width: 95%; margin: 0 auto; border: 2px groove black; padding: 0em 1em; padding-bottom: 1em;">
  <p>Context: The design company provided two plans for the same room.</p>
  <div style="width: 85%; margin: 0 auto;">
  <p><b>Which plan includes more furniture?</b></p>

</div>

---

# Preliminary Data: Results

---

# Future Steps

- Comparison with count nouns (e.g. <ex>suitcases</ex>, <ex>pieces of luggage</ex>)
- Manipulation of contexts (what dimensions matter)
- Same tasks in classifier languages

---

# Summary So Far

Observations incompatible with the Countability Hypothesis.

- Object mass nouns (can) have countable denotations, although grammatically mass.

- Japanese seems to have nouns that (can) have countable denotations.

---

# The Number Asymmetry Hypothesis

<div class="shaded">
  <strong>The Number Asymmetry Hypothesis</strong> <span class="small">(Bunt 1985, Barner & Snedeker 2005,2006, Barner, Wagner & Snedeker 2008, Bale & Barner 2009, Gillon 1992,1999, Rothstein 2009, Chierchia 2010)</span>:
  <ul style="margin-top:0pt;margin-bottom:20pt;">
    <li>Count nouns always have countable denotations.</li>
    <li>Mass nouns might or might not have countable denotations.</li>
  </ul>
</div>

- Object mass nouns (e.g. <ex>silverware</ex>) have countable denotations.
- Pure mass nouns (e.g. <ex>toothpaste</ex>) have uncountable denotations.

<b>Q</b>: Then why can't object mass nouns be directly modified by numerals?

---

# Japanese under the Number Asymm. Hyp.

> <b>All Japanese nouns are grammatically mass ([-c]) nouns</b> <span class="small">(Bale & Barner 2009, Inagaki & Barner 2009, Barner, Inagaki & Li 2009)</span>.

- Some nouns are object mass nouns (e.g. <ex>kaban かばん</ex> 'bag'), and have countable denotations.
- Others are substance mass nouns (e.g. <ex>karashi 辛子</ex> 'mustard') and have uncountable denotations.

<b>Q</b>: Then why can't object mass nouns be directly modified by numerals?

---

# The Role of Syntax: English

The Number Asymmetry Hypothesis resorts to syntax to explain selectional restrictions with mass/count <span class="small">(Bale & Barner 2009)</span>.

- Numerals syntactically select for [+c] nouns.
- <ex>Much</ex> syntactically selects for [–c] NPs.
- <ex>More</ex> has no syntactic selectional restrictions.

Measure phrases like <ex>piece</ex> make [–c] nouns syntactically compatible with numerals.

<b>Open question</b>: Why are there no numerals that are compatible with [–c] NPs?

---

# The Role of Syntax: Japanese

Correpondingly, the Number Asymmetry Hypothesis offers a syntactic view of classifiers.

<b>Stipulation</b>: Numerals are syntactically incompatible with [–c] NPs in Japanese (as in English).

Classifiers can be seen as something that makes a noun **syntactically** compatible with numerals (cf. measure phrases like <ex>piece</ex>).

<b>Remaining Question</b>: Why are there no numerals that are compatible with [–c] nouns with countable denotations, e.g. <ex>kaban かばん</ex> 'bag'?

---

# Counting Modifiers w/o Classifiers

There are counting modifiers in Japanese that require countable denotations.
<div class="indented">
<div class="wrapper">
  <div class="gword">
    <p class="target">数百-の</p>
    <p class="target">suuhyaku-no</p>
    <p class="gloss">hundreds-GEN</p>
  </div>
  <div class="gword">
    <p class="target">かばん/*汗</p>
    <p class="target">kaban/*ase</p>
    <p class="gloss">bag/*sweat</p>
  </div>
</div>
</div>

<b>NB</b>: No classifier here!

<img src="sweat.gif" style="width:20%;margin-right: 1em;margin-top:1ex;display:block;float:right;">
Then why do numerals require classifiers?

---

# Interim Summary

<div class="shaded">
<strong>The Number Asymmetry Hypothesis</strong>:
<ul style="margin-top:0;margin-bottom:1em;">
 <li>Count nouns always have countable denotations.</li>
 <li>Mass nouns might (object) or might not (substance).</li>
</ul>
</div>

<b>Syntactic stipulation</b>: Numerals require [+c] NPs.

<b>Syntactic view of classifiers</b>: In obligatory classifier languages, all nouns are [–c]. Classifiers make them **syntactically** compatible with numerals.

<b>Remaining Question</b>: Why doesn't Japanese have numerals that don't require classifiers (cf. <ex>suuhyaku 数百</ex> 'hundreds')?

---

---

# Proposal: A New Semantic Explanation

<b>Idea</b>: Classifiers are required in Japanese, not because of nouns, but because of the semantic properties of numerals <span class="small">(Krifka 1995, Bale & Coon 2014)</span>.

<div class="shaded">
  <ul>
    <li>Numerals in Japanese are singular terms/names for number concepts, and cannot function on their own as modifiers or predicates.</li>
    <li>Classifiers turn numerals into modifiers/predicates.</li>
  </ul>
</div>

Conversely, those counting modifiers that are born as modifiers/predicates do not require classifiers (e.g. <ex>suuhyaku 数百</ex> 'hundreds').

---

# Multiple Functions of Numerals in English

Numerals in English have multiple semantic functions <span class="small">(Rothstein 2013, 2017)</span>.

- As <b>nominal modifiers</b>:<br />
 <ex>I read <strong>four</strong> books last month.</ex>
- As <b>predicates</b>:<br />
 <ex>The guests are <strong>four</strong>.</ex>
- As <b>names of number concepts</b>:<br />
 <ex>The number of examiners was <strong>four</strong>.</ex>

<div class="small" style="margin-top: 5em;">(Debates about the last example: Hofweber 2005, Jackson & Penka 2017, Moltmann 2013,2017, Solt 2015.)</div>

---

# Bare Numerals in Japanese

Bare numerals in Japanese can be used as names of number concepts.

<div class="wrapper" style="margin-top: 3ex;">
  <div class="gword">
    <p class="target">参加者の</p>
    <p class="target">sankasha-no</p>
    <p class="gloss">participant-GEN</p>
  </div>
  <div class="gword">
    <p class="target">数は</p>
    <p class="target">kazu-wa</p>
    <p class="gloss">number-TOP</p>
  </div>
  <div class="gword">
    <p class="target"><strong>２０</strong>だ</p>
    <p class="target"><strong>nijuu</strong>-da</p>
    <p class="gloss">20-COP</p>
  </div>
</div>
<div class="trans">'The number of participants is 20.'</div>

---

# Bare Numerals in Japanese (cont.)

Bare numerals cannot be used as modifiers or predicates; in these cases, classifiers are necessary.

- <b style="magin-bottom:0;">Modificational</b>
  <div class="wrapper" style="margin-top:0;padding-top:0;">
    <div class="gword">
      <p class="target-small"><span style="color:black;">*</span> <strong>４</strong>の</p>
      <p class="target-small"><span style="color:black;">*</span> <strong>yon</strong>-no</p>
      <p class="gloss-small"> four-GEN</p>
    </div>
    <div class="gword">
      <p class="target-small">花</p>
      <p class="target-small">hana</p>
      <p class="gloss-small">flower</p>
    </div>
    <div class="gword">
      <p class="target-small" style="width:5em;"></p>
      <p class="target-small"></p>
      <p class="gloss-small"></p>
    </div>
    <div class="gword">
      <p class="target-small"><strong>４輪</strong>の</p>
      <p class="target-small"><strong>yon-rin</strong>-no</p>
      <p class="gloss-small">four-CL-GEN</p>
    </div>
    <div class="gword">
      <p class="target-small">花</p>
      <p class="target-small">hana</p>
      <p class="gloss-small">flower</p>
    </div>
  </div>
- <b>Predicational</b>
<div class="wrapper">
  <div class="gword">
    <p class="target-small"><span style="color:black;">*</span> 客は</p>
    <p class="target-small"><span style="color:black;">*</span> kyaku-wa</p>
    <p class="gloss-small"> guest-TOP</p>
  </div>
  <div class="gword">
    <p class="target-small"><strong>４</strong>だ</p>
    <p class="target-small"><strong>yon</strong>-da</p>
    <p class="gloss-small">four-COP</p>
  </div>
  <div class="gword">
    <p class="target-small" style="width:3em;"></p>
    <p class="target-small"></p>
    <p class="gloss-small"></p>
  </div>
  <div class="gword">
    <p class="target-small">客は</p>
    <p class="target-small">kyaku-wa</p>
    <p class="gloss-small">guest-TOP</p>
  </div>
  <div class="gword">
    <p class="target-small"><strong>４人</strong>だ</p>
    <p class="target-small"><strong>yo-nin</strong>-da</p>
    <p class="gloss-small">four-CL-COP</p>
  </div>
</div>

---

# Semantics of Numerals and Classifiers

<b>Idea</b>: Numerals in Japanese exclusively function as names for number concepts, which are abstract entities:
<div class="indented">
⟦<ex>yon</ex>⟧ = <b>4</b>
</div>

Classifiers turn such abstract entities into predicates:
<div class="indented">
⟦<ex>yon-<strong>rin</strong></ex>⟧ = λx: <u>x consists of flowers</u>. x consists of 4 disjoint flowers
</div>

NUM+CL is similar to intersective adjectives (e.g. <ex>pregnant</ex>) in meaning, which can also be used as predicates or modifiers.

---

# Variety of Classifiers

The selectional restrictions of classifiers are semantic in nature <span class="small">(cf. McCready 2009)</span>.

- ⟦<ex>yon-<strong>rin</strong></ex>⟧ = λx: <u>x consists of <b>flowers</b></u>. x consists of 4 disjoint <b>flowers</b>
- ⟦<ex>yon-<strong>nin</strong></ex>⟧ = λx: <u>x consists of <b>humans</b></u>. x consists of 4 disjoint <b>humans</b>
- ⟦<ex>yon-<strong>tsui</strong></ex>⟧ = λx. x consists of 4 disjoint <b>pairs</b>

<div class="indented" style="margin-top: 4ex;">
<div class="wrapper">
<div class="gword">
  <p class="target-small">４<strong>人</strong>の</p>
  <p class="target-small">yo-<strong>nin</strong>-no</p>
  <p class="gloss-small">four-CL-GEN</p>
</div>
<div class="gword">
  <p class="target-small">シェフ</p>
  <p class="target-small">shefu</p>
  <p class="gloss-small">chef</p>
</div>
<div class="gword">
  <p class="target-small">/</p>
  <p class="target-small">/</p>
  <p class="gloss-small"></p>
</div>
<div class="gword">
  <p class="target-small">学生</p>
  <p class="target-small">gakusei</p>
  <p class="gloss-small">student</p>
</div>
<div class="gword">
  <p class="target-small">/</p>
  <p class="target-small">/</p>
  <p class="gloss-small"></p>
</div>
<div class="gword">
  <p class="target-small"><span style="color:black;">#</span>花</p>
  <p class="target-small"><span style="color:black;">#</span>hana</p>
  <p class="gloss-small"><span style="color:white;font-weight:bold;">#</span>flower</p>
</div>
</div>
</div>

---

# Variety of Classifiers (cont.)

- ⟦<ex>yon-<strong>mai</strong></ex>⟧ = λx: <u>x consists of <b>flat objects</b></u>. x consists of 4 disjoint <b>flat objects</b>
- ⟦<ex>yon-<strong>ko</strong></ex>⟧ = λx: <u>x consists of <b>small/round objects</b></u>. x consists of 4 disjoint <b>small/round objects</b>
- ⟦<ex>yon-<strong>hon</strong></ex>⟧ λx: <u>x consists of <b>cylinder-shaped objects</b></u>. x consists of 4 disjoint <b>cylinder-shaped objects</b>

<div class="wrapper"  style="margin-top: 6ex;">
<div class="gword">
  <p class="target-small">４<strong>枚/個/本</strong>の</p>
  <p class="target-small">yo-<strong>mai/ko/hon</strong>-no</p>
  <p class="gloss-small">four-CL-GEN</p>
</div>
<div class="gword">
  <p class="target-small">パン</p>
  <p class="target-small">pan</p>
  <p class="gloss-small">bread</p>
</div>

---

# Counting Modifiers without Classifiers

Modifiers like <ex>hotondo ほとんど</ex> 'most' and <ex>suuhyaku 数百</ex> 'hundreds' are born as modifiers, so they don't need classifiers.

According to this view, whether a classifier is necessary for a given counting modifier is determined by the semantics of the modifier (not by the noun).

Some supporting evidence:
- Bale & Coon's (2014) observations
- Exceptional numerals in Japanese
- Exceptional numerals in Korean

---

# Partly Classifier Languages: Bale & Coon

Bale & Coon's (2014) observations

<ul>
  <li style="margin-bottom: 24pt;">In <b>Mi'gmaq</b> (Eastern Algonquian), 1-5 do not appear with classifiers, 6- must.</li>
  <li>In <b>Chol</b> (Mayan), native numerlas (e.g. <ex>ux</ex> 'three', <ex>waxäk</ex> 'eight') require classifiers, while Spanish-based numerals (e.g. <ex>ses</ex> 'six', <ex>nuebe</ex> 'nine') are incompatible with classifiers.</li>
</ul>

(Though it is not entirely clear if these languages have the same type of classifiers as Japanese)

---

# Partly Classifier Languages: Japanese

In Japanese too, certain numerals do not require classifiers:

<div class="wrapper">
<div class="gword">
  <p class="target-small">地球上には</p>
  <p class="target-small">chikyuu-joo-ni-wa</p>
  <p class="gloss-small">earth-surface-LOC-TOP</p>
</div>
<div class="gword">
  <p class="target-small"><strong>約1500</strong>の</p>
  <p class="target-small"><strong>yaku-sengohyaku</strong>-no</p>
  <p class="gloss-small">about-1500-GEN</p>
</div>
<div class="gword">
  <p class="target-small">火山が</p>
  <p class="target-small">kazan-ga</p>
  <p class="gloss-small">volcano-NOM</p>
</div>
<div class="gword">
  <p class="target-small">ある</p>
  <p class="target-small">aru</p>
  <p class="gloss-small">exist</p>
</div>
</div>
<div class="trans">'There are about 1500 volcanoes on Earth'</div>

<b>Open question</b>: For which numerals are classifiers optional? (Numbers expressed cannot be small)

---

# Partly Classifier Languages: Korean

In Korean, native numerals (1-9) often do not require classifiers (especially low numerals with animate nouns).

Also, <ex>hana 하나</ex> 'one' often appears without a classifier post-nominally.

<div class="wrapper">
<div class="gword">
  <p class="target-small">두(<strong>명</strong>의)</p>
  <p class="target-small">tu(-<strong>myeong</strong>-ui)</p>
  <p class="gloss-small">two(-<strong>CL</strong>-GEN)</p>
</div>
<div class="gword">
  <p class="target-small">남자</p>
  <p class="target-small">namja</p>
  <p class="gloss-small">man</p>
</div>
<div class="gword" style="margin-left: 15ex;">
  <p class="target-small">의자</p>
  <p class="target-small">uija</p>
  <p class="gloss-small">chair</p>
</div>
<div class="gword">
  <p class="target-small">하나</p>
  <p class="target-small">hana</p>
  <p class="gloss-small">one</p>
</div>
</div>

<div class="small" style="display: block; float: right;">(based on Linda Yoon Jae Shin's 2017 UCL BA thesis)</div>

<p style="margin-top: 3em;"><b>Open question</b>: These might be compounds?</p>

---

# Further Directions: Slavic Numerals

Slavic languages have several types of numerals <span class="small">(Kim 2009, Dočekal, Grimm & Ziková 2014)</span>. E.g. Czech:
- <b>Normal numerals</b> (e.g. <ex>dv-a/ě</ex>).
- <b>Aggregate numerals</b> (e.g. <ex>dv-oje</ex>): used with pluralia tantum, collective nouns (e.g. <i>sirky</i> 'matches').
- <b>Taxonomic numerals</b> (e.g. <ex>dv-ojí</ex>) are used to count sub-kinds.
- <b>Group numerals</b> (e.g. <ex>dv-ojice</ex>) are used to count members of a group. E.g. <i>dv-ojice mužů</i> 'a group of two men'.

<b>Idea</b>: These suffixes are similar to classifiers in Japanese. (Wągiel 2018)

---

# Summary

<strong>The Number Asymmetry Hypothesis</strong>:
<ul style="margin-top:0;margin-bottom:1em;">
 <li>Count nouns always have countable denotations.</li>
 <li>Mass nouns might (object) or might not (substance).</li>
</ul>

Nouns in Japanese are grammatically mass nouns.

<div class="shaded">
<img src="new.gif" style="width:4em;margin-right: 2em;margin-top:1ex;display:block;float:right;">
Classifiers are not for nouns.<br />

In classifier languages like Japanese:
<ul style="margin-top: 0px;">
  <li>Numerals are always referential;</li>
  <li>Classifiers turn such referential expressions into modifiers/predicates.</li>
</ul>
</div>

---

# Appendix: Details

---

# Numerals and Classifiers

Numerals are names for (abstract) entities (of type n) <span class="small">(Rothstein 2013, 2017, Kennedy 2015)</span>.

Classifiers take abstract entities and turn them into predicates

<p style="margin-top: -1ex;margin-bottom: .5ex;">
⟦<ex>-rin</ex>⟧<sup>w,c</sup> = λn.λx: <u>x consists of flowers in w</u>. x measures n in w wrt a salient way of counting (individual) flowers in c
</p>

<p style="margin-top: 0ex;margin-bottom: -.5ex;">
⟦<ex>-tsui</ex>⟧<sup>w,c</sup> = λn.λx. x consists of n pairs in w wrt a salient way of pairing things in c
</p>

NB: classifiers refer to contextually salient ways of counting <span class="small">(cf. Zucchi & White 2011, Rothstein 2010, 2017)</span>.

---

# Modificational and Predicative Uses

NUM+CL will be of type (e,t).

⟦<ex>san-nin</ex>⟧<sup>w,c</sup> = λx: <u>x consists of people in w</u>. x measures 3 in w wrt a salient way of counting (individual) people in c

It can modify an NP intersectively.

Being of type (e,t) it can also function as predicates:

<div class="wrapper">
<div class="gword">
  <p class="target-small">私の</p>
  <p class="target-small">watashi-no</p>
  <p class="gloss-small">me-GEN</p>
</div>
<div class="gword">
  <p class="target-small">学生は</p>
  <p class="target-small">gakusei-wa</p>
  <p class="gloss-small">student-TOP</p>
</div>
<div class="gword">
  <p class="target-small">三人だ</p>
  <p class="target-small">san-nin-da</p>
  <p class="gloss-small">three-CL-COP</p>
</div>
</div>
<div class="trans">(lit.) 'My students are three.'</div>
<div class="trans">'The number of students I have is three.'</div>

---

# Type-Shifting Back

NUM+CL in Japanese have a referential use:

<div class="indented" style="margin-top: -1ex; margin-bottom: -1ex;">
<div class="wrapper">
<div class="gword">
  <p class="target-small">学生の</p>
  <p class="target-small">gakusei-no</p>
  <p class="gloss-small">student-GEN</p>
</div>
<div class="gword">
  <p class="target-small">数は</p>
  <p class="target-small">kazu-wa</p>
  <p class="gloss-small">number-TOP</p>
</div>
<div class="gword">
  <p class="target-small">三(人)だ</p>
  <p class="target-small">san(-nin-)da</p>
  <p class="gloss-small">three(-CL-)COP</p>
</div>
</div>
<div class="trans">'The number of students is three.'</div>
</div>

<p class="shaded">
<b>Idea</b>: the property denoted by NUM+CL has a type-n counterpart  <span class="small">(cf. Chierchia 1984, Chierchia & Turner 1987, Scontras 2014, 2017)</span>
</p>

<p style="margin-top: -1ex;">
    ⟦<ex>san-nin</ex>⟧<sup>w,c</sup> = λx: <u>x consists of people in w</u>. x measures 3 in w wrt a salient way of counting (individual) people in c
  </p>

<p style="margin-top: -1ex;">
  ⦅<ex>san-nin</ex>⦆<sup>c</sup> ⇝ three-people-ness (in c)
  </p>

---

# Optional Classifiers

Expressions like <ex>suuhyaku 数百</ex> are born as modifiers:

<div class="indented">
  ⟦<ex>suuhyaku</ex>⟧<sup>w,c</sup> = λx. x measures hundreds in w wrt some way of counting
</div>

(This predicate is vague wrt how to count)

This property can also type-shift to type n, and can then combine with a classifer.

<div class="wrapper">
  <div class="gword">
    <p class="target">数百(<strong>冊</strong>)の</p>
    <p class="target">suuhyaku-(<strong>satsu</strong>)-no</p>
    <p class="gloss">hundreds-CL-GEN</p>
  </div>
  <div class="gword">
    <p class="target">本</p>
    <p class="target">hon</p>
    <p class="gloss">book</p>
  </div>
</div>

---

# Non-Classifier Languages

No classifiers in English. Modificational use is acheved by type-shifting (which is blocked in classifier languages):

<div class="indented">
⟦<ex>four</ex>⟧<sup>w,c</sup> ⇝ λP.λx. x measures 4 wrt a contextually salient way of counting P-entities in c
</div>

Note that it's necessary to refer to the intension of the NP (P), because counting is relative to a property (and context).

<img src="google.png" style="width:35%;display:block;float:right;margin-top: 1em;">
E.g. If you are counting letters, there are six. If you are counting logos, there's only one.

---

# Predicative Numerals in English

Predicative uses of numerals in English are very limited.

<div class="indented">
 # <ex>My laptops are three.</ex><br />
 (intended: I have three laptops.)
</div>

If type-shifting is only from type n to type ((s,et),et), the predicative use will not be allowed.

Acceptable cases of predicative numerals (incl. age-interpretations) are all conventionalized?

<div class="indented">
 <ex>We will soon be three.</ex><br />

<ex>My niece is five.</ex> (age interpretation)

</div>

---

# Summary

Numerals in all languages have referential uses (type n).

Numerals in classifier languages cannot be type-shifted but classifiers convert them to predicates of type (e,t).
<div class="indented" style="margin-top: -1ex;margin-bottom: -1ex;">
⟦<ex>yon-rin</ex>⟧<sup>w,c</sup> = λx: <u>x consists of flowers in w</u>. x measures 4 in w wrt a salient way of counting (individual) flowers in c
</div>

NUM+CL have type-n counterparts <span class="small">(similar to the Scontras degrees)</span>.

Numerals in non-classifier languages can be type-shifted to modifiers of type ((s,et),et)?

---

---

## Selected References
<ul >
<li style="font-size: 16pt;">Bale & Barner (2009) The interpretation of functional heads. <i>J. of Semantics</i>, 26.</li>
<li style="font-size: 16pt;">Bale & Coon (2014) Classifiers are for numerals, not nouns. <i>LI</i>, 45.</li>
<li style="font-size: 16pt;">Barner & Sndeker (2005) Quantity judgments and individuation. <i>Cognition</i>, 97.</li>
<li style="font-size: 16pt;">Chierchia (1998b) Referent to kinds across languages. <i>Nat. Lang. Sem</i>, 6.</li>
<li style="font-size: 16pt;">Chierchia & Turner (1987) Semantics and property theory. <i>Ling & Phil</i>, 11.</li>
<li style="font-size: 16pt;">Inagaki & Barner (2009) Countability in absence of count syntax. In <i>Studies in Language Sciences 8</i>.</li>
<li style="font-size: 16pt;">Rothstein (2010) Counting and the mass/count distinction <i>J. of Semantics</i>.</li>
<li style="font-size: 16pt;">Rothstein (2013) A Fregean semantics for number words. In <i>Ams. Colloq. 19</i>.</li>
<li style="font-size: 16pt;">Scontras (2017) A new kind of degree. <i>Ling & Phil</i>, 40.</li>
</ul>