RALFe

<h1 style="margin-bottom: 2em;"><img src="m.gif" style="margin: 0; padding: 0; width:3em; margin-right: -.75em; margin-bottom: -.75em; vertical-align: bottom;">inimal Sufficiency with Covert Even</h1>

## Daniele Panizza & Yasu Sudo

RALFe @Paris 8 
7 December 2018

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# Exclusive Particles and Minimal Sufficiency

Exclusive particles (<ex>just</ex>, <ex>only</ex>, etc.) give rise to exclusivity inferences.

<div class="indented">
 
 (1) <ex>Just oneF cat is in the room.</ex> 
 ⇒ ¬(n cats are in the room), for each number n > 1
 
 
 (2) <ex>Only PatrickF is in the room.</ex> 
 ⇒ ¬(x is in the room), for each relevant x
 
</div>

Minimal sufficiency reading (Grosz 2012, Coppock & Beaver 2014)

<div class="indented">

 (3) <ex>Just oneF cat makes me happy.</ex> 
 ⇒ any number of cats make me happy

</div>

---

# Note: Just vs. Only

Coppock & Beaver (2014:375) observe variation among exclusive particles.

E.g., the minimal sufficiency reading is often harder with <ex>only</ex>.

(3) <ex>Just oneF cat makes me happy.</ex> 
 ⇒ any number of cats make me happy

(4) ??<ex>Only oneF cat makes me happy.</ex>

We'll focus on <ex>just</ex>.

<!--

 <table>
 <tr>
 	<td>(4)</td><td>a. <ex>Just/Merely/Simply the thought of food makes me hungry.</ex></td>
 </tr>
 <tr>
 	<td></td><td>b. ?<ex>Only the thought of food makes me hungry.</ex></td>
 </tr>
 <tr>
 	<td></td><td>c. #<ex>Exclusively/Purely/Solely the thought of food makes me hungry.</ex></td>
 </tr>
 <tr>
 	<td></td><td>d. <ex>The mere thought of food makes me hungry.</ex></td>
 </tr>
 <tr>
 	<td></td><td>e. <ex>The sole/only thought of food makes me hungry.</ex></td>
 </tr>
</table>

A complication (Coppock & Beaver 2014:401):

(5) <ex> Only a small percentage would be enough for a big scale scam to take off.

-->

---

# Previous Analyses

Previous studies analyze the minimal sufficiency reading as a rank-order reading:

(5) <ex>I'm just a graduate student.</ex> 
⇒ Being a graduate student is not remarkable

- Grosz (2012) postulates a version of <ex>just</ex> that presupposes that the prejacent is low on the scale (and is otherwise truth-conditionally vacuous).

- Coppock & Beaver (2014) attempt to derive it without a special lexical entry.

---

# Previous Analyses (cont.)

(6) [<ex>Just oneF cat</ex>] <ex>makes me happy.</ex>

According to these analysis, <ex>just</ex> takes scope within the subject and yields the inference that <ex>one cat</ex> is relatively insignificant.

Problem: Why does't (7) have a minimal sufficiency reading?

(7) [<ex>Just oneF cat</ex>] <ex>is in the room.</ex>

Why can't this mean: something as insignificant as one cat is in the room (w/o the exclusivity inference)?

---

# More Data

Similarly:

(8) [<ex>Just a letterF from her</ex>] <ex>can cheer him up.</ex>
 ⇒ a phone call, video message, etc. from her can also cheer him up

- According to the previous analyses, <ex>just</ex> triggers the inference: a letter from her is relatively insignificant.
- No exclusivity inference.

But then:

(9) [<ex>Just a letterF from her</ex>] <ex>arrived today.</ex>
 ⇏ a phone call, video message, etc. from her also arrived today.

Why doesn't (9) have a minimal sufficiency reading?

---

# Observation about Even

We claim that <ex>just</ex> is not the source of the scalar meaning.

Obsevation: All examples of minimal sufficiency readings are felicitous with an overt <ex>even</ex>.

<table>
 <tr>
 <td>(10)</td><td>a. (<ex>Even</ex>) <ex>just oneF cat makes me happy.</ex></td>
 </tr>
 <tr>
 <td></td><td>b. (<ex>Even</ex>) <ex>just a letterF from her can cheer him up.</ex></td>
 </tr>
 <tr>
 <td></td><td>c. (<ex>Even</ex>) <ex>just the thoughtF of him sends shivers down my spine.</ex></td>
 </tr>
</table>

--
Conversely, those that do not have minimal sufficiency readings are infelicitous with an overt <ex>even</ex>.

<table>
 <tr>
 <td>(11)</td><td>a. (#<ex>Even</ex>) <ex>just oneF cat is in the room.</ex></td>
 </tr>
 <tr>
 <td></td><td>b. (#<ex>Even</ex>) <ex>just a letterF from her arrived today.</ex></td>
 </tr>
</table>

---

# Towards a Proposal

Empirical generalization: Compatibility with an overt <ex>even</ex> tracks the availability of the minimal sufficiency reading.

We propose that the scalar meaning of the minimal sufficiency reading comes from (covert) <ex>even</ex>.

In fact, <ex>just</ex> is not even necessary to get the same(-ish) reading.

<table>
 <tr>
 <td>(12)</td><td>a. <ex>Even</ex> (<ex>just</ex>) <ex>oneF cat makes me happy.</ex></td>
 </tr>
 <tr>
 <td></td><td>b. <ex>Even</ex> (<ex>just</ex>) <ex>a letterF from her can cheer him up.</ex></td>
 </tr>
 <tr>
 <td></td><td>c. <ex>Even</ex> (<ex>just</ex>) <ex>the thoughtF of him sends shivers down my spine.</ex></td>
 </tr>
</table>

---

# Deriving Minimal Sufficiency

---

# Semantics of Even

We assume that overt and covert <ex>even</ex> have the same semantic function: it introduces two presuppositions based on focus alternatives (Karttunen & Peters 1979, Crnič 2012, a.o.).
- **Scalar presupposition**: the prejacent is relatively unlikely among alternatives
- **Additive presupposition**: another alternative is also true

We assume the Roothian theory of focus (Rooth 1992).

(13) <ex>Even PatrickF danced.</ex>

- Scalar: Patrick was relatively unlikely to dance.
- Additive: Another person danced.

---

# Deriving Minimal Sufficiency

(14) (<ex>even</ex>) [S [Subj <ex>just oneF cat</ex>] [VP <ex>makes me happy</ex>] ]

The scalar meaning comes from <ex>even</ex> applying at the S-level (⇒ VP is accessible in computing the inference).

<ex>Just</ex> triggers exclusivity meaning at the DP-level (not scalar meaning as in the previous analyses).

- Subject DP means 'exactly one cat'

- <ex>Even</ex> says the prejacent (A) is relatively unlikely and another alternative is true.
<ol type="A">
 <li>Exactly one cat ⇒ I'm happy</li>
 <li>Exactly two cats ⇒ I'm happy</li>
 <li>Exactly three cats ⇒ I'm happy</li>
</ol>

---

# Deriving Minimal Sufficiency (cont.)

(15) (<ex>even</ex>) [S [Subj <ex>just a letterF from her</ex>] 
[VP <ex>can cheer him up</ex>] ]

- Subject DP means 'A letter + nothing else from her'

- <ex>Even</ex> says the prejacent (A) is relatively unlikely and another alternative is true.
<ol type="A">
 <li>A letter + nothing else from her can cheer him up</li>
 <li>A telephone call + nothing else from her can cheer him up</li>
 <li>A video message + nothing else from hercan cheer him up</li>
</ol>

---

# Minimal Sufficiency without Just

(16) <ex>even</ex> [S [Subj <ex>oneF cat</ex>] [VP <ex>makes me happy</ex>] ]

- <ex>Even</ex> says the prejacent (A) is relatively unlikely and another alternative is true.
<ol type="A">
 <li>One cat makes me happy</li>
 <li>Two cats make me happy</li>
 <li>Three cats make me happy</li>
</ol>

(17) <ex>even</ex> [S [Subj <ex>a letterF from her</ex>] [VP <ex>can cheer him up</ex>] ]

- <ex>Even</ex> says the prejacent (A) is relatively unlikely and another alternative is true.
<ol type="A">
 <li>A letter from her can cheer him up</li>
 <li>A telephone call from her can cheer him up</li>
 <li>A video message from her can cheer him up</li>
</ol>

---

# Predicting Availability of Minimal Sufficiency

---

# Not Deriving Minimal Sufficiency

We just saw that <ex>even</ex> derives the minimal sufficiency reading.

 <table>
 <tr>
 <td>(18)</td><td>a. (<ex>Even</ex>) <ex>just oneF cat makes me happy.</ex></td>
 </tr>
 <tr>
 <td></td><td>b. <ex>Even</ex> <ex>oneF cat makes me happy.</ex></td>
 </tr>
</table>

We must make sure that we don't over generate.

Clearly what matters is the predicate.

---

# Just One Cat

(20) (<ex>even</ex>) [ [Subj <ex>just oneF cat</ex>] [VP <ex>is in the room</ex>] ]

<ex>Even</ex> says the prejacent (A) is relatively unlikely and another alternative is true.
<ol type="A">
 <li>Exactly one cat is in the room</li>
 <li>Exactly two cats are in the room</li>
 <li>Exactly three cats are in the room</li>
</ol>

This scalar inference is unnatural: there being exactly one cat is less likely than there being exactly two cats?

Also the additivity inference contradicts what is said!!

---

# One Cat

Similarly for the version without <ex>just</ex>

(21) (<ex>even</ex>) [ [Subj <ex>oneF cat</ex>] [VP <ex>is in the room</ex>] ]

<ex>Even</ex> says the prejacent (A) is relatively unlikely and another alternative is true.
<ol type="A">
 <li>One cat is in the room</li>
 <li>Two cats are in the room</li>
 <li>Three cats are in the room</li>
</ol>

If numerals have exactly readings, the same story as before.

If they have at-least readings, the additive presupposition is consistent, but the scalar presupposition is not.

---

# A Letter from Her

Our story for <ex>a letter from her</ex> is a little more complicated.

First observe that (22) is felicitous:

(22) <ex>Even a letterF from her arrived today.</ex>

If the alternatives are, e.g. letter, email, voice mail, etc. then the scalar presupposition is felicitous.

Then why can't (23) mean: even something that is letter + nothing else arrived today.

(23) #<ex>Even just a letterF from her arrived today.</ex>

This should make sense with the same alternatives.

---

# A Letter from Her (cont.)

(23) #<ex>Even just a letterF from her arrived today.</ex>

<ex>Even</ex> says the prejacent (A) is relatively unlikely and another alternative is true, which should be coherent.
 <ol type="A" style="margin-left: 2em;">
 <li>A letter + nothing else from her arrived today</li>
 <li>An email + nothing else from her arrived today</li>
 <li>A voice message + nothing else from her arrived today</li>
 </ol>

It seems that <ex>just</ex> here has an exclusive reading at the sentential level, so the alternatives are:
 <ol type="A" style="margin-left: 2em;">
 <li>A letter from her but nothing else arrived today</li>
 <li>A email from her but nothing else arrived today</li>
 <li>A voice message from her but nothing else arrived today</li>
 </ol>

Then the additive inference of <ex>even</ex> will be incoherent.

---

# Scope of Just

In (24) <ex>just</ex> can take a DP-level (24a) or S-level scope (24b).

<table>
 <tr> 
 <td>(24)</td><td colspan="2"><ex>Just a letterF can cheer him up.</ex></td>
 </tr>
 <tr>
 <td></td><td>a.</td><td>Something that is nothing but a letter from her can cheer him up.</td>
 </tr>
 <tr>
 <td></td><td>b.</td><td>A letter from her can cheer him up and nothing else can cheer him up.</td>
 </tr>
</table>

In (25) <ex>just</ex> can only take an S-level scope. Why?

 <table>
 <tr> 
 <td>(25)</td><td colspan="2"><ex>Just a letterF from her arrived today.</ex></td>
 </tr>
 <tr>
 <td></td><td>a.</td><td>*Something that is nothing but a letter from her arrived today.</td>
 </tr>
 <tr>
 <td></td><td>b.</td><td>A letter from her arrived today and nothing else arrived today.</td>
 </tr>
</table>

---

# Free Choice Any

Interestingly, the availability of narrow scope reading patterns with the Free Choice reading of <ex>any</ex> (w/o subtrigging).

<table>
 <tr> 
 <td>(26)</td><td>a. <ex style="margin-left: 1.2ex;">Anything can cheer him up.</ex></td>
 </tr>
 <tr> 
 <td></td><td>b. *<ex>Anything arrived today.</ex></td>
 </tr>
</table>

<table>
 <tr> 
 <td>(27)</td><td>a. <ex style="margin-left: 1.2ex;">Anything makes me happy.</ex></td>
 </tr>
 <tr> 
 <td></td><td>b. *<ex>Anything is in the room.</ex></td>
 </tr>
</table>

<table>
 <tr> 
 <td>(28)</td><td>a. <ex style="margin-left: 1.2ex;">Anything sends shivers down my spine.</ex></td>
 </tr>
 <tr> 
 <td></td><td>b. *<ex>Anything is on the shelf.</ex></td>
 </tr>
</table>

Free Choice <ex>any</ex> (Kadmon & Landman 1993, Dayal 1998)
- Available in (some) modal contexts, e.g. (26a)
- Available in characterizing sentences, e.g. (27a), (28a)
- Unavailable in episodic sentences, e.g. (26b), (27b), (28b)

---

# A Letter from Her again

We leave open here how to explain this observation (cf. Chierchia's 2013 alternative-based analysis of Free Choice).

But with this constraint, we correctly render (23) infelicitous:

(23) #<ex>Even just a letterF from her arrived today.</ex>

<ex>Even</ex> says the prejacent (A) is relatively unlikely and another alternative is true.
 <ol type="A" style="margin-left: 2em;">
 <li>A letter from her but nothing else arrived today</li>
 <li>A email from her but nothing else arrived today</li>
 <li>A voice message from her but nothing else arrived today</li>
 </ol>

The additive inference of <ex>even</ex> is incoherent.

---

# Back to Previous Analyses

But can this constraint save the previous analyses?
According to them, <ex>Just</ex> takes narrow scope in minimal sufficiency readings and yield a scalar inference.

No, narrow scope does not always enable the minimal sufficiency reading.

<table>
 <tr> 
 <td>(29)</td><td><ex>Just the cup costs £1. The milk jug is also £1. The pot is £10. If you buy all of them together, there'll be a discount.</ex></td>
 </tr>
</table>

The previous analyses predict the inference that the cup is relatively insignificant.

Notice here <ex>even</ex> is unavailable here, so we don't predict a minimal sufficiency reading.

---

# Summary

Previous analyses
 - <ex>Just</ex> has scalar meaning (rank-order reading and minimul sufficiency reading)
 - The scale is computed based on the DP material

Our analysis
 - The scalar meaning comes from (covert) <ex>even</ex> at S-level
 - When the predicted presuppositions are infelicitous, the minimal sufficiency reading is absent
 - <ex>Just</ex> has exclusive meaning and can take DP- or S-level scope
 - DP-level <ex>just</ex> is limited in distribution (Needs to be explained in future work)
 - S-level <ex>just</ex> is incompatible with the additive presupposition of <ex>even</ex>

---

# Past Tense

For our analysis, the minimal sufficiency reading of the following sentence is puzzling.

<div class="indented">

 (30) <ex>Just oneF cat made me happy.</ex>
 

</div>

This certainly does not imply that two, three, etc. cats made me happy.

Fortunately, our empirical generalization still holds, i.e. the same happens with <ex>even</ex>
<div class="indented">

 (31) <ex>Even just oneF cat made me happy.</ex>

</div>

These sentences have 'modalized inferences' that any number of cats would have made me happy.

We leave it for future research how to account for this.

---

# References

<ul>

<li class="ref">Beaver & Coppock (2014) Principles of the Exclusive Muddle. Journal of Semantics, 31.</li>

<li class="ref">Chierchia (2013) Logic in Grammar: Polarity, Free Choice, and Intervention. OUP.</li>

<li class="ref">Crnič (2011) Getting Even. PhD dissertation, MIT.</li>

<li class="ref">Dayal (1998) Any is inherently modal. Linguistics and Philosophy, 21.</li>

<li class="ref">Grosz (2012) On the Grammar of Optative Constructions. John Benjamins.</li>

<li class="ref">Kadmon & Landman (1993) Any. Linguistics and Philosophy, 16.</li>

<li class="ref">Karttunen & Peters (1979) Conventional Implicature. Syntax and Semantics 11: Presupposition. Academic Press.</li>

<li class="ref">Rooth (1992) A theory of focus interpretation. Natural Language Semantics, 1.</li>

</ul>