Universal Quantification and Degree Modification as Slack Regulation Heather Burnett, Université de Montréal & Institut Jean Nicod Introduction

Classical Delineation Semantics (à la Klein (1980), a.o.)

A new analysis of French tou(te)s ‘all’, paying particular attention its distribution and interpretation across syntactic domains. I Tou(te)s can appear in the DP domain, where it seems to have a universal quantification function. (1)

I

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Toutes les filles sont en retard. ‘All the girls are late.’

Tout(e) can appear in the adjectival domain, where it seems to have a degree modification function. a. b.

I

Universal Interp.

La salle est toute vide. ‘The room is completely empty.’ Marie est toute triste. ‘Marie is very sad.’

Completive Interp. Intensive Interp.

Burnett (2013a): There are reasons to believe that we are looking at a single lexical item.

Puzzle: How to provide a unified analysis of tou(te)s across syntactic domains?

1. The interpretation of a gradable predicate changes depending on the set of individuals that it is being compared with. For an adjective P and a contextually given comparison class X ⊆ D, JPKcX ⊆ X .

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x >cP y iff ∃X ⊆ D: x ∈ JP KcX and y ∈ / JP KcX .

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I I

(3)

(4)

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Limited to scalar adjectives (#tout premier ‘all prime’). If P is associated with a scale that has a top endpoint, then tout P has a completive interpretation. Otherwise, P has an intensive interpretation. (Total) Top-closed scale adjective ⇒ Completive Interp.: tout chauve, tout vide, tout propre, tout lisse, tout sec, tout droit, tout plat, tout fermé. . . (Partial) Bottom-closed scale adjective ⇒ Intensive Interp.: tout sale, tout tordu, tout mouillé, tout courbé, tout croche, tout réveillé. . . (Relative) Open scale adjective ⇒ Intensive Interp.: tout grand, tout petit, tout cher, tout gentil, tout nul, tout étroit. . .

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For all scalar adjectives P and comparison classes X ⊆ D, ∼XP is a binary relation on the elements of X .

2. Tolerant

and strict

interpretation of predicates.

c x and d ∈ J P K JP KtX = {x : ∃d ∼X P X }. c JP KsX = {x : ∀d ∼X x, d ∈ J P K P X }.

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3. Tolerant/strict scales (10)

(J·Ks )

x

t/s >P

t/s (>P )

y iff ∃X ⊆ D: x ∈

(at least) approx. dry/tall really wet/tall

and y ∈ /

t/s JP KX .

Adopting an extension-based definition of scale structure: 1. If P is a relative adjective, >cP is an open scale with at least 2 degrees.

2. If P is a total adjective, >tP is a top-closed scale with at least 2 degrees. 3. If P is a partial adjective, >sP is a bottom-closed with at least 2 degrees. t/c/s 4. If P is a non-scalar adjective, >P has 2 degrees.

Thm. x ∈

for all X ⊆ D ⇔ x is at the top-endpoint of

Domain Neutral Analysis of tou(te)s t/c/s PKX

For all P and X ⊆ D, Jtou(te)s = JP KsX I Presupposition: >P has more than 2 degrees.

https://sites.google.com/site/heathersusanburnett/

Atomic-coll.

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For every DP and X ⊆ P(D), a contextually given x ∈ D.

c JDP KX

= {Q : x ∈ Q}, for

3. The three classes of predicates in (11) are distinguished based on their mereological structure. 4. Indifference relations relate properties within a CC. (13)

For every DP and X ⊆ P(D), ∼XDP is a binary relation on the elements of X .

5. ∼XDP s obey constraints with respect to how they affect the mereological structure of DP. 6. The tolerant/strict denotations of DPs are defined parallely to the adjectives, as are the scales. (14) (15)

c JDP KtX = {P : ∃Q ∼X P and Q ∈ J DP K DP X }. c JDP KsX = {P : ∀Q ∼X P, Q ∈ J DP K DP X }.

P

t/s >DP

Q iff ∃X ⊆ P(D): P ∈

t/s JDP KX

and Q ∈ /

t/s JDP KX .

Connection between precision and ∀ (for distributive P):

Connection between precision and scale structure: c/s JP KX ,

Gather-coll.

1. Predicates are interpreted in a classical mereology hD, i. 2. Definite plural subjects are interpreted as Montagovian Individuals, relativized to comparison classes of properties.

is constructed parallelly to >cP : t/s JP KX

Distributive

Mereological Extension of DelTCS (Burnett (2013b))

1. In DelTCS, context-sensitive indifference (∼P ) relations appear in the model relativized to comparison classes and subject to certain ‘coherence’/ordering constraints.

(J·Kt )

Toutes les filles sont en retard. ‘All the girls are late.’ b. Toutes les filles se sont rassemblées. ‘All the girls gathered.’ c. #Toutes les filles sont quatre. # ‘All the girls are four.’ a.

Question: Does our analysis for tou(te)s predict this pattern?

TCS Extension (à la Cobreros et al. (2012))

Tou(te)s as a slack regulator (building on Lasersohn, 1999)

Burnett (2013a): Tout(e) in the Adjectival Domain

Tou(te)s is possible with definite plurals and distributive predicates, gather-collective predicates, but not with atomic-collective predicates (Dowty, Brisson, Winter, a.o.).

2. Context-sensitivity/ordering constraints are put on the interpretation of different kinds of predicates. 3. The scale associated with a predicate P (>cP ) is derived through quantification over comparison classes.

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Tou(te)s forces a more precise interpretation of its complement. I The distribution/interpretation of tou(te)s is conditioned by scale structure and DP part structure (Dowty,1987, a.o.). I A semantic framework equipped to model connections between (im)precision, scale structure and mereological structure: Burnett (2012)’s Delineation Tolerant, Classical, Strict and its mereological extension (Burnett, 2013b).

Tou(te)s in the DP domain (restricted to definite plurals)

>tP

Thm. P ∈

c/s JDP KX

⇔ ∀y  x, y ∈ P, for distinguished x ∈ D.

Scale Structure Results 1. If >tDP is restricted only to distributive/gather predicates, >tDP is a top-closed scale with at least 2 degrees. 2. If >tDP is restricted to atomic predicates, then >tDP is a top-closed scale with 2 degrees.

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