vacuous and non-vacuous behaviors of the present tense · 2014. 2. 9. · local mp (percus, 2006;...

Vacuous and Non-Vacuous Behaviors of thePresent Tense

Laine StranahanDepartment of Linguistics, Harvard University

stranahan@fas.harvard.edu

88th Annual Meeting of the Linguistic Society of AmericaJanuary 2, 2014

Outline

1. Phenomenon

2. Background

2.1 Tense2.2 Lifetime Inference2.3 Presupposition Maximization

3. Analysis

3.1 Distributivity3.2 Strongest Meaning Hypothesis3.3 Individuals vs. Intervals

4. Open Issues

The Phenomenon

Individuals

# JFK and Joe Kennedy aretall.

# My uncles are blond.

# John and Bill are bothvery handsome. (Mittwoch,2008)

Intervals

2012 and 2016 are leapyears.

The even-numbered daysthis week are school days.

Every Tuesday this month Ifast. (Sauerland, 2002)

Semantic Types

Individuals: eTruth Values: t(Worlds: w)

Intervals: i/t

Tense as Presuppositional (Partee, 1973)

JPRESENTK = λt : t ⊇ t0.t

JPASTK = λt : t < t0.t

Johne T

i

PRESENT< i , i >

ti

asleep< i , < e, t >>

Tense as Presuppositional (Partee, 1973)

JPRESENTK = λt : t ⊇ t0.t

JPASTK = λt : t < t0.t

∃t

Johne T

i

PRESENT< i , i >

ti

asleep< i , < e, t >>

The Present Tense is Vacuous (Sauerland, 2002)

Every Tuesday this month I fast. (Sauerland, 2002)

2012 and 2016 are leap years.

The even-numbered days this week are school days.

↓JPRESENTK = λt.t

JPASTK = λt : t < t0.t

The Present Tense is Vacuous (Sauerland,2002)

JJohn is asleepK 6= ∃t Asleep(John,t)

<PRESENT, PAST >∅ t < t0

Maxim: Make your contribution presuppose as much aspossible.

JJohn is asleepK = ∃tAlive(John,t)

¬(t < t0)

Antipresupposition

The Present Tense is Vacuous (Sauerland,2002)

JJohn is asleepK 6= ∃t Asleep(John,t)

<PRESENT, PAST >∅ t < t0

Maxim: Make your contribution presuppose as much aspossible.

JJohn is asleepK = ∃tAlive(John,t)

¬(t < t0)

Antipresupposition

The Present Tense is Vacuous (Sauerland,2002)

JJohn is asleepK 6= ∃t Asleep(John,t)

<PRESENT, PAST >∅ t < t0

Maxim: Make your contribution presuppose as much aspossible.

JJohn is asleepK = ∃tAlive(John,t)

¬(t < t0)

Antipresupposition

Non-Vacuous Behavior

# JFK and Joe Kennedy are tall.

# My uncles are blond.

# John and Bill are both very handsome. (Mittwoch, 2008)

I-Level and S-Level Predicates(Carlson, 1977; Chierchia, 1995; Kratzer, 1995)

I-Level

tallblond

handsome...

S-Level

asleepavailabledrunk

...

I-Level and S-Level Predicates

I-Level PropertiesP:

∀x [∃t1[P(x , t1)]→∀t2[Alive(x , t2)→ P(x , t2)]]

S-Level PropertiesP:

∀x [∃t1[P(x , t1)]→¬∀t2[Alive(x , t2)→ P(x , t2)]]

Lifetime Inference (Musan, 1997)

John was blond. ; John is no longer alive.

1. Speaker utters “John was blond.”

2. ”John is blond” would have been more informative/relevant.

3. Speaker is trying to be maximally informative.

4. Speaker must not believe John is still blond.

5. By the semantics of “blond,” if John were alive, he would beblond.

6. John must not be alive.

Lifetime Inference (Musan, 1997)

John was blond. ; John is no longer alive.

1. Speaker utters “John was blond.”

2. ”John is blond” would have been more informative/relevant.

3. Speaker is trying to be maximally informative.

4. Speaker must not believe John is still blond.

5. By the semantics of “blond,” if John were alive, he would beblond.

6. John must not be alive.

Inferences About Lifetimes

Past Present

I-Level

“John was blond.”; Lifetime Inference→ John is no longeralive.

“John is blond.”→ John is alive.

S-Level“John was asleep.”→ John was alive.

“John is asleep.”→ John is alive.

Inferences About Lifetimes

JblondK = λt.λx .x is blond at t and x is alive at t

JasleepK = λt.λx .x is asleep at t and x is alive at t

Individual Lifetime Parameter

John is dead. JJohnK = jt t < t0

Bill is alive. JBillK = bt t ⊇ t0

“Mary was a WWII nurse.” JMaryK = mt t ⊇ 1939-1945

“Fred is asleep.” JFredK = ft t ⊇ t0

“Sam was blonde.” JSamK = st t < t0

Individual Lifetime Parameter

John is dead. JJohnK = jt t < t0

Bill is alive. JBillK = bt t ⊇ t0

“Mary was a WWII nurse.” JMaryK = mt t ⊇ 1939-1945

“Fred is asleep.” JFredK = ft t ⊇ t0

“Sam was blonde.” JSamK = st t < t0

Individual Lifetime Parameter

John is dead. JJohnK = jt t < t0

Bill is alive. JBillK = bt t ⊇ t0

“Mary was a WWII nurse.” JMaryK = mt t ⊇ 1939-1945

“Fred is asleep.” JFredK = ft t ⊇ t0

“Sam was blonde.” JSamK = st t < t0

Maximize Presupposition(Heim, 1991; Percus, 2006; Sauerland, 2008; Singh, 2011; Schlenker, 2012)

The/#a sun was shining. (Hawkins, 1991)

Both/#all of John’s eyes are blue. (Percus, 2006)

John knows/#thinks that Paris is in France. (Singh, 2011)

Maxim: Make your contribution presuppose as much aspossible.

Maximize Presupposition(Heim, 1991; Percus, 2006; Sauerland, 2008; Singh, 2011; Schlenker, 2012)

The/#a sun was shining. (Hawkins, 1991)

Both/#all of John’s eyes are blue. (Percus, 2006)

John knows/#thinks that Paris is in France. (Singh, 2011)

Maxim: Make your contribution presuppose as much aspossible.

Local MP(Percus, 2006; Singh, 2011)

Everyone with exactly two students assigned the same exercise toboth/#all of his students.

If John has exactly two students and he assigned the same exerciseto both/#all of them, then I’m sure he’ll be happy.

Mary believes that John has exactly two students and that heassigned the same exercise to both/#all of them.

Maximize Presupposition (MP):

MPALT

([S . . .X . . .]

P([S . . .X . . .])

)=

[S . . .X . . .]

P([S . . .X . . .]) ∧ ∀Y ∈ ALT (X)[¬P([S . . .Y . . .])], where:

i. ALT(X) = {Y: [S . . .Y. . .] presupposes more than [S . . .X. . .]}

ii. P(S) = presupposition(s) of S

Local MP(Percus, 2006; Singh, 2011)

Everyone with exactly two students assigned the same exercise toboth/#all of his students.

If John has exactly two students and he assigned the same exerciseto both/#all of them, then I’m sure he’ll be happy.

Mary believes that John has exactly two students and that heassigned the same exercise to both/#all of them.

Maximize Presupposition (MP):

MPALT

([S . . .X . . .]

P([S . . .X . . .])

)=

[S . . .X . . .]

P([S . . .X . . .]) ∧ ∀Y ∈ ALT (X)[¬P([S . . .Y . . .])], where:

i. ALT(X) = {Y: [S . . .Y. . .] presupposes more than [S . . .X. . .]}

ii. P(S) = presupposition(s) of S

“John is asleep.”

JPRESENTK =λt.t

∅, JPASTK =

λt.t

t < t0

ALT (PRESENT) = {PAST}

1. MP{PAST}([JAsleepK(JPRESENTK(t))](JJohnK))

2. MP{PAST}(∃t[[[λt.λx .x is asleep at t ∧x is alive at t]([λt.t](t))](j)])

3. MP{PAST}

(∃t [[λt.λx .x is asleep at t ∧ x is alive at t](t)](j)

∅

)4. MP{PAST}

(∃t [λx .x is asleep at t ∧ x is alive at t](j)

∅

)5. MP{PAST}

(∃t j is asleep at t ∧ j is alive at t

∅

)6. ∃t j is asleep at t ∧ j is alive at t

∅ ∧ ∀Y ∈ {PAST}[¬P(John be.Y asleep)]

7. ∃t j is asleep at t ∧ j is alive at t

∅ ∧ ¬P(John be.PAST asleep)

8. ∃t j is asleep at t ∧ j is alive at t

∅ ∧ ¬(t < t0)

9. ∃t j is asleep at t ∧ j is alive at t

¬(t < t0)

“John is asleep.”

1. MP{PAST}(JJohn is asleepK)...

5. MP{PAST}

(∃t j is asleep at t ∧ j is alive at t

∅

)...

9. ∃t j is asleep at t ∧ j is alive at t

¬(t < t0)

Distributivity(Link, 1987; Lasersohn, 1998; i.a.)

John and Bill are tall.My uncles are blond.

All the dogs are asleep.

Distributivity (D):JDK = λS.λP.∀x ∈ S[P(S)],

where S is the set of entities denoted by the plural or conjoinednominal

“John and Bill are tall.”

1. [JDK(JJohn and BillK)](JtallK(JPRESENTK(t)))

2.[[λS.λP.∀x ∈ S[P(x)]({j , b})]([λt.λx .x is tall at t and x is alive at t](t))

∅3.

[λP.∀x ∈ {j , b}[P(x)]](λx .∃t[x is tall at t and x is alive at t])

∅

4.∃t1[j is tall at t and j is alive at t)

∅∧

∃t2[b is tall at t and b is alive at t)

∅

Scope Ambiguity

D(MP(. . . ))

MP

(∃t1[j is tall at t and j is alive at t]

∅

)∧MP

(∃t2[b is tall at t and b is alive at t]

∅

)

MP(D(. . . ))

MP

(∃t1[j is tall at t and j is alive at t]

∅∧ ∃t2[b is tall at t and b is alive at t]

∅

)

Scope Ambiguity

D(MP(John and Bill . . . )):

1. ∀x ∈ {j , b}[MP[. . . x . . .]]2. MP[. . . j . . .]∧

MP[. . . b . . .]

3.[. . . j . . .]

¬tj < t0∧ [. . . b . . .]

¬tb < t0

→ John is alive and Bill isalive.

MP(D(John and Bill . . . )):

1. MP[∀x ∈ {j , b}[. . . x . . .]]2. MP[[. . . j . . .] ∧ [. . . b . . .]

3.[. . . j . . .] ∧ [. . . b . . .]

¬(tj < t0 ∧ tb < t0)

→ John and Bill can’t bothbe dead.

t0

JohnBill

t0

BillJohn

t0

BillJohn

t0

John BillJohn ∧ Bill

t0

John BillJohn ∧ Bill

t0

John BillJohn ∧ Bill

Scope Ambiguity

D(MP(John and Bill . . . )):

1. ∀x ∈ {j , b}[MP[. . . x . . .]]2. MP[. . . j . . .]∧

MP[. . . b . . .]

3.[. . . j . . .]

¬tj < t0∧ [. . . b . . .]

¬tb < t0

→ John is alive and Bill isalive.

MP(D(John and Bill . . . )):

1. MP[∀x ∈ {j , b}[. . . x . . .]]2. MP[[. . . j . . .] ∧ [. . . b . . .]

3.[. . . j . . .] ∧ [. . . b . . .]

¬(tj < t0 ∧ tb < t0)

→ John and Bill can’t bothbe dead.

t0

JohnBill

t0

BillJohn

t0

BillJohn

t0

John BillJohn ∧ Bill

t0

John BillJohn ∧ Bill

t0

John BillJohn ∧ Bill

Scope Ambiguity

D(MP(2012 and 2016 . . . )):

1. ∀x ∈{2012, 2016}[MP[. . . x . . .]]

2. MP[. . . 2012 . . .]∧MP[. . . 2016 . . .]

3.[. . . 2012 . . .]

¬2012 < t0∧ [. . . 2016 . . .]

¬2016 < t0

→ 2012 is present and 2016 ispresent.

MP(D(2012 and 2016 . . . )):

1. MP[∀x ∈{2012, 2016}[. . . x . . .]]

2. MP[[. . . 2012 . . .] ∧[. . . 2016 . . .]

3.[. . . 2012 . . .] ∧ [. . . 2016 . . .]

¬(2012 < t0 ∧ 2016 < t0)

→ 2012 and 2016 can’t both bepresent.

t0

2012 2016

t0

2016 2012

t0

20162012

t0

201620122012 ∧ 2016

t0

201620122012 ∧ 2016

t0

201620122012 ∧ 2016

Scope Ambiguity

D(MP(2012 and 2016 . . . )):

1. ∀x ∈{2012, 2016}[MP[. . . x . . .]]

2. MP[. . . 2012 . . .]∧MP[. . . 2016 . . .]

3.[. . . 2012 . . .]

¬2012 < t0∧ [. . . 2016 . . .]

¬2016 < t0

→ 2012 is present and 2016 ispresent.

MP(D(2012 and 2016 . . . )):

1. MP[∀x ∈{2012, 2016}[. . . x . . .]]

2. MP[[. . . 2012 . . .] ∧[. . . 2016 . . .]

3.[. . . 2012 . . .] ∧ [. . . 2016 . . .]

¬(2012 < t0 ∧ 2016 < t0)

→ 2012 and 2016 can’t both bepresent.

t0

2012 2016

t0

2016 2012

t0

20162012

t0

201620122012 ∧ 2016

t0

201620122012 ∧ 2016

t0

201620122012 ∧ 2016

Scope Ambiguity

D(MP(. . . )) MP(D(. . . ))

Individualt0

BillJohn

#John and Bill aretall.

t0

John BillJohn ∧ Bill

John and Bill are tall.

Interval t0

20162012

#2012 and 2016 are leapyears.

t0

201620122012 ∧ 2016

2012 and 2016 are leapyears.

Lifetime Parameter Updates

D(MP(. . . )) MP(D(. . . ))

Individual

Interval

0 0

Maxim: Make your contribution presuppose as much aspossible.

Lifetime Parameter Updates

D(MP(. . . )) MP(D(. . . ))

Individualt0

BillJohn

2

t0

John BillJohn ∧ Bill

t0

John BillJohn ∧ Bill

t0

John BillJohn ∧ Bill

0Interval

0 0

Strongest Meaning Hypothesis

I Dalrymple, et al. (1998): Reciprocals

I Winter (2001): Plural predication

I Chierchia, et al. (2008): Exhaustification

Strongest Update Hypothesis

If a sentence is ambiguous between two or more interpretationsresulting in different numbers of individual lifetime parameter

updates, the interpretation resulting in the greatest number ofupdates is preferred.

Lifetime Parameter Updates

D(MP(. . . )) MP(D(. . . ))

Individual # JFK and Joe Kennedyare tall.

# My uncles are blond.

# John and Bill are bothvery handsome.(Mittwoch, 2008)

0

Interval

0

2012 and 2016 are leapyears.

The even-numbered daysthis week are school days.

Every Tuesday this monthI fast. (Sauerland, 2002)

Summary

I Systematic difference between contexts in which present isvacuous and those in which it is non-vacuous

I Traditional theory & Sauerland’s (2002) vacuous present fail toaccount for both

I Apparent irreconcilability can be resolved by:I Admitting a formal realization of the distinction between

individuals and intervalsI Assuming a covert operator analysis of distributivity and

presupposition maximization with scope ambiguityI Positing disambiguation based on a preferential interpretation

principle sensitive to the difference

Questions

I MP as mobile grammatical operator vs. utterance-level maxim

I Intervals > Events > IndividualsI “2012 and 2016 are leap years.”I ?“The 87th and 88th Annual Meetings are in snowy climates.”I #“JFK and Joe Kennedy are tall.”

I Covert aspectual operators? (Thomas, 2012; i.a.)I Futurate (“The Red Sox play the Yankees tomorrow.”)I Habitual (“Every Christmas I go to California.”)I [Calendrical? (“Next Friday is a holiday.”; “2016 is a leap

year.”)]

Thank you!Uli Sauerland

Isabelle CharnavelChrissy Zlogar

References

Carlson, G. N. (1977). Reference to kinds in English. Ph.D. Dissertation, UMass Amherst.

Chierchia, G., Fox, D., & Spector, B. (2008). The grammatical view of scalar implicatures and therelationship between semantics and pragmatics. Unpublished manuscript.

Dalrymple, M., Kanazawa, M., Kim, Y., Mchombo, S., & Peters, S. (1998). Reciprocal expressions and theconcept of reciprocity. Linguistics and Philosophy, 21(2), 159-210.

Hawkins, J. A. (1991). On (in) definite articles: implicatures and (un) grammaticality prediction. Journalof linguistics, 27(2), 405-442.

Heim, I. (1991). Artikel und definitheit. Semantik: ein internationales Handbuch der Zeitgen’ossischenforschung, 487-535.

Mittwoch, A. (2008). Tenses for the living and the dead: Lifetime inferences reconsidered. Theoretical andcrosslinguistic approaches to the semantics of aspect, 171-187.

Musan, R. (1997). Tense, predicates, and lifetime effects. Natural Language Semantics, 5(3), 271-301.

Percus, O. (2006). Antipresuppositions. Theoretical and empirical studies of reference and anaphora:Toward the establishment of generative grammar as an empirical science, 52, 73.

Sauerland, U. (2002). The present tense is vacuous. Snippets, 6, 12-13.

Schlenker, P. (2012). Maximize presupposition and Gricean reasoning. Manuscript, UCLA and InstituteJean-Nicod.

Singh, R. (2011). Maximize Presupposition! and local contexts. Natural Language Semantics, 19(2),149-168.

Thomas, Guillaume. (2012). Temporal implicatures. Doctoral dissertation, Massachusetts Institute ofTechnology.

Winter, Yoad. (2001). ”Plural predication and the strongest meaning hypothesis.” Journal of Semantics18.4: 333-365.