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Introduction Ignorance Depictive sincerity Range expressions References Range Expressions Ameliorate Depictive Sincerity Violations Elizabeth Coppock Assistant Professor, Department of Linguistics Boston University Workshop on the occasion

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Introduction Ignorance Depictive sincerity Range expressions References

Range Expressions Ameliorate Depictive Sincerity Violations

Elizabeth Coppock Assistant Professor, Department of Linguistics Boston University Workshop on the occasion of Dominique Blok’s dissertation defense Utrecht, June 7, 2019

Elizabeth Coppock (BU) Range Expressions 1 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

PolitiFact’s Truth-O-Meter

“The Truth-O-Meter is based on the concept that – especially in politics – truth is not black and white.”

Elizabeth Coppock (BU) Range Expressions 2 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Depictive sincerity implicature example

Right now, the [Congressional Budget Office] says up to 20 million people will lose their insurance as Obamacare goes into effect next year.

(Mitt Romney in 2012)

Elizabeth Coppock (BU) Range Expressions 3 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Depictive sincerity implicature example

Right now, the [Congressional Budget Office] says up to 20 million people will lose their insurance as Obamacare goes into effect next year.

(Mitt Romney in 2012)

Elizabeth Coppock (BU) Range Expressions 3 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Depictive sincerity implicature example

Right now, the [Congressional Budget Office] says up to 20 million people will lose their insurance as Obamacare goes into effect next year.

(Mitt Romney in 2012)

The Congressional Budget Office calculated several estimates:

Elizabeth Coppock (BU) Range Expressions 3 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Two classes of modified numerals

Class A

  • more/fewer/less than 5

(comparative modifiers)

  • under/over 5

Class B

  • at least 5, at most 5

(superlative modifiers)

  • up to 5, maximally 5, 5 tops
  • 5 or more/fewer/less
  • from 100 to 200

(Nouwen 2010, cf. also Schwarz et al. 2012, Blok 2015)

Elizabeth Coppock (BU) Range Expressions 4 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Guess the original version

A study of more than 2,500 retired NFL players found that those who had

  • more than two

at least three

  • concussions during their careers had

triple the risk of clinical depression as those who had no concussions.

Elizabeth Coppock (BU) Range Expressions 5 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Guess the original version

A study of more than 2,500 retired NFL players found that those who had

  • more than two

at least three

  • concussions during their careers had

triple the risk of clinical depression as those who had no concussions.

Elizabeth Coppock (BU) Range Expressions 5 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Guess the original version

The maximum number of cards in an Extra Deck is 15, although it is allowed to have

  • fewer than 15

at most 14

  • in it.

Elizabeth Coppock (BU) Range Expressions 6 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Guess the original version

The maximum number of cards in an Extra Deck is 15, although it is allowed to have

  • fewer than 15

at most 14

  • in it.

Elizabeth Coppock (BU) Range Expressions 6 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Guess the original version

I asked a bunch of my mom’s friends (none of whom had

  • more than two

at least three

  • kids) what they thought about having three.

Elizabeth Coppock (BU) Range Expressions 7 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Guess the original version

I asked a bunch of my mom’s friends (none of whom had

  • more than two

at least three

  • kids) what they thought about having three.

Elizabeth Coppock (BU) Range Expressions 7 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Guess the original version

I am in my 60s and had

  • more than two

at least three

  • parents growing up.

Elizabeth Coppock (BU) Range Expressions 8 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Guess the original version

I am in my 60s and had

  • more than two

at least three

  • parents growing up.

Elizabeth Coppock (BU) Range Expressions 8 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Superlative modifiers and ignorance

A hexagon has more than four sides. #A hexagon has at least five sides. (Nouwen 2010) At least conveys ignorance; more than does not.

Elizabeth Coppock (BU) Range Expressions 9 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Empirical views on ignorance with modified numerals

Modifier QUD Received W&B M&M C&B CSS How many Yes Yes Yes Yes At least Polar Yes No Yes No Yes How many Yes Yes No Yes More than Polar No No No No No

Received view = Geurts & Nouwen 2007; Büring 2008; Cummins & Katsos 2010; Kennedy 2015 W&B = Westera & Brasoveanu 2014 M&M = Mayr & Meyer 2014 C&B = Coppock & Brochhagen 2013 CSS = Cummins et al. 2012

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Introduction Ignorance Depictive sincerity Range expressions References Elizabeth Coppock (BU) Range Expressions 11 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Situation manipulation

  • False: Mary knows x < N
  • Exact: Mary knows x = N
  • Exceed: Mary knows x > N
  • Ignorance: Mary is uncertain if x = N or x > N

x = number of clubs on Mary’s deck

Elizabeth Coppock (BU) Range Expressions 12 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

QUD manipulation

  • HowMany: Sue asks, How many face cards do you have?
  • PolarRelevant: Sue asks: Will you win this round?; Mary

responds only with relevant information (e.g., Yes, at least six/more than five of my eight cards are clubs).

  • PolarOverInf: Sue asks: Will you win this round?; Mary

reponsds providing more information than necessary (e.g., Yes, at least seven/more than six of my eight cards are clubs).

Elizabeth Coppock (BU) Range Expressions 13 / 45

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Introduction Ignorance Depictive sincerity Range expressions References at least n more than (n-1) bare n

How many (n=2/3/4) Polar (relevant: n=6) Polar (over-informative: n=7)

F a l s e E x a c t E x c e e d I g n

  • r

a n c e F a l s e E x a c t E x c e e d I g n

  • r

a n c e F a l s e E x a c t E x c e e d I g n

  • r

a n c e

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

Mean response Elizabeth Coppock (BU) Range Expressions 14 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Interim Conclusion

At least n carries an ignorance implicature:

  • Possibly n
  • Possibly more than n

Elizabeth Coppock (BU) Range Expressions 15 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Whence ignorance?

Büring (2008) (followed by Cummins & Katsos 2010 and Biezma 2013):

  • E.g. at least 4 ‘amounts to a disjunction’: 4 or more.
  • There is an ‘implicature schema’ that says, if a speaker says A
  • r B, then the speaker considers both A and B to be possible.

With inquisitive semantics, we can explain what it means to ‘amount to’ a disjunction.

Elizabeth Coppock (BU) Range Expressions 16 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Traditional vs. Inquisitive Disjunction

Traditional disjunction Inquisitive disjunction 11 10 01 00 11 10 01 00

Elizabeth Coppock (BU) Range Expressions 17 / 45

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at most vs. fewer than

Liz had at most 4 beers à la Coppock and Brochhagen:

  • logically implies that Liz had fewer than 5 beers

(like Liz had fewer than 5 beers)

  • brings up the issue of whether Liz had fewer

(unlike Liz had fewer than 5 beers) “fewer than 5” 1 2 3 4 5 6 “at most 4” 1 2 3 4 5 6

Elizabeth Coppock (BU) Range Expressions 18 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Refinement (cf. Schwarz 2016)

“at most 4” 1 2 3 4 5 6

Elizabeth Coppock (BU) Range Expressions 19 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Quality maxims for Inquisitive Semantics

Maxim of Informative Sincerity: Believe what you say.

Elizabeth Coppock (BU) Range Expressions 20 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Quality maxims for Inquisitive Semantics

Maxim of Informative Sincerity: Believe what you say. Maxim of Inquisitive Sincerity: Don’t bring up an issue that you already know how to resolve.

Elizabeth Coppock (BU) Range Expressions 20 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Alternative (among several): OT analysis

s φ Qual Quant SQual ISal NSal Simp {n} ☞ n more than n *! * more than n − 1 *! * * * at least n *! ** {n + 1} n *! * * ☞ n + 1 * more than n *! * * at least n *! * ** at least n + 1 *! * ** {k} n *! * * ☞ k * more than n *! * * more than k *! * * * more than k − 1 *! * * * at least n *! * ** at least k *! * ** [n, . . . ) n *! more than n *! * more than n − 1 *! *! * ☞ at least n ** [n + 1, . . . ) n *! * * n + 1 *! * ☞ more than n * * at least n *! * ** ☞ at least n + 1 * ** Elizabeth Coppock (BU) Range Expressions 21 / 45

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But ignorance is not all there is to the story...

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Introduction Ignorance Depictive sincerity Range expressions References

Truth value judgment experiment

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Introduction Ignorance Depictive sincerity Range expressions References

Materials

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‘True’ conditions (superlative modifiers)

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Introduction Ignorance Depictive sincerity Range expressions References

‘True’ conditions (superlative modifiers)

sup:upward:on There are at least 4 butterflies.

Elizabeth Coppock (BU) Range Expressions 25 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

‘True’ conditions (superlative modifiers)

sup:upward:on There are at least 4 butterflies. sup:upward:off There are at least 3 butterflies.

Elizabeth Coppock (BU) Range Expressions 25 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

‘True’ conditions (superlative modifiers)

sup:upward:on There are at least 4 butterflies. sup:upward:off There are at least 3 butterflies. sup:downward:on There are at most 4 butterflies.

Elizabeth Coppock (BU) Range Expressions 25 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

‘True’ conditions (superlative modifiers)

sup:upward:on There are at least 4 butterflies. sup:upward:off There are at least 3 butterflies. sup:downward:on There are at most 4 butterflies. sup:downward:off There are at most 5 butterflies.

Elizabeth Coppock (BU) Range Expressions 25 / 45

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‘True’ conditions (comparative modifiers)

Elizabeth Coppock (BU) Range Expressions 26 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

‘True’ conditions (comparative modifiers)

cmp:upward:on There are more than 3 butterflies.

Elizabeth Coppock (BU) Range Expressions 26 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

‘True’ conditions (comparative modifiers)

cmp:upward:on There are more than 3 butterflies. cmp:upward:off There are more than 2 butterflies.

Elizabeth Coppock (BU) Range Expressions 26 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

‘True’ conditions (comparative modifiers)

cmp:upward:on There are more than 3 butterflies. cmp:upward:off There are more than 2 butterflies. cmp:downward:on There are fewer than 5 butterflies.

Elizabeth Coppock (BU) Range Expressions 26 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

‘True’ conditions (comparative modifiers)

cmp:upward:on There are more than 3 butterflies. cmp:upward:off There are more than 2 butterflies. cmp:downward:on There are fewer than 5 butterflies. cmp:downward:off There are fewer than 6 butterflies.

Elizabeth Coppock (BU) Range Expressions 26 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Results for superlative modifiers

Elizabeth Coppock (BU) Range Expressions 27 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Results for superlative modifiers

98.5% There are at least 4 butterflies.

Elizabeth Coppock (BU) Range Expressions 27 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Results for superlative modifiers

98.5% There are at least 4 butterflies. 97.0% There are at least 3 butterflies.

Elizabeth Coppock (BU) Range Expressions 27 / 45

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Results for superlative modifiers

98.5% There are at least 4 butterflies. 97.0% There are at least 3 butterflies. 87.4% There are at most 4 butterflies.

Elizabeth Coppock (BU) Range Expressions 27 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Results for superlative modifiers

98.5% There are at least 4 butterflies. 97.0% There are at least 3 butterflies. 87.4% There are at most 4 butterflies. 57.6% There are at most 5 butterflies.

Elizabeth Coppock (BU) Range Expressions 27 / 45

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Why? Ignorance can’t be it.

“at most 5” 1 2 3 4 5 6 7 “at most 4” 1 2 3 4 5 6 7 “at least 4” 1 2 3 4 5 6 7

Elizabeth Coppock (BU) Range Expressions 29 / 45

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Adding highlighting

“at most 5” 1 2 3 4 5 6 7 “at most 4” 1 2 3 4 5 6 7 “at least 4” 1 2 3 4 5 6 7

Elizabeth Coppock (BU) Range Expressions 30 / 45

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A New Gricean Maxim

Maxim of Depictive Sincerity: If a sentence highlights a possibility, then the speaker considers it possible (or likely).

Elizabeth Coppock (BU) Range Expressions 31 / 45

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A New Gricean Maxim

Maxim of Depictive Sincerity: If a sentence highlights a possibility, then the speaker considers it possible (or likely). Strong pragmatic requirement!

Elizabeth Coppock (BU) Range Expressions 31 / 45

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A New Gricean Maxim

Maxim of Depictive Sincerity: If a sentence highlights a possibility, then the speaker considers it possible (or likely). Strong pragmatic requirement! Violation of strong pragmatic requirements can lead people to judge true sentences as false.

Elizabeth Coppock (BU) Range Expressions 31 / 45

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Back to the Romney example

“Right now, the [Congressional Budget Office] says up to 20 million people will lose their insurance as Obamacare goes into effect next year.”

Elizabeth Coppock (BU) Range Expressions 32 / 45

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What about at least 3?

“at least 3” 1 2 3 4 5 6 7

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Question

What if multiple possibilities are highlighted, including one that entails the speaker’s information state?

Elizabeth Coppock (BU) Range Expressions 34 / 45

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Disjunctions and highlighting

There are 1 or 2 pianos in the picture.

Elizabeth Coppock (BU) Range Expressions 35 / 45

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Disjunctions and highlighting

There are 1 or 2 pianos in the picture. 1 2 3 4 5 6 7

Elizabeth Coppock (BU) Range Expressions 35 / 45

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Disjunctions and highlighting

97.5% There are 1 or 2 pianos in the picture. 1 2 3 4 5 6 7

Elizabeth Coppock (BU) Range Expressions 35 / 45

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Disjunctions and highlighting

There are 2 or 3 elephants in the picture.

Elizabeth Coppock (BU) Range Expressions 36 / 45

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Disjunctions and highlighting

There are 2 or 3 elephants in the picture. 1 2 3 4 5 6 7

Elizabeth Coppock (BU) Range Expressions 36 / 45

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Disjunctions and highlighting

97.5% There are 2 or 3 elephants in the picture. 1 2 3 4 5 6 7

Elizabeth Coppock (BU) Range Expressions 36 / 45

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Doubly-bounded range expressions

100% There are 4 to 7 potatoes in the picture.

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Experiment: Doubly-bounded range expressions

Elizabeth Coppock (BU) Range Expressions 38 / 45

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Conditions (superlative modifiers)

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Conditions (superlative modifiers)

sup:range:on There are at least 2 and at most 4 butterflies.

Elizabeth Coppock (BU) Range Expressions 39 / 45

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Conditions (superlative modifiers)

sup:range:on There are at least 2 and at most 4 butterflies. sup:range:off There are at least 3 and at most 5 butterflies.

Elizabeth Coppock (BU) Range Expressions 39 / 45

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Conditions (superlative modifiers)

sup:range:on There are at least 2 and at most 4 butterflies. sup:range:off There are at least 3 and at most 5 butterflies. sup:bound:on There are at least 2 and at most 4 butterflies.

Elizabeth Coppock (BU) Range Expressions 39 / 45

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Conditions (superlative modifiers)

sup:range:on There are at least 2 and at most 4 butterflies. sup:range:off There are at least 3 and at most 5 butterflies. sup:bound:on There are at least 2 and at most 4 butterflies. sup:bound:off There are at least 3 and at most 5 butterflies.

Elizabeth Coppock (BU) Range Expressions 39 / 45

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Conditions (path modifiers)

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Conditions (path modifiers)

path:range:on There are 2 to 4 butterflies.

Elizabeth Coppock (BU) Range Expressions 40 / 45

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Conditions (path modifiers)

path:range:on There are 2 to 4 butterflies. path:range:off There are 3 to 5 butterflies.

Elizabeth Coppock (BU) Range Expressions 40 / 45

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Conditions (path modifiers)

path:range:on There are 2 to 4 butterflies. path:range:off There are 3 to 5 butterflies. path:bound:on There are up to 4 butterflies.

Elizabeth Coppock (BU) Range Expressions 40 / 45

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Conditions (path modifiers)

path:range:on There are 2 to 4 butterflies. path:range:off There are 3 to 5 butterflies. path:bound:on There are up to 4 butterflies. path:bound:off There are up to 5 butterflies.

Elizabeth Coppock (BU) Range Expressions 40 / 45

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Results

Elizabeth Coppock (BU) Range Expressions 41 / 45

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Proposal: Two strong pragmatic constraints

  • Highlight all possibilities you believe.
  • Do not highlight non-believed possibilities.

Elizabeth Coppock (BU) Range Expressions 42 / 45

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Discussion

  • This proposal explains the amelioration of range edge effects

by doubly-bounded range expressions.

  • It also explains why they do not disappear entirely.
  • Remaining mystery: Why disjunctions highlighting

non-believed possibilities do not behave the same way.

Elizabeth Coppock (BU) Range Expressions 43 / 45

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Thank you!

Elizabeth Coppock (BU) Range Expressions 44 / 45

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Introduction Ignorance Depictive sincerity Range expressions References

Biezma, María. 2013. Only one at least: Refining the role of discourse in building alternatives. In University of Pennsylvania Working Papers in Linguistics, vol. 36, 11–19. Penn Linguistics Club. Blok, Dominique. 2015. The semantics and pragmatics of directional numeral

  • modifiers. Proceedings of SALT 25. 471–490.

Büring, Daniel. 2008. The least at least can do. In Charles B. Chang & Hannah J. Haynie (eds.), 26th West Coast Conference on Formal Linguistics, 114–120. Somerville, MA: Cascadilla Press. Coppock, Elizabeth & Thomas Brochhagen. 2013. Raising and resolving issues with scalar modifiers. Semantics and Pragmatics 6(3). 1–57. doi:10.3765/sp.6.3. Cummins, Chris & Napoleon Katsos. 2010. Comparative and superlative quantifiers: Pragmatic effects of comparison type. Journal of Semantics 27. 271–305. doi:10.1093/jos/ffq006. Cummins, Chris, Uli Sauerland & Stephanie Solt. 2012. Granularity and scalar implicature in numerical expressions. Linguistics and Philosophy 35(2). 135–169. Geurts, Bart & Rick Nouwen. 2007. At least et al.: The semantics of scalar

  • modifiers. Language 83. 533–559. doi:10.1353/lan.2007.0115.

Elizabeth Coppock (BU) Range Expressions 44 / 45

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Kennedy, Christopher. 2015. A “de-Fregean” semantics (and neo-Gricean pragmatics) for modified and unmodified numerals. Semantics and Pragmatics 8. 1–44. doi:10.3765/sp.8.10. Mayr, Clemens & Marie-Christine Meyer. 2014. More than at least. Slides presented at the Two days at least workshop, Utrecht. Nouwen, Rick. 2010. Two kinds of modified numerals. Semantics & Pragmatics 3. 1–41. doi:10.3765/sp.3.3. Schwarz, Berhard, Brian Buccola & Michael Hamilton. 2012. Two types of class B numeral modifiers: A reply to Nouwen 2010. Semantics & Pragmatics 5. 1–25. Schwarz, Bernhard. 2016. At least and ignorance: A reply to Coppock & Brochhagen (2013). Semantics and Pragmatics 9. early access. doi:10.3765/sp.9.10. Westera, Matthijs & Adrian Brasoveanu. 2014. Ignorance in context: The interaction of modified numerals and QUDs. In Semantics and linguistic theory (salt), vol. 24, 414–431.

Elizabeth Coppock (BU) Range Expressions 45 / 45

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