Experimental perspectives on the
semantics and pragmatics of plurality
JacopoRomoli
ulster.ac.uk
Collaborators
LynTieu
CoryBill
StephenCrain
Reading
The focus of today
(1) Emily
fed giraffes
The focus of today
(1) Emily
fed giraffes
The focus of today
(1) Emily fed giraffes
(2) Emily fed a giraffe
Multiplicity inferences
(1) Emily fed giraffes
⤳ Emily fed more than one giraffe
Multiplicity inferences
(1) Emily fed a giraffe
↛ Emily fed more than one giraffe
Multiplicity inferences
Plural morphology encodes a multiplicity meaning
(Chierchia 1998, Link 1983)
Multiplicity inferences
Reasons to believe that this is not the case
Multiplicity inferences as implicature
Plural morphology is compatible with singularities
Multiplicity inference arises as an implicature
(Sauerland et al 2005, Spector 2007, Zweig 2009, Ivlieva 2013, Mayr 2015)
Multiplicity inferences
(1) Emily fed giraffes
⤳ Emily fed more than one giraffe
Multiplicity inferences and implicatures
(1) Emily fed giraffes
⤳ Emily fed more than one giraffe
(2) Emily ate an apple or a pear
⤳ Emily didn’t eat an apple and a pear
Hypothesis
Multiplicity inferences are implicatures
Prediction
Everything being equal we expect multiplicity
inferences and implicatures to behave alike
Today
How this prediction has been tested in the literature
The plan
• Background on multiplicity inferences and implicatures
The plan
• Background on multiplicity inferences and implicatures
• The implicature approach to multiplicity inferences
The plan
• Background on multiplicity inferences and implicatures
• The implicature approach to multiplicity inferences
• Previous studies
The plan
•
•
•
•
Background on multiplicity inferences and implicatures
The implicature approach to multiplicity inferences
Previous studies
Our own two experiments
The plan
•
•
•
•
•
Background on multiplicity inferences and implicatures
The implicature approach to multiplicity inferences
Previous studies
Our own two experiments
Discussion and implications
The plan
•
•
•
•
•
•
Background on multiplicity inferences and implicatures
The implicature approach to multiplicity inferences
Previous studies
Our own two experiments
Discussion and implications
Further directions
Background
Multiplicity inferences
(1) Emily fed giraffes
⤳ Emily fed more than one giraffe
Multiplicity inferences
(1) Emily fed giraffes
= Emily fed more than one giraffe
Multiplicity inferences and negation
(1) Emily didn’t feed giraffes
≠ Emily didn’t feed more than one giraffe
Multiplicity inferences and negation
(1) Emily didn’t feed giraffes
= Emily didn’t feed any giraffe
Reason to believe it’s not literal meaning
This inference disappears under negation
Scalar implicatures
(2) Emily ate an apple or a pear
⤳ Emily didn’t eat both an apple and a pear
Scalar implicatures
(2) Emily ate an apple or a pear
= Emily ate an apple or a pear but not both
Scalar implicatures and negation
(2) Emily didn’t eat an apple or a pear
≠ Emily didn’t eat (an apple or a pear but not both)
Scalar implicatures and negation
(2) Emily didn’t eat an apple or a pear
= Emily didn’t eat an apple and didn’t eat a pear
Presence and absence
Both of these inferences disappear under negation
In sum
Multiplicity inferences and scalar implicatures
• how they arise
• how they disappear under negation
• their similarity
Deriving scalar implicatures
Scalar implicatures
(1) Emily ate an apple or a pear
⤳ Emily didn’t eat an apple and a pear
(2) Emily ate some of the apples
⤳ Emily didn’t eat all of the apples
Weak literal meanings
(2) Emily ate an apple or a pear
= Emily ate an apple or a pear or both
Scalar implicatures
(2) Emily ate an apple or a pear
⤳ Emily didn’t eat an apple and a pear
Weak literal meanings
(2) Emily ate some of the apples
= Emily ate some or all of the apples
Scalar implicatures
(2) Emily ate some of the apples
⤳ Emily didn’t eat all of the apples
Gricean reasoning
• Hear an utterance
• Comparison with alternative utterance
• If competitor stronger than assertion then false
Grice 1975, Horn 1972, Gazdar 1979, Sauerland 2004
Gricean reasoning
• The speaker said A
• The speaker might have said B
• If B is stronger than A, B is false
How do we obtain competitors?
Replace certain words in the assertion
<some, all>, <or, and> …
Deriving scalar implicatures
(1) Emily ate an apple or a pear
(2) Emily ate an apple and a pear
Deriving scalar implicatures
(1) Emily ate an apple or a pear
(2) Emily ate an apple and a pear
⤳ Emily didn’t eat an apple and a pear
Deriving their absence
(1) Emily didn’t eat an apple or a pear
≠ Emily didn’t (eat an apple or a pear but not
both)
Deriving their absence
(1) Emily didn’t eat an apple or a pear
(2) Emily didn’t eat an apple and a pear
(2) isn’t stronger than (1) hence no inference here
In sum
A scalar implicature algorithm
A theory of competitors
Deriving multiplicity inferences as
implicatures
Multiplicity inferences
(1) Emily fed giraffes
= Emily fed at least one giraffe
Multiplicity inferences
Plural and singular sentences are equivalent
Emily fed giraffes = Emily fed a giraffe
Multiplicity inference
(1) Emily fed giraffes
⤳Emily fed more than one giraffe
Two ingredients
• Enriching the Gricean algorithm
• Assumptions about the competitors of singular
and plural
Back to the Gricean reasoning
• The speaker said A
• The speaker might have said B
• If B is stronger than A, B is false
Adding an extra step
• The speaker said A
• The speaker might have said B
• B would have had C as an inference
• If B and C is stronger than A, B and C is false
Kratzer and Shimoyama 2002, Spector 2007, Fox 2007, Chierchia 2013
Competitors
• <some, all>
• <or, and>
• <plural, singular>
Competitors
SG
plural competes with singular
PL
Competitors
• <some, all>
• <or, and>
• <plural, singular>
• <singular, plural, more-than-one>
Competitors
MORE-THAN-ONE
SG
PL
singular competes with plural and more than one
Deriving multiplicity inferences as scalar
implicatures
<plural,singular>
(1) Emily fed giraffes
(2) Emily fed a giraffe equivalent by assumption
both mean = Emily fed at least one giraffe
The inference of the singular
(1) Emily fed a giraffe
⤳ Emily fed just one giraffe
The inference of the singular
<singular,plural,more-than-one>
(1) Emily fed a giraffe
(2) Emily fed more than one giraffe
(2) is stronger than (1)
The inference of the singular
(1) Emily fed a giraffe
(2) not (Emily fed more than one giraffe)
The inference of the singular
(1) Emily fed a giraffe but not more than one
= Emily fed just one giraffe
The inference of the plural
(1) Emily fed giraffes
(2) Emily fed a giraffe but not more than one
(2) is stronger than (1)
The inference of the plural
(1) Emily fed giraffes
(2) It’s false that (Emily fed a giraffe but not more than one)
= Emily fed more than one giraffe
Deriving the absence under negation
(3) Emily didn’t feed giraffes
≠ Emily didn’t feed more than one giraffe
Deriving the absence under negation
(1) Emily didn’t feed a giraffe
(2) Emily didn’t feed more than one giraffe
(2) is not stronger than (1) so no inference here
Deriving the absence under negation
(3) Emily didn’t feed giraffes
(1) Emily didn’t feed a giraffe
(1) is therefore equivalent to (3) so no inference here
In sum
A unified approach of the multiplicity inferences and scalar
implicatures
• can account for when they arise
• can account for their parallel behaviour under
negation
One last thing
Forcing multiplicity inferences under negation:
(1) Emily didn’t feed giraffes … she fed only one!
Finally
same for scalar implicatures
(2) Emily didn’t eat an apple or a pear … she ate
both!
One last thing
Whatever account for this mark reading with scalar
implicatures can be extended to multiplicity
inferences
In sum
Hypothesis:
Multiplicity inferences = Scalar implicatures
In sum
Prediction:
everything being equal they’ll behave uniformly
More precisely
We know that scalar terms differ in their rate of
implicature calculation in adults (Van Tiel et al 2016)
More precisely
The comparison with different populations gives
us a better angle at testing this prediction
Look for interactions
More precisely
Children and adults tend to differ on scalar implicatures
We expect a similar difference with multiplicity inference
Previous studies
More precisely
Children typically differ from adults in their behaviour with
scalar implicatures
(Paris 1973; Braine & Rumain 1981; Noveck 2001; Chierchia et al. 2001; Gualmini et al.
2001; Papafragou & Musolino 2003; Barner et al. 2011)
Scalar implicatures
(2) Bunny painted the car or the truck
⤳ Bunny didn’t paint both the car and the truck
(3) Some of the horses jumped over the fence
⤳ Not all of the horses jumped over the fence
Scalar implicatures
Some of the horses jumped over the fence
⤳ not ( all of horses jumped over the fence )
Implicature: NO
No implicature: YES
Scalar implicatures
Some of the horses jumped over the fence
⤳ not ( all of horses jumped over the fence )
Implicature: NO
No implicature: YES
Adults: NO
Children: YES
Scalar implicatures
Bunny painted the car or the truck
⤳ not ( Bunny painted the car and the truck )
Implicature: NO
No implicature: YES
Scalar implicatures
Bunny painted the car or the truck
⤳ not ( Bunny painted the car and the truck )
Implicature: NO
No implicature: YES
Adults: NO
Children: YES
Scalar implicatures
We expect a similar difference with multiplicity
inferences
Sauerland et al. (2005)
Tested 3-5-year-olds on plurals
Experiment: an alien from another planet asked
participants questions to learn about life on Earth
Sauerland et al. (2005)
(1) Does a dog have tails?
Multiplicity Inference:
Does a dog have more than one tail? (NO)
Sauerland et al. (2005)
(1) Does a dog have tails?
No Multiplicity Inference:
Does a dog have one or more tails? (YES)
Sauerland et al. (2005)
Results:
children gave more yes-responses than adults (96% yes)
Similar behaviour to what they do with scalar implicatures
Sauerland et al. (2005)
Limitations of the study (Pearson et al. 2010):
• Multiplicity Inferences typically disappear in polar
questions
Sauerland et al. (2005)
Limitations of the study (Pearson et al. 2010):
• Multiplicity Inferences typically disappear in polar
questions
• Stimuli involved generic interpretations: children could
have misinterpreted (1) as Do dogs have tails?
Our Experiments
Experiment 1
Tested 4-year-olds’ computation of multiplicity
inferences in both positive and negative sentences
Truth Value Judgment Task (Crain & Thornton 1998)
Experiment 1
Stories told through cartoon images on laptop
computer
Puppet appeared on screen to utter test sentences
Participants judged puppet’s statements by filling out
scorecard
Design
2x2x2 design
Group : adults vs. children
Number : SG vs. PL, between subjects
Polarity : Positive vs. Negative, within subjects
Each participant received 2 training items, 6 test items, and
8 control items (presented in pseudo-randomized order)
Design
Positive
Negative
Plural
Sue picked apples
Sue didn’t pick apples
Singular
Sue picked an apple
Sue didn’t pick an apple
Example Plural trial
Emily is visiting the pig farm today.
It’s lunchtime for the pigs.
Example Plural trial
Emily has an apple, and that’s just enough
to feed the first pig!
Example Plural trial
Oh no! What about the other pigs? The
farmer says, “That’s okay, Emily! I’ll feed
the others later!”
Example Plural trial
So in the end, Emily only fed this pig!
Example Plural trial
Experimenter: Hey Ellie, what happened in the story? Puppet: Emily fed pigs!
Target conditions
Positive
Negative
Plural
Emily fed pigs (target: NO)
Emily didn’t feed giraffes (target: NO)
Singular
Emily fed a pig (target: YES)
Emily didn’t feed a giraffe (target:
NO)
Positive controls
PL positive control
Sammy painted birds
(target: yes)
Singular positive control
Sammy painted a bird
(target: yes)
Negative controls
PL and SG negative controls
Sammy didn’t draw dogs (target: YES)
Sammy didn’t draw a dog (target: YES)
Negation controls
Sally didn’t eat the chocolate (target: YES)
Sally didn’t eat the apple (target: NO)
Participants
28 English-speaking children (4;01-5;09, M=4;11) tested at
Macquarie University
Excludes 2 children who did not correctly answer at least 6/8
controls
43 English-speaking adults tested at Macquarie University
Excludes 1 adult who did not pass at least 6/8 controls
[Exp.1] Singular results
100
% yes−responses
75
group
adult
50
child
25
POS:Emilyfedapig
NEG:Emilydidn’tfeedagiraffe
0
NEG
POS
Polarity
[Exp.1] Plural results
Multiplicity Inference computation
% MI responses
100
Group
Adult
50
Child
0
POS
NEG
Polarity
POS:Emilyfedpigs
NEG:Emilydidn’tfeedgiraffes
[Exp.1] Plural results
Multiplicity Inference computation
% MI responses
100
POS:No!=Multiplicityinference
NEG:Yes!=Multiplicityinference
Group
Adult
50
Child
0
POS
NEG
Polarity
POS:Emilyfedpigs
NEG:Emilydidn’tfeedgiraffes
[Exp.1] Plural results
Multiplicity Inference computation
% MI responses
100
Group
Adult
50
Child
0
POS
NEG
Polarity
A logit mixed model was /itted on the data; we then used 𝜒2 statistics with one degree of freedom
to compare models with and without given /ixed effects, revealing:
• Signi/icant effect of Polarity (𝜒2(1)=15.41, p<.001)
• Signi/icant effect of Group (𝜒2(1)=10.58, p<.01)
• No signi/icant interaction (𝜒2(1)=1.64, p=.20)
Summary
Significant effect of Polarity:
more Multiplicity Inferences in positive than in negative
sentences — consistent with scalar implicature approach
Multiplicity Inference computation
% MI responses
100
Group
Adult
50
Child
0
POS
NEG
Polarity
Summary
Significant effect of Group: children compute fewer
Multiplicity Inferences than adults — consistent with previous
scalar implicature findings
Multiplicity Inference computation
% MI responses
100
Group
Adult
50
Child
0
POS
NEG
Polarity
Summary
Question: how would the same children have performed on
standard cases of implicature?
Experiment 2
Tested 4-year-olds’ computation of multiplicity
inferences in both positive and negative sentences and
scalar implicatures targets
Experiment 2
Truth Value Judgment Task (Crain & Thornton 1998)
Stories told through cartoon images on laptop
Puppet appeared on screen to utter test sentences
Participants judged puppet’s statements by filling out
scorecard
Design
Factors:
Group : Children vs. Adults
Condition : PL vs. SI, within subject
(Within Plural condition) Polarity:
Positive vs. Negative, within subject
Example SI trial
Lion loves to help his mom with the groceries.
Look at these apples and oranges! Lion wants to
carry the fruit, but they’re very heavy!
Example SI trial
Lion carries these four apples over here.
Example SI trial
Then his arms are full, so he leaves the oranges
on the ground. So remember, Lion only carried
these four apples here!
Now let’s see if Ellie’s paying attention.
Example SI trial
Experimenter: Okay, Ellie, so Lion didn’t carry any oranges.
What about the apples?
Puppet: Lion carried some of the apples!
Example PL trial
Zebra is visiting his favourite garden today. Look at
these oranges and bananas! Zebra wants to pick the
fruit, but he only has a very small basket.
Example PL trial
Zebra picks this banana over here.
Example PL trial
Now he has no more room in the basket, so he leaves
the rest of the fruit in the tree. So remember, Zebra
only picked this banana here! Now let’s see if Ellie’s
paying attention.
Example PL trial
Experimenter: Okay, Ellie, so Zebra didn’t pick any oranges.
What about bananas?
Puppet: Zebra picked bananas!
Test conditions
Plural Positive test
Zebra picked bananas (target: NO)
Scalar Implicature test
Plural Negative test
Kangaroo didn’t pick pears (target: NO)
Lion carried some of the apples (target: NO)
Control conditions
Plural Positive control
Zebra carried watermelons (target: YES)
Negation control
Kangaroo didn’t carry the houses (target: YES)
Kangaroo didn’t carry the boxes (target: NO)
Plural Negative control
Sheep didn’t carry carrots (target: YES)
Participants
17 English-speaking children (4;01-5;05, M=4;07) tested at
Macquarie University, Australia
All children correctly answered at least 6/8 controls and were
included in analysis
27 English-speaking adults tested individually at Macquarie using
same materials
[Exp.2] Plural results
Multiplicity Inference computation
% MI responses
100
Group
Adult
50
Child
POS:Zebrapickedbananas
NEG:Kangaroodidn’tpickpears
0
POS
NEG
Polarity
[Exp.2] Plural results
Multiplicity Inference computation
% MI responses
100
Group
Adult
50
Child
0
POS
NEG
Polarity
A logit mixed model was /itted on the data; we then used 𝜒2 statistics with
one degree of freedom to compare models with and without given /ixed effects, revealing:
• Signi/icant effect of Polarity (𝜒2(1)=6.74, p<.01)
• Signi/icant effect of Group (𝜒2(1)=17.31, p<.001)
• Signi/icant interaction (𝜒2(1)=6,2, p<.01)
[Exp.2] PL vs. SI results
Inference computation
% Inference responses
100
Group
Adult
50
Child
0
MI
SI
Inference type
A logit mixed model was /itted on the data; we then used 𝜒2 statistics with
one degree of freedom to compare models with and without given /ixed effects, revealing:
• No effect of Inference Type (𝜒2(1)=.2, p=.66)
• Signi/icant effect of Group (𝜒2(1)=48.57, p<.001)
• No signi/icant interaction (𝜒2(1)=8e-04, p=.98)
Summary
Plural data: Significant effect of Polarity:
more Multiplicity Inferences in positive than in negative sentences — consistent
with Implicature approach
Summary
Plural data: Significant effect of Polarity:
more Multiplicity Inferences in positive than in negative sentences — consistent
with Implicature approach
Significant effect of Group:
children compute fewer Multiplicity Inferences than adults — consistent with
previous scalar implicature findings
Summary
•
Comparing Multiplicity Inference with “some” implicature:
•
No effect of Inference Type — consistent with Implicature approach
•
Significant effect of Group: children compute fewer inferences than adults
— consistent with previous implicature findings
•
No interaction: no evidence that the difference between groups with SIs is
different from that with MIs
Summary
•
Comparing Multiplicity Inference with “some” implicature:
•
No effect of Inference Type — consistent with Implicature approach
•
Significant effect of Group: children compute fewer inferences than adults
— consistent with previous implicature findings
•
No interaction: no evidence that the difference between groups with SIs is
different from that with MIs
➡
Data very much in line with an implicature approach to plurality
Discussion
Going back to the hypothesis
Scalar implicature approach to MIs:
Multiplicity inferences = Scalar implicatures
In sum
Prediction:
everything being equal MIs and SIs will behave uniformly
More precisely
Scalar diversity
(Van Tiel et al 2016)
Looking at the comparison with different
populations
More precisely
Children and adults tend to differ on scalar implicatures
We expect a similar difference with multiplicity inference
Our results
This is indeed what we found:
- The difference between adults and children with MIs
mirrors the difference between them with SIs
- Neither group treated the two inferences differently
Our results
These set of results is consistent with the scalar
implicature approach
Further directions
Follow up experiment:
Manipulating negative and positive with both inference type using
disjunctions (currently running)
Further directions
Other populations:
Comparing MIs and SIs in typical compared to other
populations to look for similar patterns
Further directions
Other populations:
Comparing MIs and SIs in typical compared to other populations to
look for similar patterns
MIs and SIs in individuals with Broca’s aphasia
Kennedy et al under review
Further directions
The inference of plural on mass nouns
In languages where plural can appear on mass nouns (e.g.
Greek, Turkish, Persian … )
Further directions
The inference of plural on mass nouns
In languages where plural can appear on mass nouns (e.g.
Greek, Turkish, Persian … )
a corresponding abundance inference
Further directions
In English
(1) *John spilt waters
Further directions
In Greek
(1) O Yanis ehise nera
The John spilt water-PL
Further directions
(1) O Yanis ehise nera
The John spilt water-PL
⤳John spilled much water
Further directions
(1) Emily fed pigs ⤳Emily fed more than one pig
(2) John spilt waters ⤳John spilt much water
Further directions
Intuitively the analogous inference of the plural on count nouns
Multiplicity inferences and abundance inferences
A unified account of the inferences of the plural
Kane et al 2015
Further directions
(1) O Yanis ehise nera
The John spilt water-PL
Further directions
(1) O Yanis ehise nera
The John spilt water-PL
In sum
A lot remains to be done on investigating experimentally the
inferences of plurals
In sum
A lot remains to be done on investigating experimentally the
inferences of plurals
- in comparison with other inferences
In sum
A lot remains to be done on investigating experimentally the
inferences of plurals
- in comparison with other inferences
- across populations
In sum
A lot remains to be done on investigating experimentally the
inferences of plurals
- in comparison with other inferences
- across populations
- across name types
Thanks!
Acknowledgements
•
We are grateful to the participants of our study at Macquarie.
•
The research leading to these results has received funding from:
‣ Australian Research Council Centre of Excellence in Cognition and its
Disorders (CE110001021)
‣ European Research Council under the European Union's Seventh Framework
Programme (FP/2007-2013) / ERC Grant Agreement n.313610, ANR-10IDEX-0001-02 PSL*, and ANR-10-LABX-0087 IEC
Appendix
Discussion: Early stages
•
Future work: how can we reconcile our findings from preschoolers with
findings from younger children? In particular:
‣
Children begin producing plural morphemes around 22 months of age
(Brown1973;Mervis&Johnson1991;Fensonetal.1994;Barneretal.2007)
24-month-olds display sensitivity to plurality when presented with multiple
cues of plural marking (verb marking, determiner some, -s morpheme)
(Woodetal.2009)
24-month-olds display sensitivity to plural meanings when presented with
the /s/ plural morpheme (Daviesetal.,Toappear)
‣
‣
Discussion: Early stages
•
Woodetal.(2009) show that 2-year-old children expect to find ‘more than
one’ object when they hear multiple cues of plurality (PL verbal agreement
are, determiner some, and PL -s), though not when PL is marked on the
noun alone
-
“Now, I am going to put some cars in the box. [...] Wow! There are some cars in
my box! Could you get the cars for me?”
“Now, I am going to put my cars in the box. Wow! I see my cars in my box!
Could you get my cars for me?”
-
Discussion: Early stages
•
Daviesetal.(Toappear) show that 24-month-olds can indeed demonstrate
understanding of plural morphology, but only when presented with the
voiceless /s/ allomorph, not the voiced /z/ allomorph
•
Indicates a role for phonetic salience in the acquisition of plural morphology
and its meaning
•
Future work: how does phonetic salience impact the acquisition of scalar
alternatives more generally?
Discussion: Early stages
•
•
•
•
•
In our task, 4-year-olds saw an exactly one situation but accepted a plural
description
Data from younger children suggest they are sensitive to the difference
between singular and plural, and can produce the Plural morpheme in some
appropriate contexts
Children may accept the Plural in contexts where they themselves would not
produce the Plural
Evokes a further parallel with Scalar Implicatures: children have been
reported to be pragmatically tolerant in the case of “some” (Katsos&
Bishop2011)
4-year-olds might associate plural morphology with “more than one”
meaning, but be more tolerant than adults are of the use of the plural in
singular contexts
Deriving plurality inferences •
PL and SG are equivalent:
(1)
•
SG/PL
Enrich SG (1a) by comparing it to More-than-one (2), yielding (3)
(2)
(3)
•
a. Jack fed a giraffe
b. Jack fed giraffes
Jack fed more than one giraffe
Jack fed a giraffe but not more than one
enriched SG
Enrich PL (1b) by comparing it to enriched SG (3), yielding (4)
(4)
Jack fed a giraffe and it’s false that (Jack fed a giraffe but
not more than one)
= Jack fed more than one giraffe
enriched PL
Deriving plurality inferences •
PL and SG are logically equivalent:
(1)
•
SG/PL
Enrich SG (1) by comparing it to More-than-one (2), yielding (3)
(2)
(3)
•
⟦giraffes⟧ = ⟦giraffe⟧ = { a, b, c, a⊕b, a⊕c, c⊕b, a⊕b⊕c }
⟦more than one giraffe⟧ = { a⊕b, a⊕c, c⊕b, a⊕b⊕c }
⟦giraffe⟧ ∧¬⟦more than one giraffe⟧ = { a⊕b⊕c }
enriched SG
Enrich PL (1) by comparing it to enriched SG (3), yielding (4)
(4)
⟦giraffes⟧∧¬(⟦giraffe⟧∧¬⟦more than one giraffe⟧) = { a⊕b, a⊕c, c⊕b, a⊕b⊕c }
enriched PL
Deriving plurality inferences •
Plural meanings as scalar implicatures (Spector 2007; Magri 2014)
‣ Plural (PL) and singular (SG) have meaning in (1a)
‣ SG is compared to (1b), yielding (2a)
‣ PL compared to (2a), generating (2b)
(1)
a. ⟦giraffes⟧ = ⟦giraffe⟧ = { a, b, c, a⊕b, a⊕c, c⊕b, a⊕b⊕c }
b. ⟦more than one giraffe⟧ = { a⊕b, a⊕c, c⊕b, a⊕b⊕c }
(2)
a. ⟦giraffes⟧ ∧¬⟦more than one giraffe⟧ = { a⊕b⊕c }
b. ⟦giraffes⟧∧¬(⟦giraffe⟧∧¬⟦more than one giraffe⟧) = { a⊕b, a⊕c, c⊕b, a⊕b⊕c }
SG/PL
enriched SG
enriched PL
DE environments
PL and SG have an equivalent weak plain meaning
• Under negation they have an equivalent strong plain meaning
and do not undergo strengthening
•
(1)
(2)
Jack didn’t feed a giraffe
Jack didn’t feed giraffes
Deriving plurality
Plural morphology has a semantics equivalent to that of singular
morphology
• The plurality inference is calculated as a kind of implicature (Spector
•
2007; Zweig 2009; Ivlieva 2013; Magri 2014)
•
Alternatives involve abstract PL and (enriched) SG features (Spector
2007; Magri 2014)
(1)
Jack fed giraffes
⤳ Jack fed more than one giraffe
Relevant alternatives
MORE-THAN-ONE
SG
PL
MORE-THAN-ONE
SG
PL
(Spector 2007)
Plural and Singular are logically
equivalent (=at least one)
• More-than-one entails Singular
(and Plural)
•
•
Singular has two scalar alternatives:
- <Singular, Plural>
- <Singular, More-than-one>
Relevant alternatives
MORE-THAN-ONE
SG
PL
MORE-THAN-ONE
SG
PL
(Spector 2007)
Plural and Singular are logically
equivalent (=at least one)
• More-than-one entails Singular
(and Plural)
•
•
Singular has two scalar alternatives:
- <Singular, Plural>
- <Singular, More-than-one>
Relevant alternatives
MORE-THAN-ONE
SG
PL
MORE-THAN-ONE
SG
PL
(Spector 2007)
Plural and Singular are logically
equivalent (=at least one)
• More-than-one entails Singular
(and Plural)
•
•
Singular has two scalar alternatives:
- <Singular, Plural>
- <Singular, More-than-one>
[Exp.1] Plural results
100
% yes−responses
75
group
adult
50
child
25
0
NEG
POS
Polarity
[Exp.1] Justifications for PL
100
% yes−responses
75
group
adult
50
child
NO-responses (40%)
• “Because she didn’t feed all of them.”
• “Because Emily didn’t feed all the pigs.”
• “Because she didn’t feed pigs, she
only fed a pig.”
• “Because she was only going to feed
that big fat pig.”
25
0
NEG
POS
Polarity
YES-responses (60%)
• “Because she feed a pig.”
• “Because she said the pig has been
feeded, and that happened.”
• “Because Emily fed pigs.”
[Exp.1] Justifications for PL
100
NO-responses (81%)
• “Because she said Emily didn’t feed the
giraffes, and she did.”
% yes−responses
75
group
adult
50
child
25
0
NEG
POS
Polarity
YES-responses (19%)
• “Because she feeded two biscuits for the giraffe.”
• “Because she only did one diamond.”
• “Because she coloured that one, but not the other ones.”
• “Because they didn’t eat that one, they eated that one.”
• “Because she picked that one and not the other ones.”
[Exp.2] Plural results
100
% yes−responses
75
group
adult
50
child
25
0
NEG
POS
Polarity
[Exp.2] PL vs. SI results
100
% yes−responses
75
group
adult
50
child
25
0
PL
SI
Condition
Conclusion
•
If Multiplicity Inferences are implicatures, all else being equal, we expect children to
perform similarly on the two kinds of inferences
Conclusion
•
If Multiplicity Inferences are implicatures, all else being equal, we expect children to
perform similarly on the two kinds of inferences
•
Our results indicate that children indeed compute fewer of both kinds of
inferences than adults
Conclusion
•
If Multiplicity Inferences are implicatures, all else being equal, we expect children to
perform similarly on the two kinds of inferences
•
Our results indicate that children indeed compute fewer of both kinds of
inferences than adults
•
No interaction group x inference type and correlational results from Exp.2 also
suggest a connection between the two kinds of inferences in development