The Universal Quantifiers in Acquisition
Recommended readings:
Crain, S., R. Thornton, C. Boster, L. Conway, D. Lillo-Martin and E. Woodams (1996) ‘Quantification without qualification’, Language Acquisition, 3(2), 83-153.
What do children have to learn in order to use the universal quantifiers every and all and the existential quantifier a?
1. The difference between nominal quantifier (every) and sentential quantifier (always)
2. The difference between quantifiers and referential expressions (the)
3. The syntactic structure and the semantic representation of the nominal quantifier
4. The mapping between syntactic structure and semantic representation (and its constraints)
Inhelder and Piaget, 1964
Even eight years old children do not understand the meaning of the universal quantifier.
Q: Is every square black?
A: No.
Q: Why?
A: Because there are some black circles
Some children who are shown a picture containing an ‘extra object’ provide systematic non-adult responses.
Why do children answer this way?
Could it be that children interpret the question in a symmetrical manner?
This is not compatible with what is known about quantification in adults.
What do children know about the universal quantifier?
The Partial Competence view
In addition to the adult interpretation, children’s grammars license a non-adult interpretation for sentences containing the universal quantifier every:
Philip 1995 - The Event Quantification Account
Method: Judgment with pictures, some with extra object and some with extra subject.
Is every farmer riding a donkey? ?Is a farmer riding every donkey
Children: No, there is another donkey. No, this farmer doesn't.
Children prefer perfect one-to-one symmetrical interpretations with universal quantification, and quantify over entire events rather than objects, suggesting that children and adults exploit different logical forms. They misanalyze the universal quantifier every, interpreting it (roughly) as an unselective binder quantifying over events.
(1) For every event e, such that a farmer or a donkey takes part in e, e is an event of a farmer riding a donkey.
Drozd 2001 - The Weak Quantification Account (Presuppositionality Account)
Children misanalyze the universal quantifier every, interpreting it as a weak quantifier, like many in (2).
(2) Many Scandinavians won the Nobel Prize
Meaning: Among Nobel Prize winners, there are many Scandinavians
(3) For every donkey, a farmer is riding the donkey.
For "is every farmer riding a donkey?", adult speakers must represent two distinct sets, a presupposed set of farmers and a set of donkey-riding farmers and check if they are identical. Children compare the set of donkey-riding farmers they see not with a presupposed set of farmers but with what they consider to be the normal or expected frequency of donkey-riders given the farmers in the context. This analysis stem from the presuppositions children have when presented with a picture before the question is asked.
Problems: Continuity, Learnability, Conservativity, Compositionality
Why would children do it and how do they get out of this non-adultlike situation?
Why might children think there is a ‘missing’ farmer?
Drozd, Kenneth f. and van Loosbroek, Erik. (2006). The effect of context on children’s interpretations of universally quantified sentences. In Veerle van Geenhoven (ed.) Semantics Meets Acquisition, Dordrecht: Kluwer. - TALI
The Full Competence view
Children have the adult knowledge. Their non-adult behavior is an experimental artifact.
Freeman et al., 1982 - Every, All and Principles of Discourse
“When a speaker asks a question about the presence of ‘all the Xs’, he is implicitly requesting the hearer to carry out an exhaustive search to check that no X is missing. Asking someone such a question is only legitimate ‘socio-dialogically’ if there is at least the possibility that some X is (or some Xs are) in actuality missing.”
(p. 64)
“… children try to understand what people mean, not only what words mean” (p. 69).
Brooks & Braine 1996 -
Subjects: children ages 4-10
Task: Picture selection testing comprehension
All of the men are carrying a box There is a man carrying all of the boxes
Findings: 4 years old - 83% correct responses, 5 years old - 90% correct responses.
Children, like adults, understand the basic property of universal quantifiers. They know that universal quantifiers such as all and every function like modifiers which quantify over the noun phrase which contains them.
The Salience Hypothesis:
Differences in children’s responses across tasks might be due to the salience of the objects that figure into children's interpretation (e.g., Gordon, 1996).
Roeper, T., U. Strauss, and B. Z. Pearson: 2004, ‘The acquisition path of quantifiers: Two kinds of spreading’. Ms. UMass, Amherst HERMINA
Crain et al., 1996 – The Condition of Plausible Dissent
Children’s symmetrical interpretations are errors due to flaws in experimental design. They have no difficulty with the interpretation of quantifiers if "felicitous" contexts are provided.
Basic assumptions:
· Children try to understand what people mean
· Questions, like other utterances, should be pragmatically adequate (Felicity Conditions)
· Yes/No questions are asked only when there are two possible answers (Plausible Dissent)
· If a question is inadequate for the context (there is only one answer), children will try to "fix" it.
> The task should present situations in which both options are possible
Subject: 14 children ages 3;5 - 5;10 who gave symmetrical responses on Philip's task.
Task: Truth value judgment with props
Characters and Crucial Props:
· Three skiers (a mom and her two girls)
· Five bottles of soda and five cups of apple cider
Protocol:
Situation: After skying
Mother: Let’s go in now and get a drink <mom and girls go over to drinks set out on a table>. I’ll have a cup of this nice hot apple cider. This will help calm me down <mom takes a cup of cider>.
Girl 1: Oh, look at these sodas. I want this bottle of orange soda.
Girl 2: I want this bottle of cola.
Mom: Girls, don’t take a bottle of soda. You should have a cup of hot apple cider so you get nice and warm. You can have soda another time.
Girl 1: OK. I’ll take this cup; it’s full to the top.
Girl 2: I want a full cup too. Are any of these other cups of cider full? Oh, this one looks very full. I’ll have this one. Mmm, it’s good.
Kermit: That was a hard story, but I think I know something that happened. Every skier drank a cup of hot apple cider.
Child: Yes.
Findings: 88% yes responses. They even produced sentences with the universal quantifier in similar situations.
Conclusions:
1. Children’s non-adult responses fail to emerge in tasks which satisfy the felicity conditions of asking yes/no questions, or making positive and negative judgments
2. Children distinguish the nominal quantifier from the sentential quantifier and know its meaning.
Do children know how to map semantic relations onto syntactic structure?
All the above sentences had a linear mapping and did not require syntactic operations.
Which structure can resolve this issue? Quantifier Raising (QR)
"Every dwarf ate a pizza" is ambiguous.
(1) For every X, X a dwarf, there is a Y, Y a pizza, such as X ate Y
(2) There is a Y, Y a pizza, for every X, X a dwarf, X ate Y
By the second reading, the existential quantifier has a wide scope, which does not stem from the linearity of the sentence. This is achieved by syntactic QR before semantic interpretation.
Do children do QR?
Crain at al (1996) - children accept the second reading in 92% of the cases.
Q: Is this the end?
A: No. The second reading is a subset of the universal reading.
Q: So? Which structure can resolve this issue?
"A flower pot was placed in front of every house" is ambiguous
(1) There is Y, Y a flower pot, for every X, X a house, Y was placed in front of X
(2) For every X, X a house, there is a Y, Y a flower pot, such as Y was placed in front of X
By the second reading, the universal quantifier has a wide scope, which does not stem from the linearity of the sentence.
Brooks & Braine (1996)
80% of 4 years old accepted the second reading for "a boat is built by each boy"
Conclusion: Children generate the syntactic structure before mapping iot onto the semantic interpretation.
Predictive and Non-predictive Mode in Acquisition -
Logical Words: Some and Or
Recommended Reading: Chierchia, G., S. Crain, M. T. Guasti, and R. Thornton (1998) “'Some' and 'or': A study on the emergence of Logical Form.” In Proceedings of the 22nd Boston University Conference on Language Development, 97-108. Sommerville, MA: Cascadilla Press.
Semantics and Pragmatics of some and or?
Judgments of the truth value of sentences with logical words such as some and or depend on two systems:
Semantic knowledge - permitting judgments of truth in felicitous contexts
Pragmatic knowledge - Grice’s Principle of Cooperation, articulated into specific maxims of relevance, quantity, etc.
The dog or the lion chased the cat
• Semantically, A or B is true when A, B, or A&B are true
• Pragmatically, A or B implies not (A and B) – either A is true or B is true but not both.
Some dog chased the cat
• Semantically, some A is true when one A, two As … Every A are true
• Pragmatically, some A implies not (every A) – any number of As smaller than all is true
Prediction: As soon as children become “cooperative”, they will display adult-like behavior in their use of logical words
Scalar Implicatures
Scalar Terms: Some, many, most, every
The truth conditions for some and every are related
Every (many, most) boy swam => Some boy swam
The truth conditions for some and every are in a subset/superset relation
“Some boy swam” is true in many circumstances:
every boy swam
...
two boys swam
one boy swam
“Every boy swam” is true in just one of these circumstances - every boy swam
Scalar terms: or, and
The truth conditions for and and or are also in a subset/superset relation
Fred bought a hamburger and a hot dog (S1) => Fred bought a hamburger or a hot dog (S2)
A scalar (conversational) implicature
If you know there was pizza and ice cream, then using or instead of and is odd. Use of or is felicitous in circumstances of uncertainty.
A or B conversationally implies not A and B
Some A conversationally implies not every A
A Pragmatic Implicature
(1) Some student brought wine and cheese
(2) Some student brought wine and some student brought cheese
S1 entails S2 but not vice versa
• Adults see easily that if (2) is true, (1) isn’t necessarily true
• They have some difficulty seeing that if (1) is true, (2) is also true
Sharon Armon-Lotem
Universal Quantifiers in Acquisition
Why?
If the speaker knows that the same person performed both actions, the more cooperative way of saying so is:
Some student bought wine and cheese
· The difficulty with the judgment is due to a pragmatic implicature of disjointness that arises from two occurrences of the indefinite NP, some N.
· The implicature of disjointness arises from two occurrences of the indefinite NP, some N.
· The implicature can be suspended in certain contexts, e.g., when there is uncertainty about the outcome
Contexts which trigger the implicatures are implicature raising contexts
Contexts in which the scalar implicature does not arise are implicature erasing contexts
When is the implicature erased? Conditions of Uncertainty
Making a Bet: I bet that John will pick a red circle or a blue triangle
Making a Prediction: I predict that John will pick a red circle or a blue triangle
These observations led to reexamining the conclusion that children's logical reasoning does not conform to classical logic
· Previous studies used implicature raising context
· The findings leave open the possibility that children know both the semantics and the pragmatics constraints.
Prediction: children will behave differently in implicature raising contexts and implicature erasing contexts
The descriptive mode - implicature raising context
• In the descriptive mode (i.e., an extensional context), the sentence in (1a) will be judged as false in the natural context, in which (1b) is true (i.e., if every boy ate a Tootsie-Roll):
(1) a. Some boy ate a Tootsie-Roll
b. Every boy ate a Tootsie-Roll
The predictive mode - implicature erasing contexts.
• The implicature can be suspended given the appropriate context, e.g., in the predictive mode (an intensional context), as shown in (2):
(2) Jay invited his three best friends, Paul, Peter and Mike for a post-Halloween feast, where they were planning to eat all the candies they got. His mom said: “I expect that some boy will eat Tootsie-Rolls.” Suppose that they all ate Tootsie-Rolls. Was Jay’s mother right?
• Adults accept this.
The question is whether children recognize the implicature as pragmatic and can cancel it in appropriate contexts, thus using or and some with a 'pure semantic' interpretation.
Strategy: test them in both contexts.
Chierchia, G., S. Crain, M. T. Guasti, and R. Thornton (1998) “'Some' and 'or': A study on the emergence of Logical Form.” In Proceedings of the 22nd Boston University Conference on Language Development, 97-108. Sommerville, MA: Cascadilla Press. CHANNY
Conclusion (repeated):
Children semantic knowledge is consistent with classical logic
Children are sensitive to certain pragmatic principles
The Acquisition of scalar implicatures - the data revisited
Recommended Reading: Noveck, I.: 2001, ‘When children are more logical than adults: Experimental investigations of scalar implicature’, Cognition 78, 165–188.
Smith (1980) - Do some elephants have trunks? Yes!
A question - no felicity conditions
Brain and Rumain (1981/3) - Actually argue that children favor the exclusive reading - this led to Chierchia et al (1998)
Chierchia et al (1998)
Descriptive vs. predictive mode:
Children semantic knowledge is consistent with classical logic
Children are sensitive to certain pragmatic principles
(1) Children can consistently access the inclusive-or reading of disjunction.