Drozd (1998) also suggests a context dependent explanation called the Weak Quantification Hypothesis, focusing on the fact that children are dependent on context when they deal with quantifiers in a sentence. Before we discuss Drozd’s hypothesis in detail, we had better look at the difference between ’weak’ and ’strong’ quantifiers.
Milsark (1977) defined ’weak’ determiners as those which create NPs which sound good in there is or there are sentences, NPs with strong determiners sound odd in there contexts, as we can see in the following sentences:
(31) There is book . . . There are some apples . . . There are two ladybirds . . . There are many children . . .
There is a few people . . . (in some dialects) There zxq few people . . .
There is no space . . . *There is the book . . . *There are both . . . *There are a l l . . . *There is every . . . *There is each . . . *There are m o st. . . *There are neither. . .
Barwise and Cooper (1981, p. 182) then made a division between weak and strong quantifiers, as shown in (32):
(32) Weak quantifiers: a, some, one, two, three, many, a few , few, no Strong quantifiers: the, both, all, every, each, most, neither
Given a simple sentence of the form [D N is a N / are Ns], the determiner contained in it is defined as:
(i) positive strong if it is judged automatically valid; (ii) negative strong if contradictory; or
(iii) weak if contingent on the interpretation.
For example, every train is a train is true in every model, neither train is a train is false in every model in which it is defined and many trains are trains is true just in case there are many trains. Therefore, every, neither and m any are classified as positive strong, negative strong and weak, respectively.
Drozd (1998) proposes that weak quantifiers, unlike strong quantifiers, have particular properties of contextual dependence and inference, and argues that young children actually interpret universal quantifiers as weak quantifiers, when they are faced with sentences such as All the boys are riding an elephant. To explain spreading errors by children, he introduces two conditions: Symmetry and Intersectivity, as in (33):
(33) Drozd (1998)
Symmetry Property: Det(N)(VP) iff Det(VP)(N)
(Two/Many/* All the/*Many of the) boys are riding an elephant iff (Two/Many/* All the/*Many of the) elephant-riders are boys.
Intersectivity Property: Det(N)(VP) iff Det(NnVP)(N)
(Two/Many/* All the/* Many of the) boys are riding an elephant iff (Two/Many/* All the/*Many of the) boys who are riding an elephant are riding an elephant.
Focusing on the fact that sentences with weak quantifiers (e.g., two, many) and sentences with proportional or strong quantifiers (e.g., every, many o f the, two o f the) in subject position exhibit different inferential properties, he argues that only sentences with weak quantifier subjects observe the above Symmetry and Intersectivity conditions.
According to the Symmetry Property, a determiner quantifier is symmetric if either N or VP can be used to restrict the domain of quantification for the determiner. Drozd (1998) gives the example of the sentence. Many Americans won an Olympic medal in Atlanta. He explains that in this sentence the (weak) cardinal quantifier many is symmetric because its value can be fixed by appealing to what we expect 'many' Ns (Americans) should be or what we expect 'many' VPs (Olympic medal winners in Atlanta) to be. In the former case, the sentence is false, because the 200 or so American medal winners in Atlanta do not constitute 'many' of 265 million Americans; for example, it is not true that Many Americans are Olympic medal winners. In the latter case, however, since Americans won more Olympic medals than any other nationality in Atlanta, constituting comparably 'many' of the medal winners, for example, it is true that Many Olympic medal winners were Americans. On the other hand, strong determiner quantifiers do not show this kind of interpretive flexibility. For example, a sentence like All the Americans won an Olympic medal in Atlanta, is false because all the Americans could not be Olympic medal winners. Obviously there is no flexibility in interpretation here.
The hypothesis predicts that children interpret universal determiner quantifiers like every/all the in the question Are all the hoys riding an elephant? in the context
of three boys riding an elephant each and an extra elephant, as symmetric determiner quantifiers, contrary to normal adult behaviour. Children are expected to assign a value to all the based on the expected number of elephant riders in VP rather than on the expected number of boys in N, as in the case of cardinal many. The expected number of elephant riders in the context is four, but the actual number of elephant riders is only three. Therefore children incorrectly answer no to the question.
On the other hand, given a context in which there are four boys, of whom three are riding an elephant each and one boy is alone, children interpret all the as an intersective determiner quantifier. That is, children ignore the extra boy in the context because it is not an instance of a boy who is riding an elephant and so lies outside the domain of quantification for intersective all the in the sentence Are all the boys riding an elephant?. Children incorrectly answer yes to the question because every elephant-riding boy is indeed riding at least one elephant
However, Drozd (1998) did not make explicit what precisely children are supposed to know about 'weak' and 'strong' quantifiers and how a child eventually learns the strong quantification system of his/her language.
2.12 Concluding Remarks
As reviewed above, the previous researchers, except Crain et al. (1996) which used a different methodology, found evidence for young children's quantifier spreading and tried to explain the phenomenon in terms of their own hypothesis or theoretical assumptions. Some treated it in terms of non-linguistic factors, some tried to explain it from a pragmatic discourse point of view, and some gave a purely linguistic analysis of the same phenomenon. Inhelder and Piaget (1958; 1964) tried to explain it in terms of non-linguistic, that is, cognitive, factors, and suggested that the spreading error disappears in the maturation of their logical thinking at the stage
of emergence of concrete operational reasoning which, they argue, comes around the age of seven or eight. Bucci (1978) also gave a maturational kind of explanation with regard to children's understanding of quantifiers, suggesting that children's understanding of syntactic structure underspecifies the scope of universal quantifiers. Both theories, however, fail to provide the actual representations that children assign to sentences with universal quantifiers.
On the other hand, Roeper and Matthei (1974), Philip and Aurelio (1991), Roeper and de Villiers (1991), and Philip (1995) tried to explain the same phenomenon from a purely linguistic point of view. Roeper & Matthei's quantifier- as-adverb hypothesis is quite convincing, positing that quantifiers initially have an adverbial character, and so unselectively bind arguments available in the sentence (cf. Lewis (1975)), but they also fail to give systematic and functional explanations to answer why specially young children treat quantifiers differently from adults and what causes their unique interpretation. Philip's (1995) event quantification hypothesis provides a more systematic analysis with regard to the children's universal quantification, but it fails to explain how and when children acquire quantification over individuals after they have acquired quantification over events. Drozd (1998) claims that young children treat strong quantifiers like every and all as weak quantifiers like two and many^ but he does not make explicit what children know about 'weak' and 'strong' quantifiers and further how they eventually learn the strong quantification system in their acquisition.
Donaldson and Lloyd (1974) tried to explain the phenomenon in terms of spatial relations, restricting it to the concepts of 'spatiality' or 'canonicity,' and Freeman et al. (1982) tried to account for it in terms of pragmatic (discourse) analysis factors, suggesting that the phenomenon occurs from the influence of different 'topic- setting cues' so that children's behaviour with the quantification is understandable from the discourse point of view. Even more strongly, Crain et al. (1996) deny the existence of children's symmetrical responses to universal quantification which had
been reported in previous research since Inhelder and Piaget, and claim that all the errors found in children in the previous research are due to the use of infelicitous contexts in the experimental design. They claim that young children, like adults, have full grammatical knowledge of universal quantification. On the other hand. Brooks and Braine (1996) suggest that quantifier spreading errors occur when children mistakenly assign an exhaustive representation to a sentence with a universal quantifier instead of the use of an appropriate collective or distributing representation.
What 1 would like to stress here is that quantifier spreading is a general phenomenon which is found in a certain young age group of children between approximately four to seven or eight, until their grammatical knowledge is fully developed. This spreading occurs crosslinguistically and perhaps universally in a range of constructions. Here 1 concentrate on why young children typically give a different interpretation from adults in certain contexts and try to explain what the difference between them is with regard to universal quantification.
In addition, this phenomenon is reported to be found in adult aphasies as well (Avrutin and Philip (1994); Saddy (1995)).^ This fact makes me think that this phenomenon might be neither exclusively cognitive nor exclusively linguistic, but dependent on contributions from the language faculty and from the central system of the child's mind in the sense of Fodor (1983). That is, a non-linguistic cognitive factor seems to be clearly operative in this phenomenon. However, this is not simply 'the plausibility conditions' or 'infelicitous contexts' suggested by Freeman et al. or Crain et al., but rather comes from interaction among the components of the interpreter's (here children) mind or mind modules. Therefore, in the next chapter, 1 will develop a version of the Modularity Hypothesis (borrowing the term from Fodor's Modularity of Mind) to explain the children's non-adult like interpretation with regard to universal quantification and attempt to explain it, based on the ideas of Fodor's (1983) (perceptual) modules. Smith and Tsimpli's (1995) "conceptual"
modules (or Tsimpli and Smith's (1998) "quasi-modules"), and Sperber and Wilson's (1986; 1995) Relevance Theory.
At the same time, this spreading phenomenon by children is also argued to be clearly 'linguistic' in origin, due to the fact that spreading errors are only found in a certain young age group and then disappear. Something must be missing in this period of acquisition. Therefore, I assume that the phenomenon of quantifier spreading can be determined by a combination of clearly 'cognitive' and clearly 'linguistic' factors. That is, both non-linguistic cognitive and linguistic factors are operative in children's behaviour with universal quantification. This will be argued in detail in the next chapter.