Experiment I: Quantifier Spreading in English
Context 6: There are three bears, among them just one bear is holding three honeypots and the other two are not, just standing, a piglet, and an
4.10 Discussion
4.10.5 Transitive Constructions vs Intransitive Constructions
Through the discussion in the previous sections, we found that the children involved in the present experiment made more errors in the case of intransitive constructions than transitive constructions. In this section, details of the results of the two different constructions are shown. For the comparison, the sentences belonging to Group 1 are compared to those in Group 3, and the sentences in Group 4 to those in Group 7.
Category A: the sentences 1, 2, 3 vs. Category B: 20 ,2 1 ,2 2
<Table 27> Error rates and p-values between transitive and intransitive constructions
Category (Sentence No.) Error rate (%) p-value
A(l,2,3)/B(20,21,22) 51/72 <0.001
C(4,5,6)/D(23,24,25) 73/86 0.23
As shown in Table 27, a very high significant difference was found in the comparison of Categories A and B, with p<0.001. In the case of right spreading, the children made higher errors with intransitive sentences than with transitive sentences. However, in the case of left spreading, they made high errors in both cases, 73% and 86% respectively.
4.10.6 Bare Plurals
The children involved in this task showed an average 53% of non-adult-like responses (spreading errors) in sentences with bare plurals without an overt quantifier. These children were as concerned about the honeypot left out or being held by the other agent as they were with the sentences with universal quantifiers. They still gave symmetrical and exhaustive interpretations to the sentences with bare plurals. To compare the results from the sentences with bare plurals and those with universal quantifiers, four categories were made:
Category A: vs.
10. Are bears holding a honeypot?
Category C: vs.
14. Are bears holding honeypots?
Category B:
1. Is every bear holding a honeypot? 2. Is each bear holding a honeypot? 3. Are all the bears holding a honeypot? Category D:
7. Is every bear holding honeypots? 8. Is each bear holding honeypots? 9. Are all the bears holding honeypots?
<Table 28> Error rates and p-values between bare plurals and universal quantifiers Category (Sentence No.) Error rate (%) p-value
A(10)/B(l,2,3) 51/51 0.75
C(14)/D(7,8,9) 55/50 0.05
As we can see in Table 28, the children involved here did not show any difference in their interpretation between the sentences with bare plurals and those with universal quantifiers. The substitution of universal quantifiers into bare plurals in subject position of the simple transitive sentences did not have any effect on their interpretation. The big difference between the p-values 0.75 and 0,05 in the table, even though the difference of percentage rates are quite small between the categories A vs. B (51%/51%) and the categories C vs. D (55%/50%), looks odd. This is due to, as discussed in the previous section (see 3.10.1 for cross-reference), the evidence for differences between the success rates for different types of question comes from only some of the children: those who have responded to both types of question and who get some correct and some incorrect answers. If we combine the categories A & C and B & D together, the error rates and p-value between them are as in Table 29:
<Table 29> Error rates and p-values between bare plurals and universal quantifiers Category (Sentence No.) Error rate (%) p-value
A(10,14)/B(l,2,3,7,8,9) 53/51 0.73
The children treated bare plurals as belonging to the same category as universal quantifiers.
4.10.7 The+NPs
As has already been discussed, the+NPs has a quantifying effect just like universal quantifiers, and even adults give an exhaustive interpretation to it. In this section, the detailed figures about how much young children give the exhaustive interpretation to the+NPs are given and they are compared to those for universal quantifiers. Four categories are again made for the comparison: sentence 15 is compared to sentences 1,2 and 3; and 19 to 7, 8 and 9.
Category A: vs.
15. Are rAg bears holding a honeypot?
Category C: vs.
19. Are the bears holding honeypots?
Category B:
1. Is every bear holding a honeypot? 2. Is each bear holding a honeypot? 3. Are all the bears holding a honeypot?
Category D:
7. Is every bear holding honeypots? 8. Is each bear holding honeypots? 9. Are all the bears holding honeypots?
<Table 30> Error rates and p-values between rAg+NPs and universal quantifiers Category (Sentence No.) Error rate (%) p-value
A(15)/B(l,2,3) 43/51 0.39
C(19)/D(7,8,9) 47/50 0.006
No significant difference was found between the categories A and B, with p=.39, but it was found between C and D, with .006. If we combine the categories A & C and B & D together, error rates and p-value between them are as in Table 31:
<Table 31> Error rates and p-value between the+NPs and universal quantifiers Category (Sentence No.) Error rate (%) p-value
As shown in Table 31, 45% errors were found in the case of the+NPs and 51% errors in the case of universal quantifiers on average. Moderate strong evidence, p=0.04, is found in p-value test between A and B.
The comparison between transitive and intransitive constructions with the+NPs, without universal quantifiers, was made as follows:
Category A: vs. Category B:
15. Are the bears holding a honeypot? 26. Are the babies behind a mummy elephant?
19. Are the bears holding honeypots? 27. Are the babies behind mummy elephants?
<Table 32> Error rates and p-value between transitive and intransitive with the+NPs
Category (Sentence No.) Error rate (%) p-value
A(15,19)/B(26,27) 45/67 0.02
As shown in Table 32, 45% spreading errors were found in the case of transitive sentences and 67% in the case of intransitive sentences. More errors were found in the latter, but not significantly. The children involved in this task interpreted the babies as all the babies in the sentence "Are the babies behind a mummy elephant?", hence, as meaning "Are all the babies behind a mummy elephant?" and insisted that the sentence is true only when every baby is behind a mummy elephant. They gave an exhaustive interpretation to the+NPs, the babies. Further, they interpreted the same sentence, as meaning "Are the babies behind all the mummy elephants?", giving the exhaustive interpretation to the argument in adjunct position, a mummy elephant. This is similar to categorial syllogisms: for example, "All of the A are B" is interpreted as meaning "All of the A are B and all of the B are A".
Further, to find out the difference between the sentences with the+NPs and those with universal quantifiers in the case of intransitive constructions, the result
from the sentences 20, 21 and 22 can be compared to that from the sentences 26 and 27.
Category A: vs. Category B:
20. Is every ladybird on a caterpillar? 26. Are the babies behind a mummy elephant?
21. Is each ladybird on a caterpillar? 27. Are the babies behind mummy elephants?
22. Are all the ladybirds on a caterpillar?
<Table 33> Error rates and p-value between universal quantifiers and the+NPs in the case of intransitive construction
Category (Sentence No.) Error rate (%) p-value
A(20,21,22)/B(26,27) 72/67 0.23
As shown in Table 31, no significant difference was found between the sentences with universal quantifiers and the+NPSy with p=0.23. The children involved in this task made high errors in both cases, treating them as belonging to the same category, that is, quantifying elements.
In conclusion, the majority of English children involved in this experiment showed the phenomenon of quantifier spreading in all types of construction. They spread the scope of universal quantifiers such as every, each and all to the other argument in the sentence from the argument which contains them. It was found that when the other NP was placed in the adjunct position, that is, inside PP, the children made more spreading errors than in the case of its placement in the argument position. It was also found that they made higher errors in the case where the universal quantifiers occupied the object position, rather than the subject position.
The overall average spreading error rate was 68%: 58% of right spreading (sentences involved 1, 2, 3, 7, 8, 9, 20, 21 and 22); 80% of left spreading (4, 5, 6, 11, 12, 13, 23, 24 and 25). A very highly significant difference was found between right
and left spreading: the children made much higher errors in the case of left spreading than in the case of right spreading.
No significant difference was found between the three types of universal quantifiers, every, each and all: 68% errors in the sentences with every', 70% with each', and 67% with all, with p=0.94. The children did not make any difference in their interpretation, treating them as belonging to the same category, universal quantifiers. The syntactic and semantic distinctions between the quantifiers do not seem to affect children’s behaviour with universal quantification.
Further, no difference was found between sentences with a singular NP and those substituted with plural NPs: on average 62% errors in the former; and 66% in the latter. More specifically, to find out whether there is any difference between the lexical variations in subject position, the sentences 4, 5 and 6; 11, 12 and 13; and 16, 17 and 18 were compared. 73% errors were found in the first; 81% in the second; and 76% in the last. No significant difference was found between them, with p=0.25. The change of lexical item did not have any effect on children’s universal quantification.
More than half of the children involved, 53%, made similar spreading errors in the sentences with bare plurals: this is higher than the case of universal quantifiers, 51% (sentences involved: 1, 2, 3, 7, 8 and 9). Further, on average 51% spreading errors were found in the sentences with the+NPs (15, 19, 26 and 27). Again, the change of universal quantifiers into bare plurals or the+NPs in the same position did not have any effect on children’s comprehension with regard to universal quantification.
The results can be summarized in the following Tables: <Table 32> Spreading error rates: right/left
Right (1,2,3,7,8,9,20,21,22) Left (4,5,6,11,12,13,23,24,25)
<Table 33> Spreading error rates between lexical variations (sentences involved in brackets) every (1,4,7,11,16,20 23) each (2,5,8,12,17,21 24) all (3,6,9,13,18,22 25) bare plurals (10,14) the+NPs (15,19,26,27) 70% 71% 70% 53% 51%
<Table 34> Spreading error rates: transitive/intransitive+PP
Transitive (1,2,3,4,5,6) Intransitive+PP (20,21,22,23,24,25)
62% 79%
<Table 35> Spreading error rates with universal quantifiers and a singular NP/plurals/the+NPs uq- a singular NP (1,2,3,4,5,6) uq - plural NPs (7,8,9,11,12,13) uq - the+NPs (16,17,18) 62% 66% 76%