The interaction of quantifiers and context in determining discourse focusWilliam Levine

University of Arkansas

Background

Studies of quantifiers have shown a strong dissociation between the quantity apparently denoted and the derived meaning (e.g., Sanford, Moxey, & Paterson, 1996). For instance, Sanford et al. showed that few and a few denoted 13% and 15% of a set of individuals (as in Few/A few of the students were at the meeting), respectively. However, when participants were asked to write continuations for such sentences given the prompt They ..., sentences beginning with A few produced continuations in which 97% of the time the referent of they was the students at the meeting. By contrast, sentences beginning with Few produced continuations in which 67% of the time the referent of they was the students who did not go to the meeting. These results not only demonstrate the powerful influence of quantifiers on meaning, but are remarkable because they suggest that people are willing to interpret (or produce) pronouns that refer to implicit entities.

Moxey and Sanford and their colleagues have labeled this sort of finding complement set focusing, because the interpretation of quantifiers such as few appears to lead to focus on the complement of the set of individuals for whom the predicate is true. Moxey, Sanford, and Dawydiak (2001) have argued that complement set focusing is driven by implicit denials associated with certain negative quantifiers. According to this implicit denial hypothesis, negative quantifiers cause comprehenders to invoke an inferential process to search for a reason why the predicate of a quantified statement might be false for the complement set. Evidence for this hypothesis has come primarily from content analysis of continuations that refer to the complement set, which tend to provide reasons why the predicate is false for the complement set, suggesting that negative quantifiers invoke denial of a supposition of a state of affairs (e.g., more students were expected at the meeting).

The current research was conducted to provide a test of the implicit denial hypothesis, by making the to-be-denied supposition explicit. If complement set focus is due to implicit denial, then a negative quantifier that conflicts with an explicit supposition should lead to increased levels of complement set focus, and an even greater proportion of continuations providing reasons why the predicate is false for the complement set. The current research was also conducted to provide evidence that the inferential process that leads to complement set focusing is also invoked routinely for positive quantifiers; evidence for this should emerge if a positive quantifier conflicts with an explicit supposition, leading to a greater proportion of continuations providing reasons why the predicate is true for the reference set.

Experiment 1

In this experiment, participants read quantifiers sentences such as

In the flu outbreak, few/a few people got sick. They ...

and wrote continuations. These quantifier sentences were presented either without context (no bias condition) or after context designed to induce different kinds of expectations. With respect to the example above, the expectation was either that a lot of people would get sick (REFSET bias) or that few people would get sick (COMPSET bias), as illustrated below:

REFSET biasThe flu vaccine produced for this year was terribly ineffective.

COMPSET biasThe flu vaccine produced for this year was very effective.

In accord with past findings, for the baseline condition, continuations for the positive quantifier (i.e., a few) were expected to be such that they overwhelmingly referred to the REFSET; for the negative quantifier (i.e., few), continuations were expected to produce mixed focus.

When the negative quantifier is in conflict with the explicit supposition (with REFSET bias), according to the implicit denial hypothesis, there should be greater COMPSET and less REFSET focusing than in the baseline condition, and the content of continuations should reveal a greater proportion of reasons why the predicate is not true of the COMPSET.

When the positive quantifier is in conflict with the explicit supposition (with COMPSET bias), there should still be a strong REFSET focus, but the content of the continuations should reveal more reasons why the predicate is true for the REFSET.

Results

Content Analysis

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no bias ref bias comp bias

% REFSET continuations

a few (+)

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Quantifier Bias Reasons why Reasons why not Other A few none 58% 0% 42% refset 39% 0% 61% compset 50% 3% 47%

Few none 29% 19% 52% refset 18% 25% 57% compset 32% 36% 32%

Experiment 2

Given the partial support of the implicit denial hypothesis provided by Experiment 1, a stronger quantifier manipulation was employed in Experiment 2: more than half versus less than half. These two quantifiers denote roughly 60% and 40% of a set of individuals, respectively (Sanford et al., 1996). With a greater distinction in denoted quantities, it was expected that the interaction of biasing context with these quantifiers would be stronger than in Experiment 1.

Results

Discussion

In Experiment 1, the results generally supported the implicit denial hypothesis. When a negative quantifier conflicted with an explicit supposition, reference set focus decreased, complement set focus increased, and there was a small numerical increase in the proportion of reasons why the predicate was not true of the complement set. However, little evidence for inferential processing was in evidence for positive quantifiers.

The results of Experiment 2 were surprising, and suggest an interaction between supposition, quantifier polarity, and the size of the proportion denoted by a quantifier. In particular, for negative quantifiers that denote medium-sized proportions, contextual bias (i.e., the supposition) appears to carry more weight than implicit denial in meaning extraction; however, for negative quantifiers that denoted small proportions, implicit denial appears to be a powerful cue for meaning extraction. Discovering the reasons for these differences should prove to be an interesting avenue for future research.

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