Negative polarity and the comparative

Summary and Conclusions

In this paper I have given a rather simple and, I believe, elegant semantics for the comparative,¹ which explains the distribution of certain negative polarity items and correctly predicts the validity of inferences concerning comparatives. It was argued that a distinction has to be made between NP-comparatives and S-comparatives, in order to capture the very different semantic properties of these two constructions. In this respect the present paper differs from previous treatments of the semantics of the comparative, such as Cresswell (1976) and Klein (1980). According to the theory presented above, the comparative adjective denotes a Boolean homomorphism in the NP-comparative construction (just like all extensional transitive verbs), but it denotes an anti-additive function in the S-construction.

The semantics for the S-comparative shares some basic features with the semantic analysis of the comparative in Klein (1980). It differs, however, in that grading relations have been introduced here as primitive notions, whereas Klein proposed to explain them away by a suitable theory of contextual interpretation of positive adjective. By introducing grading relations as primitive notions, I have been able to simplify the semantics for the S-comparative to a considerable degree. However, a Klein-style theory of context could be placed on top of the present theory, if one wanted to do so. The present paper also differs from the contributions by Cresswell and Klein in that it does not provide an explicit syntax to complement the semantics. I have refrained from giving a fragment in the style of Montague-grammar, because I felt that I did not have anything substantial to contribute there.

The semantics for the S-comparative provided here can account for the possibility of the Dutch negative polarity item ook maar occurring in the S-comparative (though not in the NP-comparative). There were two reasons for focussing on ook maar: first, it calls our attention to an important logical property of the S-comparative, viz. its anti-additivity, and, secondly, it points out an area where Ladusaw's theory of negative polarity needs further elaboration, to wit, the differences in distribution that are found among the various negative polarity items, as illustrated here by the Dutch examples ook maar and hoeven (cf. (45) above). Still a lot of work, even on the basic level of description, has to be done in this area, but the progress made so far by Ladusaw (1979) and Zwarts (1981, to appear) at least warrants the expectation that this work will not be without its rewards. These works also show that the model-theoretic approach to semantics is especially well-suited to giving an explanatory account of polarity phenomena. I hope that the present paper may help to convince those who still hold that formal semantics is irrelevant for linguistic purposes.