Cross-Linguistic Investigation into Universal Quantification and other Related Notions and their Semantic Map

In the literature of quantification, many studies are directed specifically at universal quantifier expressions which require that something is true with every relevant thing, since the universal quantifier ? is one of the two standard quantifiers in first-order predicate logic. Yet, despite the abundant research, the picture of universal quantification in Chinese is still murky and a consensus is not even reached on how universal quantification is instantiated in Chinese. For instance, one of such quantifiers, Chinese dou, conventionally treated as a universal quantifier, is also analyzed as a marker of focus, scalar presupposition, anti-expectation, sum formation, maximality, exhaustification. This project aims to push forward the study of universal quantification by meeting a three-fold objective. First, it seeks to pin down the range of universal quantifier expressions in Chinese and straighten out the relation and difference between universal quantification and the above mentioned notions. The guiding hypothesis is: The basic semantic component of expressions like "dou" is universal quantification and the diverse effects they bring forth are attributed to the sorts of entities they quantify over and the ways of quantificational mapping. Second, it provides an in-depth account of all the expressions related to universal quantification in Chinese. In particular, it aims to fill the gaps of existing theories by tackling universal quantificational phenomena less studied or untouched upon in Chinese, e.g., the co-occurrence of multiple universal quantifiers, and the bound variable interpretations of mei-CL-NPs 'every-NP'/ge-NPs 'each-NP' and one-CL-NPs which may change the conventional views of the former as a generalized quantifier and the latter as an indefinite introducing a new discourse referent. Third, based on the study above, it further draws on cross-linguistic data to complete the semantic map of universal quantification, which may uncover the shared conceptual space of universal quantification across languages. The project will contribute to the study of quantification and indefinites by linking up and sorting out the related notions to universal quantification. Empirically, the study will enrich the picture of universal quantification by unraveling new quantificational patterns in Chinese and other languages and analyzing them in a unified conceptual framework. More importantly, the project is unique in that the theoretical claims will be further verified and strengthened by plotting the semantic map of universal quantification. The outcomes can further deepen the connection among standard logical equipment, the processing of natural language in the human mind, language typology and language acquisition.