Common nouns as modally non-rigid restricted variables

I argue that common nouns should be analyzed as variables, rather than as predicates which take variables as arguments. This necessitates several unusual features to the analysis, such as allowing variables to be modally non-rigid, and assigning their values compositionally. However, treating common nouns as variables offers a variety of theoretical and empirical advantages over a more traditional analysis: It predicts the conservativity of nominal quantification, simplifies the analysis of articleless languages, derives the weak reading of sentences with donkey anaphora, solves the proportion problem presented by quantifiers like ‘most’, improves the analysis of the temperature paradox, allows a more unified analysis of bare plurals, and regularizes the correspondence between syntactic categories and semantic types.