Numerical expressions are linguistic forms related to numbers or quantities, which directly reflect the relationship between linguistic symbols and mathematical cognition. Featuring some unique properties, numeral systems are somewhat distinguished from other language subsystems. For instance, numerals can appear in various grammatical positions, including adjective positions, determiner positions, and argument positions. Thus, linguistic research on numeral systems, especially the research on the syntax and semantics of numerical expressions, has been a popular and recurrent topic.
For the syntax of complex numerals, two analyses have been proposed in the literature. The traditional constituency analysis maintains that complex numerals are phrasal constituents, which has been widely accepted and defended as a null hypothesis. The nonconstituency analysis, by contrast, claims that a complex numeral projects a complementative structure in which a numeral is a nominal head selecting a lexical noun or a numeral-noun combination as its complement. As a consequence, additive numerals are transformed from full NP coordination. Whether numerals denote numbers or sets has aroused a long-running debate. The number-denoting view assumes that numerals refer to numbers, which are abstract objects, grammatically equivalent to nouns. The primary issue with this analysis comes from the introduction of a new entity, numbers, into the model of ontology. The set-denoting view argues that numerals refer to sets, which are equivalent to adjectives or quantifiers in grammar. One main difficulty of this view is how to account for numerals in arithmetic sentences.
The Cultural Challenge in Mathematical Cognition
