Numbers, Kinds, and the Identification Problem

Abstract I defend two theses concerning the semantics of number words, such as ‘two’. First, as nouns, they have taxonomic meanings whereby they describe or refer to kinds. Secondly, since numerical singular terms refer to numbers, if anything, numbers are kinds. Jointly, these two theses have several significant implications for the philosophy of mathematics. For example, they provide a natural and independently motivated resolution to a revenge version of Benacerraf’s Identification Problem.