Abstract

The standard semantic analysis of sentences such as ‘The number of planets in the solar system is eight’ is that they are identity statements that identify certain mathematical objects, namely numbers. The analysis thereby facilitates arguments for a controversial philosophical position, namely realism about mathematical objects. Accordingly, whether or not this analysis is accurate should concern philosophers greatly. Recently, several authors have offered rival analyses of sentences such as these. In this paper, I will consider a wide range of linguistic evidence and show that all of these analyses, including the standard analysis, suffer significant drawbacks. I will then outline and present further evidence in favour of my own analysis, developed elsewhere, according to which such sentences are identity statements that identify certain kinds of facts. I also defend a novel and plausible approach to the semantics of interrogative clauses that corroborates my analysis. Finally, I discuss how realists about mathematical objects should proceed in light of the arguments presented in this paper.