Why do numbers exist? A psychologist constructivist account

Inquiry, pp. 1–33

Abstract

In this paper, I study the kind of questions we can ask about the existence of numbers. In addition to asking whether numbers exist, and how, I argue that there is also a third relevant question: why numbers exist. In platonist and nominalist accounts this question may not make sense, but in the psychologist account I develop, it is as well-placed as the other two questions. In fact, there are two such why-questions: the causal why-question asks what causes numbers to exist and the teleological why-question asks for what purpose numbers exist. I argue that in a psychologist constructivist account, in which numbers are understood to exist as referents of a particular type of culturally shared concepts, both why-questions can get plausible answers.

Authors 1

1. Markus Pantsar corresponding Aachen Human Technology Center

   RWTH Aachen University · University of Helsinki

   Affiliation as printed

   Human Technology Center

   University of Helsinki

   Faculty of Arts, Discipline of Philosophy, History and Art, University of Helsinki, Helsinki, Finland

   RWTH Aachen, Human Technology Center, Aachen, Germany