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date: 12 December 2019

Abstract and Keywords

There are many kinds of number. This chapter concentrates on finite cardinal numbers, as they have a basic role in our thinking. Numbers cannot be seen, heard, touched, tasted, or smelled; they do not emit or reflect signals; they leave no traces. So what kind of thing are they? How can we have knowledge of them? The aim of this chapter is to present and assess the main answers to these questions – classical and neo-classical, nominalism, mentalism, fictionalism, logicism, and the set-size view. All views are disputed, including the view I will argue for, the set-size view. The final section relates the finite cardinal numbers to the natural numbers.

Keywords: cardinal number, nominalism, mentalism, fictionalism, logicism, set-size, structure of natural numbers

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