Introduction

Abstract

There are various concepts of number. This is already indicated by the different words for numbers that show up in the language of ordinary life. These are usually listed by grammarians under the following headings: The whole numbers [Anzahlen] or cardinal numbers (numeralia cardinalia), the ordinal numbers (n. Ordinalia), the type numbers (n. specialia), the numbers of repetition (n. iterativa), the multiplicative numbers (n. multiplicative), and the fractional numbers (n. partitiva. That the whole number comes first in this sequence is, as with the other characteristics names which it also bears — the “basic” or “cardinal” number — not founded on mere convention. Linguistically it assumes a privileged position because all of the remaining number terms proceed only through slight modifications from the words for the whole numbers. (E.g., two, second, of two kinds, double, twice, half).¹ The latter are thus genuine terms for basic numbers. In this way language guides us to the thought that the corresponding concepts also may all stand in an analogous relation of dependence to those of the whole numbers, and may represent certain ideas, richer in content, where the whole numbers form mere constituents.