A CRITERIA-BASED APPROACH TO NUMBERS

Criteria for possible number sequences N

1. All x ∈ N must be well distinguished.

2. N must be a progression.

3. N must be infinite.

Definition of numbers as numerical tools, based on these criteria

Any sequence that fulfils these criteria can fulfil numerical purposes, that is, it can be used as a sequence N of numerical tools. As long as this sequence is only used in number assignments for finite sets and does not serve as a basis for complex mathematics, the third feature (infiniteness) is optional.

A POSSIBLE SET N DRAWN FROM VERBAL ENTITIES: THE ENGLISH COUNTING SEQUENCE C

Generation of the elements of C by inductive definition

Elements of C are defined via their phonological representations. I define six classes of C: ‘Ones’ (one to nine), ‘Teens’ (ten to nineteen), ‘Tys’ (twenty to ninety-nine), ‘Hundreds’ (one hundred to nine hundred and ninety-nine), ‘Thousands’ (one thousand to nine hundred and ninety-ninethousand ninehundred andninety-nine), and ‘Millions’ (open-ended, from one million). Elements of the initial class of primitive counting words, Ones, are defined as a list, that is, by enumeration.

Apart from the two initial classes, each class consists of two subclasses: (1) the m-class of elements whose immediate constituents are combined by a rule of a multiplicative character (for example six-ty, two hundred), and (2) the a-class of elements whose immediate constituents are combined by a rule of an additive character (for example sixty-three, two hundred and ten).