Book contents
- Frontmatter
- Contents
- Acknowledgments
- Introduction
- 1 Numbers and objects
- 2 What does it mean to be a number?
- 3 Can words be numbers?
- 4 The language legacy
- 5 Children's route to number: from iconic representations to numerical thinking
- 6 The organisation of our cognitive number domain
- 7 Non-verbal number systems
- 8 Numbers in language: the grammatical integration of numerical tools
- Appendix 1 Number assignments
- Appendix 2 The philosophical background
- Appendix 3 Numerical tools: possible sets N
- Appendix 4 Conceptualisation of number assignments
- Appendix 5 Semantic representations for number word constructions
- References
- Index
Appendix 3 - Numerical tools: possible sets N
Published online by Cambridge University Press: 22 September 2009
- Frontmatter
- Contents
- Acknowledgments
- Introduction
- 1 Numbers and objects
- 2 What does it mean to be a number?
- 3 Can words be numbers?
- 4 The language legacy
- 5 Children's route to number: from iconic representations to numerical thinking
- 6 The organisation of our cognitive number domain
- 7 Non-verbal number systems
- 8 Numbers in language: the grammatical integration of numerical tools
- Appendix 1 Number assignments
- Appendix 2 The philosophical background
- Appendix 3 Numerical tools: possible sets N
- Appendix 4 Conceptualisation of number assignments
- Appendix 5 Semantic representations for number word constructions
- References
- Index
Summary
A CRITERIA-BASED APPROACH TO NUMBERS
Criteria for possible number sequences N
All x ∈ N must be well distinguished.
N must be a progression.
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).
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- Numbers, Language, and the Human Mind , pp. 304 - 313Publisher: Cambridge University PressPrint publication year: 2003