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
1 - Numbers and objects
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 striking feature of numbers is their enormous flexibility. A quality like colour, for instance, can only be conceived for visual objects, so that we have the notion of a red flower, but not the notion of a red thought. In contrast to that, there seem to be no restrictions on the objects numbers can apply to. In 1690 John Locke put it this way, in his ‘Essay Concerning Human Understanding’:
number applies itself to men, angels, actions, thoughts; everything that either doth exist, or can be imagined.
(Locke 1690: Book II, ch. XVI, § 1)This refers to our usage of numbers as in ‘four men’ or ‘four angels’, where we identify a cardinality. This number assignment works for any objects, imagined or existent, no matter what qualities they might have otherwise; the only criterion here is that the objects must be distinct in order to be counted. In a seminal work on numbers from the nineteenth century, the mathematician and logician Gottlob Frege took this as an indication for the intimate relationship between numbers and thought, a relationship that will be a recurring topic throughout this book:
The truths of arithmetic govern all that is numerable. This is the widest domain of all; for to it belongs not only the existent, not only the intuitable, but everything thinkable. Should not the laws of number, then, be connected very intimately with the laws of thought?
(Frege 1884: § 14)And this is only one respect in which numbers are flexible.
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- Information
- Numbers, Language, and the Human Mind , pp. 9 - 42Publisher: Cambridge University PressPrint publication year: 2003