(DRAFT: Liable to change)

Development of Cardinal and Ordinal Competences

Extending ideas in Chapter 8 of The Computer Revolution in Philosophy
http://www.cs.bham.ac.uk/research/projects/cogaff/crp/#chap8

Aaron Sloman
School of Computer Science, University of Birmingham

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Installed: 7 Nov 2015
Last updated: XXX

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About this paper

This paper is one of a collection of documents with "afterthoughts" about ideas and theories presented in my 1978 book Sloman (1978,2015) (The Computer Revolution in Philosophy). That book was reorganised and re-formatted during 2015, to provide a single web document with many internal cross references and links to external related documents.

This paper is available here:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/cardinal-ordinal.html
A PDF version may be added later.

A partial index of discussion notes is in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/AREADME.html

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Procedural bases of cardinal and ordinal competences

There are many researchers who try to answer questions about numerical competences, including questions such as these:

• What numerical competences are possessed by animals of species X, Y, ...?
• What (if any) numerical competences to human babies have at birth?
• At what ages do various competences develop in humans?
• Are the competences innate or learnt from older individuals or acquired independently empirically?

Unfortunately, my impression is that most of them do not understand the mathematical structures of the concepts they are using to define their search goals. For example, the use of both cardinal and ordinal numbers requires the ability to create and manipulate one-to-one correspondences. In Chapter 8 of my 1978 book Sloman (1978) I tried to spell out some of the mechanisms involved, including mechanisms that generate two processes in parallel and coordinate them so that they remain in synchrony, as is required for counting objects or events.

Requirements that were taken for granted when the book was written (relating to Piaget's research on number competences in children) have been made explicit in notes added February 2016:
http://www.cs.bham.ac.uk/research/projects/cogaff/crp/#note-ch-8-20160217

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REFERENCES AND LINKS

• Aaron Sloman, 1978,2015, The Computer Revolution in Philosophy: Philosophy, Science and Models of Mind, Harvester Press (and Humanities Press), Hassocks, Sussex, First edition 1978,
  Revised free online version, 2015 http://www.cs.bham.ac.uk/research/cogaff/62-80.html#crp

• Aaron Sloman, 2015 (Work in progress), Afterthoughts on The Computer Revolution in Philosophy
  http://www.cs.bham.ac.uk/research/projects/cogaff/crp/crp-afterthoughts.html

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Maintained by Aaron Sloman
School of Computer Science
The University of Birmingham