Numbers, Language, and the Human Mind

Heike Weiss is Assistant Professor of Linguistics at the Institute for German Linguistics and Language, Humboldt-Universität zu Berlin. She has published in the fields of linguistics, cognitive science, philosophy, and didactics of mathematics.

• 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.

'Heike Wiese builds the case for numerical cognition growing out of the symbolic cognition at the base of language - not as a parasitic spin-off, or a mere naming of numerical concepts, but as an ability whose roots extend to the same underlying cognitive operations. This account of the cognitive basis of number concepts is breathtaking in its synthetic scope, impeccable in its thoroughness of analysis, and stunning in its originality. It breaks new ground in bringing the rich history of mathematical-philosophical analyses into clear correspondence with recent cognitive-science investigations of reasoning about and acquiring numerical knowledge, and it brings insights from both paradigms to illuminate the mystery of the evolutionary and semiotic origins of number. Out of this effort to find a new synthesis have emerged a number of remarkable insights - about the nature of the precursors to number concepts in animal cognition, the origins and basis for the special human capacity for systematic numerical cognition, and the relationships between mathematical thinking and symbolic-linguistic abilities. Each of these could stand alone as the initiator of a whole body of further research (and likely will). But the book offers something more than this. Heike Wiese's book is proof that a work of theoretical rigor and scientific originality can be presented in unassumingly lucid prose, accessible to anyone with a serious curiosity about the nature of mathematical knowledge.' Terrence Deacon, University of California, Berkeley