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Numbers, Language, and the Human Mind [Pehme köide]

(Humboldt-Universität zu Berlin)
  • Formaat: Paperback / softback, 360 pages, kõrgus x laius x paksus: 229x152x20 mm, kaal: 530 g, 4 Tables, unspecified
  • Ilmumisaeg: 09-Apr-2009
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521108659
  • ISBN-13: 9780521108652
Teised raamatud teemal:
  • Formaat: Paperback / softback, 360 pages, kõrgus x laius x paksus: 229x152x20 mm, kaal: 530 g, 4 Tables, unspecified
  • Ilmumisaeg: 09-Apr-2009
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521108659
  • ISBN-13: 9780521108652
Teised raamatud teemal:
What constitutes our number concept? What makes it possible for us to employ numbers the way we do; which mental faculties contribute to our grasp of numbers? What do we share with other species, and what is specific to humans? How does our language faculty come into the picture? This 2003 book addresses these questions and discusses the relationship between numerical thinking and the human language faculty, providing psychological, linguistic and philosophical perspectives on number, its evolution and its development in children. Heike Wiese argues that language as a human faculty plays a crucial role in the emergence of systematic numerical thinking. She characterises number sequences as powerful and highly flexible mental tools that are unique to humans and shows that it is language that enables us to go beyond the perception of numerosity and to develop such mental tools.

Arvustused

'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 'An elegant and witty integration of mathematics, psychology, and linguistics, Heike Wiese's new book offers an important advance in explicating the cognitive foundations of number. Wiese rigorously demonstrates how the uses of numbers for counting, ordering, and naming arise through the interaction of prelinguistic capacities with the expressive power of the language faculty, confirming in detail a hypothesis that has been in the air for some years now. Not only that, she makes it fun. I couldn't put the book down.' Ray Jackendoff, Brandeis University 'A refreshing and engaging investigation of the relationship between language and our human capacity for numerical thought. Wiese does a wonderful job of laying out the elaborate and many-layered connections between different kinds of number concepts, symbolic systems for representing and manipulating number (including but not limited to natural language), and the fundamental categories by which we understand the world - objects, subjects, and events. This book will appeal to anyone interested in numerical cognition or in the relationship between language and thought. Karen Wynn, Yale University 'This book is sure to become a classic in its field. it provides an impressive synthesis of findings and leading ideas across multiple fields, including the philosophy of mathematics an invaluable reference work for virtually anyone interested in 'exploring the distinctive way in which numerical cognition is intertwined with the human language faculty. W's rich and impressive work is going to be essential reading for many years to come.' Language

Muu info

Winner of Susanne K. Langer Award for Outstanding Scholarship in the Ecology of Symbolic Form 2005.This 2003 book discusses the relationship between numerical thinking and the human language faculty.
Acknowledgments ix
Introduction 1(8)
Numbers and objects
9(34)
Cardinal number assignments: `3 pens', `3 kg', `3 °C'
18(15)
Ordinal number assignments: `the third runner'
33(4)
Nominal number assignments: `bus #3', `football player #3'
37(3)
Overview: how to use numbers
40(3)
What does it mean to be a number?
43(25)
The intersective analysis of numbers
44(8)
The itemising approach to numbers
52(5)
The relational view of numbers
57(3)
A criteria-based view of numbers
60(8)
Can words be numbers?
68(26)
Counting words are special
70(9)
Counting words are non-referential
79(6)
Counting words are acquired differently
85(4)
A cut with Occam's razor
89(2)
Counting words as numerical tools
91(3)
The language legacy
94(57)
Before language: quantitative capacities in infants and animals
95(1)
Number sense and beyond
95(18)
Symbolic reference and the evolution of language
113(8)
Matching patterns in symbolic reference and number assignments
121(3)
Language opens the way for numerical cognition: further support
124(7)
A possible scenario for the emergence of numerical tools
131(12)
Language and number as human faculties
143(8)
Children's route to number: from iconic representations to numerical thinking
151(29)
The acquisition of a counting sequence
153(4)
Pre-numerical props for number assignments
157(3)
Gateway to number
160(14)
Language and the emergence of counting and cardinality
174(6)
The organisation of our cognitive number domain
180(39)
Representation of counting words as numerical tools
181(1)
Concepts of numerical quantity
182(1)
Abstract cardinalities
183(5)
Measure concepts
188(14)
Concepts of numerical rank
202(7)
Concepts of numerical label
209(5)
The architecture of the number domain
214(5)
Non-verbal number systems
219(45)
Arabic numerals as a non-verbal number sequence
222(14)
The development of non-verbal numerals: from iconic representations to numerical tools
236(5)
Two alternative number sequences: the correlation between counting words and arabic numerals
241(23)
Numbers in language: the grammatical integration of numerical tools
264(33)
Counting words and their referential cousins
265(5)
How to express numerical concepts: the organisation of number word constructions
270(4)
Referential number words are not outcasts
274(14)
The return of the counting words
288(9)
Appendix 1 Number assignments 297(3)
Appendix 2 The philosophical background 300(4)
Appendix 3 Numerical tools: possible sets N 304(10)
Appendix 4 Conceptualisation of number assignments 314(5)
Appendix 5 Semantic representations for number word constructions 319(3)
References 322(18)
Index 340
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.