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Language and Mathematics: An Interdisciplinary Guide [Hardback]

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  • Formāts: Hardback, 344 pages, weight: 623 g
  • Sērija : Language Intersections
  • Izdošanas datums: 06-Jun-2016
  • Izdevniecība: De Gruyter Mouton
  • ISBN-10: 1614515549
  • ISBN-13: 9781614515548
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  • Hardback
  • Cena: 206,22 €
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Language and Mathematics: An Interdisciplinary GuidePalielināt
  • Formāts: Hardback, 344 pages, weight: 623 g
  • Sērija : Language Intersections
  • Izdošanas datums: 06-Jun-2016
  • Izdevniecība: De Gruyter Mouton
  • ISBN-10: 1614515549
  • ISBN-13: 9781614515548
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781614515548.html
Keywords:

This book explores the many disciplinary and theoretical links between language, linguistics, and mathematics. It examines trends in linguistics, such as structuralism, conceptual metaphor theory, and other relevant theories,to show that language and mathematics have a similar structure, but differential functions, even though one without the other would not exist.

List of figures
viii
Preface x
1 Common Ground
1(65)
1.1 Logic
6(30)
1.1.1 Formalism in linguistics and mathematics
8(10)
1.1.2 Syntax
18(6)
1.1.3 Formal analysis
24(8)
1.1.4 The structure of logic
32(4)
1.2 Computation
36(16)
1.2.1 Modeling formal theories
40(6)
1.2.2 Cognitive science
46(4)
1.2.3 Creativity
50(2)
1.3 Quantification
52(4)
1.3.1 Compression
53(2)
1.3.2 Probability
55(1)
1.4 Neuroscience
56(8)
1.4.1 Neural structure
57(5)
1.4.2 Blending
62(2)
1.5 Common ground
64(2)
2 Logic
66(66)
2.1 Formal mathematics
69(27)
2.1.1 Logos and mythos
70(2)
2.1.2 Proof
72(9)
2.1.3 Consistency, completeness, and decidability
81(4)
2.1.4 Non-Euclidean logic
85(3)
2.1.5 Cantorian logic
88(3)
2.1.6 Logic and imagination
91(5)
2.2 Set theory
96(7)
2.2.1 Diagrams
98(3)
2.2.2 Mathematical knowledge
101(2)
2.3 Formal linguistics
103(15)
2.3.1 Transformational-generative grammar
104(4)
2.3.2 Grammar rules
108(2)
2.3.3 Types of grammar
110(4)
2.3.4 Formal semantics
114(4)
2.4 Cognitive linguistics
118(7)
2.4.1 Conceptual metaphors
119(4)
2.4.2 Challenge to formalism
123(2)
2.5 Formalism, logic, and meaning
125(7)
2.5.1 A Godelian critique
127(1)
2.5.2 Connecting formalism and cognitivism
128(1)
2.5.3 Overview
129(3)
3 Computation
132(61)
3.1 Algorithms and models
134(13)
3.1.1 Artificial intelligence
138(1)
3.1.2 Knowledge representation
139(5)
3.1.3 Programs
144(3)
3.2 Computability theory
147(12)
3.2.1 The Traveling Salesman Problem
147(6)
3.2.2 Computability
153(6)
3.3 Computational linguistics
159(15)
3.3.1 Machine Translation
160(3)
3.3.2 Knowledge networks
163(4)
3.3.3 Theoretical paradigms
167(5)
3.3.4 Text theory
172(2)
3.4 Natural Language Processing
174(5)
3.4.1 Aspects of NLP
175(3)
3.4.2 Modeling language
178(1)
3.5 Computation and psychological realism
179(14)
3.5.1 Learning and consciousness
180(4)
3.5.2 Overview
184(9)
4 Quantification
193(62)
4.1 Statistics and probability
195(7)
4.1.1 Basic notions
197(3)
4.1.2 Statistical tests
200(2)
4.2 Studying properties quantitatively
202(17)
4.2.1 Benford's Law
203(3)
4.2.2 The birthday and coin-tossing problems
206(3)
4.2.3 The Principle of Least Effort
209(7)
4.2.4 Efficiency and economy
216(3)
4.3 Corpus linguistics
219(5)
4.3.1 Stylometric analysis
219(2)
4.3.2 Other techniques
221(1)
4.3.3 The statistics on metaphor
222(2)
4.4 Probabilistic analysis
224(13)
4.4.1 The Monty Hall Problem
226(7)
4.4.2 The Prosecutor's Fallacy
219(9)
4.4.3 Bayesian Inference
228(2)
4.4.4 General implications
230(7)
4.5 Quantifying change in language
237(11)
4.5.1 Lexicostatistics and glottochronology
237(8)
4.5.2 Economy of change
245(3)
4.6 Overview
248(7)
5 Neuroscience
255(42)
5.1 Neuroscientific orientations
256(12)
5.1.1 Computational neuroscience
257(5)
5.1.2 Connectionism
262(2)
5.1.3 Modularity
264(2)
5.1.4 Research on metaphor
266(2)
5.2 Math cognition
268(16)
5.2.1 Defining math cognition
270(2)
5.2.2 Charles Peirce
272(2)
5.2.3 Graphs and math cognition
274(2)
5.2.4 Neuroscientific findings
276(8)
5.3 Mathematics and language
284(10)
5.3.1 Mathematics and figurative cognition
285(2)
5.3.2 Blending theory
287(7)
5.4 Concluding remarks
294(3)
Bibliography 297(30)
Index 327
Marcel Danesi, University of Toronto, Canada.