Language and Mathematics: An Interdisciplinary Guide

✍ Scribed by Marcel Danesi

• Publisher: De Gruyter Mouton
• Year: 2016
• Tongue: English
• Leaves: 344
• Series: Language Intersections; 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Contents
List of figures
Preface
1 Common Ground
1.1 Logic
1.1.1 Formalism in linguistics and mathematics
1.1.2 Syntax
1.1.3 Formal analysis
1.1.4 The structure of logic
1.2 Computation
1.2.1 Modeling formal theories
1.2.2 Cognitive science
1.2.3 Creativity
1.3 Quantification
1.3.1 Compression
1.3.2 Probability
1.4 Neuroscience
1.4.1 Neural structure
1.4.2 Blending
1.5 Common ground
2 Logic
2.1 Formal mathematics
2.1.1 Lógos and mythos
2.1.2 Proof
2.1.3 Consistency, completeness, and decidability
2.1.4 Non-Euclidean logic
2.1.5 Cantorian logic
2.1.6 Logic and imagination
2.2 Set theory
2.2.1 Diagrams
2.2.2 Mathematical knowledge
2.3 Formal linguistics
2.3.1 Transformational-generative grammar
2.3.2 Grammar rules
2.3.3 Types of grammar
2.3.4 Formal semantics
2.4 Cognitive linguistics
2.4.1 Conceptual metaphors
2.4.2 Challenge to formalism
2.5 Formalism, logic, and meaning
2.5.1 A Gödelian critique
2.5.2 Connecting formalism and cognitivism
2.5.3 Overview
3 Computation
3.1 Algorithms and models
3.1.1 Artificial intelligence
3.1.2 Knowledge representation
3.1.3 Programs
3.2 Computability theory
3.2.1 The Traveling Salesman Problem
3.2.2 Computability
3.3 Computational linguistics
3.3.1 Machine Translation
3.3.2 Knowledge networks
3.3.3 Theoretical paradigms
3.3.4 Text theory
3.4 Natural Language Processing
3.4.1 Aspects of NLP
3.4.2 Modeling language
3.5 Computation and psychological realism
3.5.1 Learning and consciousness
3.5.2 Overview
4 Quantification
4.1 Statistics and probability
4.1.1 Basic notions
4.1.2 Statistical tests
4.2 Studying properties quantitatively
4.2.1 Benford’s Law
4.2.2 The birthday and coin-tossing problems
4.2.3 The Principle of Least Effort
4.2.4 Efficiency and economy
4.3 Corpus linguistics
4.3.1 Stylometric analysis
4.3.2 Other techniques
4.3.3 The statistics on metaphor
4.4 Probabilistic analysis
4.4.1 The Monty Hall Problem
4.4.2 The Prosecutor’s Fallacy
4.4.3 Bayesian Inference
4.4.4 General implications
4.5 Quantifying change in language
4.5.1 Lexicostatistics and glottochronology
4.5.2 Economy of change
4.6 Overview
5 Neuroscience
5.1 Neuroscientific orientations
5.1.1 Computational neuroscience
5.1.2 Connectionism
5.1.3 Modularity
5.1.4 Research on metaphor
5.2 Math cognition
5.2.1 Defining math cognition
5.2.2 Charles Peirce
5.2.3 Graphs and math cognition
5.2.4 Neuroscientific findings
5.3 Mathematics and language
5.3.1 Mathematics and figurative cognition
5.3.2 Blending theory
5.4 Concluding remarks
Bibliography
Index