Conceptual Spaces: The Geometry of Thought

by Peter Gardenfors

Overview

Within cognitive science, two approaches currently dominate the problem of modeling representations. The symbolic approach views cognition as computation involving symbolic manipulation. Connectionism, a special case of associationism, models associations using artificial neuron networks. Peter Gärdenfors offers his theory of conceptual representations as a bridge between the symbolic and connectionist approaches.

Symbolic representation is particularly weak at modeling concept learning, which is paramount for understanding many cognitive phenomena. Concept learning is closely tied to the notion of similarity, which is also poorly served by the symbolic approach. Gärdenfors's theory of conceptual spaces presents a framework for representing information on the conceptual level. A conceptual space is built up from geometrical structures based on a number of quality dimensions. The main applications of the theory are on the constructive side of cognitive science: as a constructive model the theory can be applied to the development of artificial systems capable of solving cognitive tasks. Gärdenfors also shows how conceptual spaces can serve as an explanatory framework for a number of empirical theories, in particular those concerning concept formation, induction, and semantics. His aim is to present a coherent research program that can be used as a basis for more detailed investigations.

Product Details

ISBN-13:	9780262572194
Publisher:	MIT Press
Publication date:	01/30/2004
Series:	A Bradford Book
Edition description:	New Edition
Pages:	318
Product dimensions:	6.06(w) x 9.06(h) x 0.63(d)
Age Range:	18 Years

About the Author

Peter Gärdenfors is Professor of Cognitive Science at Lund University, Sweden. He is the author of Conceptual Spaces: The Geometry of Thought (MIT Press) and other books.

Table of Contents

Preface
1 Dimensions
1.1 The Problem of Modeling Representations
1.2 Conceptual Spaces as a Framework for Representations
1.3 Quality Dimensions
1.4 Phenomenal and Scientific Interpretations of Dimensions
1.5 Three Sensory Examples: Color, Sound, and Taste
1.6 Some Mathematical Notions
1.7 How Dimensions Are Identified
1.8 Integral and Separable Dimensions
1.9 On the Origins of Quality Dimensions
1.10 Conclusion
2 Symbolic, Conceptual, and Subconceptual
Representations
2.1 An Analogy for the Three Kinds of Representations
2.2 Symbolic Representations
2.3 Subconceptual Representations
2.4 Conceptual Representations
2.5 Connections to Neuroscience
2.6 Comparisons
2.7 The Jungle of Representations
3 Properties
3.1 Program
3.2 Properties in Intensional Semantics
3.3 Criticism of the Traditional View of Properties
3.4 Criteria for Natural Regions of Conceptual Spaces
3.5 Natural Properties
3.6 Reconsidering the Problems
3.7 The Relativism of Conceptual Spaces
3.8 Connections to Prototype Theory
3.9 Voronoi Tessellations of a Space
3.10 Higher Level Properties and Relations
3.11 Conclusion
4 Concepts
4.1 Concepts versus Properties
4.2 Modeling Concepts
4.3 The Role of Similarity in Concept Formation
4.4 Combining Concepts
4.5 Learning Concepts
4.6 Nonmonotonic Aspects of Concepts
4.7 Concept Dynamics and Nonmonotonic Reasoning
4.8 Objects as Special Kinds of Concepts
4.9 Four Geometric Categorization Models
4.10 The Shell Space
4.11 Experiments
5 Semantics
5.1 What Is a Semantics?
5.2 Six Tenets of Cognitive Semantics
5.3 Analysis of Some Aspects ofLexical Semantics
5.4 An Analysis of Metaphors
5.5 The Learnability Question
5.6 Communicating Referents
5.7 Can Meanings Be in the Head?
5.8 Conclusion: The Semantic Program
6 Induction
6.1 Three Levels of Induction
6.2 The Symbolic Level
6.3 The Conceptual Level
6.4 The Role of Theoretical Concepts
6.5 The Subconceptual Level
6.6 Correlations between Domains
6.7 Conclusion: What Is Induction?
7 Computational Aspects
7.1 Computational Strategies on the Three Levels
7.2 Conceptual Spaces as Emergent Systems
7.3 Smolensky's Treatment of Connectionism
7.4 Not All Computation Is Done by Turing Machines
7.5 A System for Object Recognition
7.6 Conclusion
8 In Chase of Space
8.1 What Has Been Achieved?
8.2 Connections among Levels
8.3 Conclusion: The Need for a New Methodology
Notes
References
Illustration Credits
Index

What People are Saying About This

Endorsement

This is a fearless book that casts a wide net around key issues in cognitive science. It offers the kind of coherent, unified view that the field badly needs.—Steven Sloman, Associate Professor, Cognitive and Linguistic Sciences, Brown University

From the Publisher

This is a fearless book that casts a wide net around key issues in cognitive science. It offers the kind of coherent, unified view that the field badly needs.

— Steven Sloman , Associate Professor, Cognitive and Linguistic Sciences, Brown University

Steven Sloman

This is a fearless book that casts a wide net around key issues in cognitive science. It offers the kind of coherent, unified view that the field badly needs.