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Computation, Dynamics, and Cognition
     

Computation, Dynamics, and Cognition

by Marco Giunti
 

ISBN-10: 0195090098

ISBN-13: 9780195090093

Pub. Date: 03/28/2002

Publisher: Oxford University Press, USA

Currently there is growing interest in the application of dynamical methods to the study of cognition. Computation, Dynamics, and Cognition investigates this convergence from a theoretical and philosophical perspective, generating a provocative new view of the aims and methods of cognitive science. Advancing the dynamical approach as the methodological frame best

Overview

Currently there is growing interest in the application of dynamical methods to the study of cognition. Computation, Dynamics, and Cognition investigates this convergence from a theoretical and philosophical perspective, generating a provocative new view of the aims and methods of cognitive science. Advancing the dynamical approach as the methodological frame best equipped to guide inquiry in the field's two main research programs—the symbolic and connectionist approaches—Marco Giunti engages a host of questions crucial not only to the science of cognition, but also to computation theory, dynamical systems theory, philosophy of mind, and philosophy of science.

In chapter one Giunti employs a dynamical viewpoint to explore foundational issues in computation theory. Using the concept of Turing computability, he precisely and originally defines the nature of a computational system, sharpening our understanding of computation theory and its applications. In chapter two he generalizes his definition of a computational system, arguing that the concept of Turing computability itself is relative to the kind of support on which Turing machine operate. Chapter three completes the book's conceptual foundation, discussing a form of scientific explanation for real dynamical systems that Giunti calls "Galilean explanation."

The book's fourth and final chapter develops the methodological thesis that all cognitive systems are dynamical systems. On Giunti's view, a dynamical approach is likely to benefit even those scientific explanations of cognition which are based on symbolic models. Giunti concludes by proposing a new modeling practice for cognitive science, one based on "Galilean models" of cognitive systems.

Innovative, lucidly-written, and broad-ranging in its analysis, Computation, Dynamics, and Cognition will interest philosophers of science and mind, as well as cognitive scientists, computer scientists, and theorists of dynamical systems. This book elaborates a comprehensive picture of the application of dynamical methods to the study of cognition. Giunti argues that both computational systems and connectionist networks are special types of dynamical systems. He shows how this dynamical approach can be applied to problems of cognition, information processing, consciousness, meaning, and the relation between body and mind.

Product Details

ISBN-13:
9780195090093
Publisher:
Oxford University Press, USA
Publication date:
03/28/2002
Pages:
192
Product dimensions:
6.38(w) x 9.38(h) x 0.76(d)
Lexile:
1450L (what's this?)

Table of Contents

ONE Mathematical Dynamical Systems and Computational Systems
3(52)
1 Introduction
3(4)
2 Mathematical dynamical systems
7(5)
3 Computational systems
12(11)
4 The emulation relation
23(5)
5 Reversible versus irreversible systems
28(9)
6 The realization relation
37(5)
7 Virtual systems, the reversible realizability of irreversible systems, and the existence of reversible universal systems
42(4)
8 Appendix: Proofs of selected theorems
46(4)
9 Notes
50(5)
TWO Generalized Computational Systems
55(58)
1 Introduction
55(2)
2 Turing machines on pattern field F
57(10)
3 Is the concept of computability on pattern field F reducible to the usual concept of Turning computability?
67(11)
4 Is a nonrecursive pattern field necessary for computing nonrecursive functions?
78(5)
5 The concept of computability on pattern field F is a generalization of the usual concept of computability
83(5)
6 Computational systems on pattern field F
88(4)
7 Appendix: Proofs of selected theorems
92(14)
8 Notes
106(7)
THREE Galilean Models and Explanations
113(26)
1 Introduction
113(1)
2 Real dynamical systems versus mathematical dynamical systems
114(1)
3 Models of K-systems
115(1)
4 Galilean explanations and the traditional practice of dynamical modeling
116(3)
5 Galilean explanations are based on Galilean models of K-systems
119(1)
6 Galilean frameworks of K-systems
120(4)
7 Explicit versus implicit specification of the set of state transitions of a possible Galilean model of a K-system
124(5)
8 The inductive method for constructing Galilean frameworks of K-systems
129(2)
9 The deductive method for constructing Galilean frameworks of K-systems
131(2)
10 Appendix: Proofs of selected theorems
133(4)
Notes
137(2)
FOUR Cognitive Systems and the Scientific Explanation of Cognition
139(24)
1 Introduction
139(1)
2 Cognitive systems as dynamical systems
140(5)
2.1 All cognitive systems are dynamical systems: the meaning
140(1)
2.2 All cognitive systems are dynamical systems: the argument
141(4)
3 Two conceptual repertoires for the explanation of cognition: computation theory and dynamical systems theory
145(8)
3.1 Dynamical systems theory and the explanation of cognition based on symbolic models
146(2)
3.2 Computation theory and the explanation of cognition based on neural networks or other continuous dynamical models
148(5)
4 Cognitive systems and their models
153(7)
4.1 Simulation models of cognitive systems
154(1)
4.2 Galilean models of cognitive systems
155(3)
4.3 A new possibility for cognitive science: P-explanatory and correct Galilean frameworks of cognitive systems
158(1)
4.4 The Galilean approach to cognitive science
159(1)
Notes
160(3)
References 163(10)
Index 173

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