Computation, Dynamics, and CognitionCurrently 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. |
Contents
| 3 | |
Generalized Computational Systems | 55 |
Galilean Models and Explanations | 113 |
Cognitive Systems and the Scientific Explanation of Cognition | 139 |
References | 163 |
Index | 173 |
Other editions - View all
Common terms and phrases
alphabet Ac bijection blank cascade MDS cell x0 cellular automata coefficient cognitive science cognitive system computable on F computation theory computational system concept of computability condition 2d corresponds decoding defined denoted by numeral differential or difference doubly infinite tape dynamical system MDS dynamical systems theory effective relative emulating system emulation relation eventually periodic orbits evolution functions explanation of cognition f is computable F with alphabet F(Ac field F finite number finite strings function f Galilean explanation halting problem identity function instantiates internal state q0 irreversible system isomorphic to MDS K-magnitudes K-property K-system lemma logically irreversible mathematical dynamical system MDS2 MDSs merging orbits model of KRS nonblank symbol nonnegative nonrecursive number denoted numeric function oracle machines orb(x orb(y pattern field possible Galilean model proof real dynamical system real system recursive functions recursive relative regular enumeration set of values strongly irreversible theorem tion total recursive transition g Turing machine
Popular passages
Page 8 - ... computational systems as models of cognition. The First Premise The first premise of my argument is that all models currently employed in cognitive science are mathematical dynamical systems. A mathematical dynamical system is an abstract mathematical structure that can be used to describe the change of a real system as an evolution through a series of states. If the evolution of the real system is deterministic, that is, if the state at any future time is determined by the state at the present...
Page x - M that represents all possible states through which the system can evolve; M is called the state space (or sometimes the phase space) of the system. The third element is a set of functions {#'} that tells us the state of the system at any instant t provided that we know the initial state; each function in {g'} is called a state transition (or a tadvance) of the system.
Page 142 - McClelland eds. 1986) employs neural networks; and models of the third type are typically proposed by nonconnectionist researchers who nevertheless believe that cognition should be studied by means of dynamical methods and concepts. Nonconnectionist researchers favoring a dynamical perspective are active in many fields; for examples, see Port and van Gelder (1995).
Page 143 - ... which, at any time step, is in exactly one of a finite number of internal states {q,}. The behavior of the machine is specified by a set of instructions, which are conditionals of the form: If the internal state is q-,, and the symbol on the square where the head is located is aj, write symbol a k (move one square to the right, move one square to the left) and change internal state to q,. Each instruction can thus be written as a quadruple of one of the three types: q&ft k q h qfljRq,, q^Lq,,...
Page 150 - Since I have informally characterized a computational system as a cascade that can be effectively described, let us ask first what a description of a cascade is. If we take a structuralist viewpoint, this question has a precise answer. A description (or a representation) of a cascade consists of a second cascade isomorphic to it where, by definition, a cascade MDS, - <T, Л/;, {h'}> is isomorphic to a given cascade Л /AS' ~ <T,M,{g'} just in case there is a bijection f:M->M, such that, for any t...
Page 144 - ... be the set of the nonnegative integers. Since the future behavior of the machine is determined when the content of the tape, the position of the head, and the internal state are fixed, we may take the state space M to be the set of all triples (tape content, head position, internal state). And, finally, the set of state transitions (g'} is determined by the set of quadruples of the machine.
Page 143 - That a system specified by differential or difference equations is a mathematical dynamical system is obvious, for this concept is expressly designed to describe this class of systems in abstract terms. That a neural network is a mathematical dynamical system is also not difficult to show. A complete state of the system can in fact be identified with the activation levels of all the units in the network, and the set of state transitions, on the other hand, is determined by the differential (or difference)...
Page 114 - A mathematical dynamical system, on the other hand, is an abstract mathematical structure that can be used to describe the change of a real system as an evolution through a series of states. If the evolution of the real system is deterministic, that is, if the state at any future time is determined by the state at the present time, then the abstract mathematical structure consists of three elements, as discussed in chapter l.The first element is a set Tthat represents time.
Page 152 - Also note that the same conclusion holds for any continuous system specified by differential (or difference) equations. Since all these systems are continuous (in time or state space), none of them is computational. Summing up the Argument We have thus seen that (I) all models currently employed in cognitive science are mathematical dynamical systems...
Page 143 - Turing machines, or monogenie production systems, etc.) and it then shows that the systems of this special type are mathematical dynamical systems. Given the strong similarities between different types of symbolic processors, it is then not difficult to see how the argument given for one type could be modified to fit any other type. Here, I limit myself to show that an arbitrary Turing machine is in fact a mathematical dynamical system.