Cognition and the Power of Continuous Dynamical Systems

Author: Schonbein, Whit

Source: Minds and Machines, Volume 15, Number 1, February 2005 , pp. 57-71(15)

Publisher: Springer

Buy & download fulltext article:

Price: $47.00 plus tax (Refund Policy)

Abstract:

Traditional approaches to modeling cognitive systems are computational, based on utilizing the standard tools and concepts of the theory of computation. More recently, a number of philosophers have argued that cognition is too ‘subtle’ or ‘complex’ for these tools to handle. These philosophers propose an alternative based on dynamical systems theory. Proponents of this view characterize dynamical systems as (i) utilizing continuous rather than discrete mathematics, and, as a result, (ii) being computationally more powerful than traditional computational automata. Indeed, the logical possibility of such ‘super-powerful’ systems has been demonstrated in the form of analog artificial neural networks. In this paper I consider three arguments against the nomological possibility of these automata. While the first two arguments fail, the third succeeds. In particular, the presence of noise reduces the computational power of analog networks to that of traditional computational automata, and noise is a pervasive feature of information processing in biological systems. Consequently, as an empirical thesis, the proposed dynamical alternative is under-motivated: What is required is an account of how continuously valued systems could be realized in physical systems despite the ubiquity of noise.

Keywords: artificial neural networks; cognition; computational complexity; connectionism; dynamic systems theory

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11023-004-1345-6

Affiliations: 1: Department of Philosophy, Mount Holyoke College, 50 College Street, 01075-6401, MA, South Hadley, USA, Email: wschonbe@mtholyoke.edu

Publication date: 2005-02-01