Journal of Experimental & Theoretical Artificial Intelligence
Analog computation via neural networks
Theoretical Computer Science
On the effect of analog noise in discrete-time analog computations
Neural Computation
Spikes: exploring the neural code
Spikes: exploring the neural code
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Minds and Machines
The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions
On the nature of minds, or: truth and consequences
Journal of Experimental & Theoretical Artificial Intelligence - Pluralism and the Future of Cognitive Science
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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.