Cognition and the power of continuous dynamical systems

Minds and Machines 15 (1):57-71 (2004)
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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

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Whit Schonbein
Sandia National Laboratories

Citations of this work

Computation in physical systems.Gualtiero Piccinini - 2010 - Stanford Encyclopedia of Philosophy.
The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
Varieties of Analog and Digital Representation.Whit Schonbein - 2014 - Minds and Machines 24 (4):415-438.
On the nature of minds, or: Truth and consequences.Shimon Edelman - 2008 - Journal of Experimental and Theoretical Ai 20:181-196.
Misbehaving Machines: The Emulated Brains of Transhumanist Dreams.Corry Shores - 2011 - Journal of Evolution and Technology 22 (1):10-22.

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References found in this work

The Language of Thought.Jerry A. Fodor - 1975 - Harvard University Press.
Concepts: Where Cognitive Science Went Wrong.Jerry A. Fodor - 1998 - Oxford, GB: Oxford University Press.
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Holism: A Shopper's Guide.Jerry A. Fodor & Ernest Lepore - 1992 - Cambridge, Mass., USA: Blackwell. Edited by Ernest LePore.
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.

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