Cognition and the Power of Continuous Dynamical Systems
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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.
Keywordsartificial neural networks cognition computational complexity connectionism dynamic systems theory
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- Davis, M. 1965The Undecidable: Basic Papers on Undecidable Propositions,Unsolvable Problems and Computable FunctionsRaven PressHewlett, NYGoogle Scholar
- Fodor, J. 1975The Language of ThoughtMIT PressCambridge, MAGoogle Scholar
- Fodor, J. 1998Concepts: Where Cognitive Science Went WrongOxford University PressOxford, UKGoogle Scholar
- Fodor, J., Lepore, E. 1992Holism: A Shopper’s GuideBlackwell PublishersOxford, UKGoogle Scholar
- Haugeland, J. 1991‘Representational genera’Ramsey, W.Stich, S.P.Rumelhart, D.E. eds. Philosophy and Connectionist TheoryErlbaumHillsdale, NJGoogle Scholar
- Horgan, T., Tienson, J. 1996Connectionism and the Philosophy of PsychologyMIT PressCambridge, MAGoogle Scholar
- Rieke, F. 1997Spikes: Exploring the Neural CodeMIT PressCambridge, MAGoogle Scholar
- Siegelmann, H.T. 2000‘Finite versus infinite neural computation’Calude, C.S.Paun, G. eds. Finite vs Infinite:Contributions to an Eternal DileitmmaSpringerLondonGoogle Scholar
- Turing, A.M. (1936), ‘On Computable Numbers, with an Application to the Entscheidungsproblem’, Proceedings of the London Mathematical Society 42(series 2), pp. 230–256.Google Scholar
- Van Gelder, T. 1997‘Dynamics and Cognition’Haugeland, J eds. Mind Design IIMIT PressCambridge, MA421476Google Scholar