Minds and Machines

, Volume 15, Issue 1, pp 57–71 | Cite as

Cognition and the Power of Continuous Dynamical Systems

Article

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Casey, M.P. 1996‘The Dynamics of Discrete-Time Computation with Application to Recurrent Neural Networks and Finite State Machine Extraction’.Neural Computation811351178CrossRefGoogle Scholar
  2. Davis, M. 1965The Undecidable: Basic Papers on Undecidable Propositions,Unsolvable Problems and Computable FunctionsRaven PressHewlett, NYGoogle Scholar
  3. Eliasmith, C. 2001‘Attractive and In-discrete’Minds and Machines11417426MATHCrossRefGoogle Scholar
  4. Fields, C.A. 1989‘Consequences of Nonclassical Measurement for the Algorithmic Description of Continuous Dynamical Systems’.Journal of Experimental and Theoretical Artificial Intelligence1171189CrossRefGoogle Scholar
  5. Fodor, J. 1975The Language of ThoughtMIT PressCambridge, MAGoogle Scholar
  6. Fodor, J. 1998Concepts: Where Cognitive Science Went WrongOxford University PressOxford, UKGoogle Scholar
  7. Fodor, J., Lepore, E. 1992Holism: A Shopper’s GuideBlackwell PublishersOxford, UKGoogle Scholar
  8. Hadley, R.F. 2000‘Cognition and the Computational Power of Connectionist Networks’.Connection Science1295110CrossRefGoogle Scholar
  9. Haugeland, J. 1991

    ‘Representational genera’

    Ramsey, W.Stich, S.P.Rumelhart, D.E. eds. Philosophy and Connectionist TheoryErlbaumHillsdale, NJ
    Google Scholar
  10. Hopcroft, J.E., Ullman, J.D. 1979Introduction to Automata Theory,Languages and ComputationAddison-WesleyReading, MAMATHGoogle Scholar
  11. Horgan, T., Tienson, J. 1996Connectionism and the Philosophy of PsychologyMIT PressCambridge, MAGoogle Scholar
  12. Horgan, T. 1997‘Connectionism and the Philosophical Foundations of Cognitive Science’.Metaphilosophy28130CrossRefGoogle Scholar
  13. Maass, W., Orponen, P. 1998‘On the Effect of Analog Noise on Discrete Time Analog Computations’.Neural Computation1010711095CrossRefGoogle Scholar
  14. Maass, W., Sontag, E. 1999‘Analog Neural Nets with Gaussian or Other Common Noise Distribution Cannot Recognize Arbitrary Regular Languages’.Neural Computation11771782CrossRefGoogle Scholar
  15. McLaughlin, B. 1993‘The Connectionism/Classicism Battle to Win Souls’.Philosophical Studies71 163190CrossRefGoogle Scholar
  16. Rieke, F. 1997Spikes: Exploring the Neural CodeMIT PressCambridge, MAGoogle Scholar
  17. Siegelmann, H.T., Sontag, E.D. 1994‘Analog Computation via Neural Networks’.Theoretical Computer Science131331360MATHCrossRefMathSciNetGoogle Scholar
  18. Siegelmann, H.T. 1999Neural Networks and Analog Computation: Beyond the Turing LimitBirkhäuserBostonMATHGoogle Scholar
  19. Siegelmann, H.T. 2000

    ‘Finite versus infinite neural computation’

    Calude, C.S.Paun, G. eds. Finite vs Infinite:Contributions to an Eternal DileitmmaSpringerLondon
    Google Scholar
  20. 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
  21. Van Gelder, T. 1995‘What Might Cognition be, if not Computation?’.Journal of Philosophy91345381CrossRefGoogle Scholar
  22. Van Gelder, T. 1997

    ‘Dynamics and Cognition’

    Haugeland, J eds. Mind Design IIMIT PressCambridge, MA421476
    Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of PhilosophyMount Holyoke CollegeSouth HadleyUSA

Personalised recommendations