Stability of Correct Reasoning

  • T. Poston


A note by Aizerman somewhat misrepresents the work of Smale and its implications for control theory, and calls for the creation of systems of argument ‘correct to within pathological cases’ of which, however, examples exist already (though not using fuzzy sets as Aizerman suggests).




  1. 1.
    M. A. Aizerman, “Some Unsolved Problems in the Theory of Automatic Control and Fuzzy Proofs” IEEE Trans. on Automatic Control 116-118 (February, 1977).Google Scholar
  2. 2.
    S. Smale, “Structurally stable systems are not dense” Amer. J. Math. 88, 491–496 (1966).MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    S. Smale, “A structurally stable differentiable homeomorphism with an infinite number of periodic points” Proc. Int. Symp. on Non-linear Vibrations 1961 (Izdat. Akad. Ukrain. SSR, Kiev1963) pp. 365–366.Google Scholar
  4. 4.
    T. Poston and I. N. Stewart, Catastrophe Theory and Its Applications (Pitman, London/S. Francisco 1978; Saienshu-Sha, Tokyo, 1979).MATHGoogle Scholar
  5. 5.
    T.-Y. Li and J. A. Yorke, “Period three implies chaos” Amer. Math. Monthly 82, 985–992 (1975).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© The World Organisation of General Systems and Cybernetics 1978

Authors and Affiliations

  • T. Poston
    • 1
  1. 1.Battelle Advanced Studies CentreGenevaSwitzerland

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