Induction and Logical Types

  • M. C. Goodall


The theory of cognitive systems deals with an old subject, inductive inference, from a new point of view, that of constructibility. The latter has the merit of bringing to light almost immediately a basic paradox: a machine that can be defined cannot be intelligent. Suppose this machine has a basic strategy Q 0; then either this is fixed, in which case it cannot be intelligent, being incapable of self-improvement, or Q 0 must be the subject of another strategy Q 1 to which the same argument applies, and so on.


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  1. Cowan, J. D. and Winograd, S. 1961. Phil. Trans. Roy. Soc. (in press).Google Scholar
  2. Gödel, K. 1931. Monatshefte f. Math. u. Phys. 38, 173.Google Scholar
  3. Goodall, M. C. 1962. A fundamental complementarity principle for inductive logic. Nature (to be published).Google Scholar
  4. Herdan, G. 1960. Type-token mathematics. N. Holland.Google Scholar
  5. McCulloch, W. S. 1956. Biological stability. Brookhaven Symposium.Google Scholar
  6. Post, E. L. 1921. Am. J. Math. 43, 163.CrossRefGoogle Scholar
  7. Russell, B. 1903. Principles of mathematics.Google Scholar
  8. Russell, B. and Whitehead, A.N. 1910. Principia mathematica.Google Scholar
  9. Shannon, C. E. 1948. Bell Syst. Tech. J. 27, 379.Google Scholar

Copyright information

© Plenum Press, Inc. 1962

Authors and Affiliations

  • M. C. Goodall
    • 1
  1. 1.Research Laboratory of ElectronicsMassachusetts Institute of TechnologyCambridgeUSA

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