Induction and Logical Types
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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