Some remarks on the Rationality of Induction
This paper begins with a rigorous critique of David Stove's recent bookThe Rationality of Induction. In it, Stove produced four different proofs to refute Hume's sceptical thesis about induction. I show that Stove's attempts to vindicate induction are unsuccessful. Three of his proofs refute theses that are not the sceptical thesis about induction at all. Stove's fourth proof, which uses the sampling principle to justify one particular inductive inference, makes crucial use of an unstated assumption regarding randomness. Once this assumption is made explicit, Hume's thesis once more survives.
The refutation of Stove's fourth proof leads to some observations which relate Goodman's ‘grue’ paradox with randomness of a sample. I formulate a generalized version of Goodman's grue paradox, and argue that whenever a sample, no matter how large, is drawn from a predetermined smaller interval of a population that is distributed over a larger interval, any conclusion drawn about the characteristics of the population based on the observed characteristics of the sample is fatally vulnerable to the generalized grue paradox.
Finally, I argue that the problem of justification of induction can be addressed successfully only from a cognitive point of view, but not from a metaphysical one. That is, we may ask whether an inductive inference is justified or not within the ‘theories’ or ‘cognitive structures’ of a subject, but not outside them. With this realization, induction is seen as a cognitive process, not unlike vision, that is useful at times, and yet has its own illusions that may make it a serious obstacle to cognition at other times.
KeywordsCognitive Process Generalize Version Small Interval Cognitive Structure Large Interval
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