Hume's solution of the Goodman paradox and the reliability Riddle (mill's problem)

Philosophical Studies 132 (2):137 - 159 (2007)
Many solutions of the Goodman paradox have been proposed but so far no agreement has been reached about which is the correct solution. However, I will not contribute here to the discussion with a new solution. Rather, I will argue that a solution has been in front of us for more than two hundred years because a careful reading of Hume’s account of inductive inferences shows that, contrary to Goodman’s opinion, it embodies a correct solution of the paradox. Moreover, the account even includes a correct answer to Mill’s question of why in some cases a single instance is sufficient for a complete induction, since Hume gives a well-supported explanation of this reliability phenomenon. The discussion also suggests that Bayesian theory by itself cannot explain this phenomenon. Finally, we will see that Hume’s explanation of the reliability phenomenon is surprisingly similar to the explanation given lately by a number of naturalistic philosophers in their discussion of the Goodman paradox.
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    Rudolf Carnap (1947). On the Application of Inductive Logic. Philosophy and Phenomenological Research 8 (1):133-148.

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