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Sterkenburg, Tom F. (2019): Putnam's Diagonal Argument and the Impossibility of a Universal Learning Machine. In: Erkenntnis, Vol. 84, No. 3: pp. 633-656
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Abstract

Putnam construed the aim of Carnap's program of inductive logic as the specification of a universal learning machine, and presented a diagonal proof against the very possibility of such a thing. Yet the ideas of Solomonoff and Levin lead to a mathematical foundation of precisely those aspects of Carnap's program that Putnam took issue with, and in particular, resurrect the notion of a universal mechanical rule for induction. In this paper, I take up the question whether the Solomonoff-Levin proposal is successful in this respect. I expose the general strategy to evade Putnam's argument, leading to a broader discussion of the outer limits of mechanized induction. I argue that this strategy ultimately still succumbs to diagonalization, reinforcing Putnam's impossibility claim.