Putnam's Diagonal Argument and the Impossibility of a Universal Learning Machine

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Sterkenburg, Tom F.
preprint description
Putnam (1963) construed the aim of Carnap's program of inductive logic as the specification of an "optimum" or "universal" learning machine, and presented a diagonal proof against the very possibility of such a thing. Yet the ideas of Solomonoff (1964) and Levin (1970) 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 learning machine. This paper takes 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 Bayesian induction. I argue that this strategy ultimately still succumbs to diagonalization, reinforcing Putnam's impossibility claim.