Abstract
Schurz (2019, ch. 4) argues that probabilistic accounts of induction fail. In particular, he criticises probabilistic accounts of induction that appeal to direct inference principles, including subjective Bayesian approaches (e.g., Howson 2000) and objective Bayesian approaches (see, e.g., Williamson 2017). In this paper, I argue that Schurz’ preferred direct inference principle, namely Reichenbach’s Principle of the Narrowest Reference Class, faces formidable problems in a standard probabilistic setting. Furthermore, the main alternative direct inference principle, Lewis’ Principal Principle, is also hard to reconcile with standard probabilism. So, I argue, standard probabilistic approaches cannot appeal to direct inference to explicate the logic of induction. However, I go on to defend a non-standard objective Bayesian account of induction: I argue that this approach can both accommodate direct inference and provide a viable account of the logic of induction. I then defend this account against Schurz’ criticisms.
Highlights
3 I consider a problem for the Principle of the Narrowest Reference Class which shows that in a standard probabilistic framework one cannot appeal to this direct inference principle to provide an adequate account of induction
While the standard Bayesian framework, which appeals to CBCP and Conditionalisation, requires that evidence be expressible in the domain of the probability function, i.e., in the algebra of Ω, the alternative version of objective Bayesianism does not require this
A non-standard variant of objective Bayesianism—that of Williamson (2010; 2017) offers a way out, though: it provides a probabilistic account of inductive inference that does not suffer from these problems that beset the standard approaches
Summary
The more famous of the two, the problem of inductive justification, is the problem that there seems to be no justification of inductive inference which could convince sceptical detractors that we ought to draw even simple inductive inferences This is the problem usually attributed to David Hume, and the problem over which most ink has been spilt. The second problem is perhaps the more pressing of the two This is the problem of inductive logic—the problem that there seems to be no viable logic of inductive inference that can tell us which inductive inferences we ought to draw. 3 I consider a problem for the Principle of the Narrowest Reference Class which shows that in a standard probabilistic framework one cannot appeal to this direct inference principle to provide an adequate account of induction. I argue that a non-standard version of objective Bayesianism can successfully accommodate direct inference
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