What If the Principle of Induction Is Normative? Formal Learning Theory and Hume’s Problem

Abstract

This article argues that a successful answer to Hume’s problem of induction can be developed from a sub‐genre of philosophy of science known as formal learning theory. One of the central concepts of formal learning theory is logical reliability: roughly, a method is logically reliable when it is assured of eventually settling on the truth for every sequence of data that is possible given what we know. I show that the principle of induction (PI) is necessary and sufficient for logical reliability in what I call simple enumerative induction. This answer to Hume’s problem rests on interpreting PI as a normative claim justified by a non‐empirical epistemic means–ends argument. In such an argument, a rule of inference is shown by mathematical or logical proof to promote a specified epistemic end. Since the proof concerning PI and logical reliability is not based on inductive reasoning, this argument avoids the circularity that Hume argued was inherent in any attempt to justify PI.

Acknowledgements

I would like to thank attendees at a 2007 session of the Society for Exact Philosophy, at which an earlier version of this article was presented. I would also like to thank Grant Dowell, Tamra Frei, and two anonymous referees of this journal for helpful comments and suggestions.

Notes

[1] See Hume (2008, §4, pt 2), and Hume (1978, bk 1, pt 3, §6). The label ‘Hume’s problem’ is intended to indicate that the argument is a problem posed by Hume for those who claim that inductive inference has a rational basis in something other than habit or custom.

[2] See Salmon (1967), Howson (2000), Hayek and Hall (2002), and Ladyman (2002, 40–52) for surveys.

[3] The classic text in this sub‐genre is Kelly (1996); also see Martin and Osherson (1998).

[4] And non‐empirical epistemic means‐ends approaches to justifying inductive rules are not limited to the formal learning theory genre (see Schurz 2008).

[5] The point about PI and logical reliability made here also goes for more elaborate versions of Goodman’s riddle (see Steel 2009).

[6] Indeed, since by the standard mineralogical definition emeralds are green beryls, there is good case for claiming that ‘all emeralds are green’ is an analytic truth. However, I set aside that point for the purposes of this discussion.

[7] For a defence of this reading of Goodman’s riddle, see Israel (2004).