Hume's Problem Solved

By Gerhard Schurz. 2019

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Gerhard Schurz’s new book is an ambitious attempt to solve Hume’s problem of induction by techniques developed in computational learning theory. The book advances two major theses. The first is negative: We have no epistemic justification of the reliability of induction (Chs. 2-4), where “reliable” means truth-preserving with high probability. The negative thesis motivates Schurz to investigate the weaker claim: We have an epistemic justification of the optimality of induction (Ch. 5-8), where “optimal” means no worse than any alternative method. In other words, we cannot tell whether induction is reliable or not, but if any prediction method is reliable, then induction is. So, we have good reason to use induction for prediction. This line of support for induction is familiar since Reichenbach (1938), but in light of the problems of Reichenbach’s proposal (Sec. 5.3), Schurz defends the positive thesis of optimality in two steps. First, Schurz argues a priori that the method of meta-induction he describes is optimal in all possible worlds (Chs. 5-7). This is the main part of the book, where he draws on insights from computational learning theory. Schurz then combines the a priori result with the observation that object-induction has been more successful than other methods, to argue a posteriori that objectinduction is optimal (Ch. 8). I will fill out below some details of these points, and note one concern about the optimality approach. Schurz’s negative thesis, to be more precise, is that we have no non-circular epistemic justification of the reliability of induction in the sense (“narrow sense”) of making a prediction based on the observed regularity. Central to his negative thesis is the charge of circularity, e.g. the higher order justification of induction based on its past success assumes, tacitly, the reliability of induction for which the observed regularity relied on is the past success of induction. Some Bayesians may object to the charge of circularity here because by the axioms of the probability calculus the hypothesis is confirmed (the probability of the hypothesis goes up) by the observation entailed by the hypothesis. The hypothesis that all emeralds are green, for example, is confirmed (its probability goes up) by the observations of green emeralds, where there is no epistemic circularity. Schurz’s response to this objection is a version of the tacking problem (Sec. 4.1). The general hypothesis that all emeralds are green is a conjunction: All observed emeralds are green and all non-observed emeralds are green. This conjunction is confirmed by the observation of green emeralds only because the first conjunct is confirmed by the observation while the second conjunct tacked onto it remains unconfirmed. So, the Bayesian argument for the general hypothesis does not justify an inductive prediction. Indeed, the observation of green emeralds also confirms the anti-inductive general hypothesis: All observed emeralds are green and all non-observed emeralds are not green. So, we need justification for using the inductive general hypothesis, instead of the anti-inductive general hypothesis, in making a prediction. It should be noted here that Schurz distinguishes the problem of language-dependence introduced by Goodman (1955) from Hume’s problem of induction (Secs. 1.2, 4.2). Schurz therefore grants that the anti-inductive prediction is indeed anti-inductive, setting aside the challenge that it is inductive relative to an alternative language. Hume’s problem remains in

Subfields: General Social Sciences

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