The important recent book by Schurz ( 2019 ) appreciates that the no-free-lunch theorems (NFL) have major implications for the problem of (meta) induction. Here I review the NFL theorems, emphasizing that they do not only concern the case where there is a uniform prior—they prove that there are “as many priors” (loosely speaking) for which any induction algorithm _A_ out-generalizes some induction algorithm _B_ as vice-versa. Importantly though, in addition to the NFL theorems, there are many _free lunch_ theorems. (...) In particular, the NFL theorems can only be used to compare the expected performance of an induction algorithm _A_, considered in isolation, with the expected performance of an induction algorithm _B_, considered in isolation. There is a rich set of free lunches which instead concern the statistical _correlations_ among the generalization errors of induction algorithms. As I describe, the meta-induction algorithms that Schurz advocates as a “solution to Hume’s problem” are simply examples of such a free lunch based on correlations among the generalization errors of induction algorithms. I end by pointing out that the prior that Schurz advocates, which is uniform over bit frequencies rather than bit patterns, is contradicted by thousands of experiments in statistical physics and by the great success of the maximum entropy procedure in inductive inference. (shrink)

This article poses a challenge to Schurz’s proposed metainductive justification of induction. It is argued that Schurz’s argument requires a notion of optimality that can deal with an expanding pool of prediction strategies.

In the first section, five major attempts to solve the problem of induction and their failures are discussed. In the second section, an account of meta-induction is introduced. It offers a novel solution to the problem of induction, based on mathematical theorems about the predictive optimality of attractivity-weighted meta-induction. In the third section, how the a priori justification of meta-induction provides a non-circular a posteriori justification of object-induction, based on its superior track record, is explained. In the fourth section, four (...) important extensions and refinements of the method of meta-induction are presented. The final section, summarizes the major impacts of the program of meta-induction for epistemology, the philosophy of science and cognitive science. (shrink)

In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value. Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, (...) can be translated into classical logic by introducing additional intensional operators into the language. Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic. (shrink)

In this paper, the contributions to the account of meta-induction (Schurz 2019) collected in this volume are critically discussed and thereby, new insights are developed. How broad and expandable the program of meta-induction is can be learned from Ortner’s contribution. New insights about the transition from the a priori justification of meta-induction to the a posteriori justification of object-induction emerge from the reflection of Shogenji’s paper. How meta-induction may be applied also to religious prophecies and that their meta-inductive justification does (...) not fail for a priori reasons but because of missing evidence for predictive success is learned from the discussion of Pitts’ contribution. That meta-induction does not rely on a particular prior distribution, while the no free lunch theorem depends implicitly on a uniform prior, is the major conclusion drawn from the discussion of Wolpert’s article. How the problem of induction is treated in different versions of the Bayesian account is learned from the discussion of Willliamson’s paper. That meta-induction can also be employed for abduction, and that abductive theory-revision can offer meta-inductive aggregation methods is a new insight emerging from the reflection of Aliseda’s contribution. (shrink)

We often need to have beliefs about things on which we are not experts. Luckily, we often have access to expert judgements on such topics. But how should we form our beliefs on the basis of expert opinion when experts conflict in their judgments? This is the core of the novice/2-expert problem in social epistemology. A closely related question is important in the context of policy making: how should a policy maker use expert judgments when making policy in domains in (...) which she is not herself an expert? This question is more complex, given the messy and strategic nature of politics. In this paper we argue that the prediction with expert advice framework from machine learning provides helpful tools for addressing these problems. We outline conditions under which we should expert PWEA to be helpful and those under which we should not expect these methods to perform well. (shrink)

It is undeniable that inductive reasoning has brought us much good. At least since Hume, however, philosophers have wondered how to justify our reliance on induction. In important recent work, Schurz points out that philosophers have been wrongly assuming that justifying induction is tantamount to showing induction to be reliable. According to him, to justify our reliance on induction, it is enough to show that induction is optimal. His optimality approach consists of two steps: an analytic argument for meta-induction (that (...) is, induction over inductive methods) and an application of meta-induction to empirical findings concerning the predictive accuracy of our actual inductive practices as compared to various non-inductive methods. The present article agrees with Schurz’s general conclusion but also argues that it leaves an important aspect of our inductive practices unaccounted for, to wit, that these practices have so far been highly successful; to satisfy the optimality requirement, induction only needs to be as successful as random guessing. To explain the success of induction, I turn to insights from social epistemology, also highlighted in Schurz’s work, and make these formally explicit in a framework that combines the Hegselmann–Krause model for opinion dynamics and Carnap’s system of λ rules. Within this framework, I use a standard evolutionary algorithm to show how communities of interacting agents may, through variation and selection, come to consist of highly successful inductive reasoners. (shrink)

Confronted with the problem of induction, Hans Reichenbach accepts that we cannot justify that induction is reliable. He tries to solve the problem by proving a weaker proposition: that induction is an optimal method of prediction, because it is guaranteed not to be worse and may be better than any alternative. Regarding the most serious objection to his approach, Reichenbach himself hints at an answer without spelling it out. In this paper, I will argue that there are two workable strategies (...) to rehabilitate Reichenbach’s account. The first leads to the widely discussed method of meta-induction, as proposed by Gerhard Schurz. The second strategy has not been suggested thus far. I will develop the second strategy and argue for it being, in some respects, superior to the first and closer to Reichenbach’s own position. (shrink)

Douven (in press) observes that Schurz's meta-inductive justification of induction cannot explain the great empirical success of induction, and offers an explanation based on computer simulations of the social and evolutionary development of our inductive practices. In this paper, I argue that Douven's account does not address the explanatory question that Schurz's argument leaves open, and that the assumption of the environment's induction-friendliness that is inherent to Douven's simulations is not justified by Schurz's argument.