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)

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.

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. Yet (...) the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (shrink)

According to the Feigl–Reichenbach–Salmon–Schurz pragmatic justification of induction, no predictive method is guaranteed or even likely to work for predicting the future; but if anything will work, induction will work—at least when induction is employed at the meta-level of predictive methods in light of their track records. One entertains a priori all manner of esoteric prediction methods, and is said to arrive a posteriori at the conclusion, based on the actual past, that object-level induction is optimal. Schurz’s refinements largely solve (...) the notorious short-run problem. A difficulty is noted, however, related to short-run worries but based on localized disagreement about the past, a feature characteristic of real debates (especially early modern) involving induction in intellectual history. Given the evidence about past events, _unfiltered by induction_, meta-induction might support a partly non-inductive method—especially as judged by proponents of esoteric prediction methods, who presumably believe that their methods have worked. Thus induction is justified meta-inductively in contexts where it was uncontroversial, while not obviously justified in key contexts where it has been disputed. This objection, momentarily sensed by Reichenbach regarding clairvoyance, is borne out by the Stoics’ use of meta-induction to justify both science and divination and by ancient Hebrew examples of meta-induction. Schurz’s recently introduced criteria for acceptance of testimony play a crucial role in arriving at object-level induction using meta-induction, but one might question them. Given the need for judgment in accepting testimony, it is unclear that the subjectivity of Howson’s Bayesian answer to Hume’s problem is overcome. (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)

I evaluate Schurz's proposed meta-inductive justification of induction, a refinement of Reichenbach's pragmatic justification that rests on results from the machine learning branch of prediction with expert advice. My conclusion is that the argument, suitably explicated, comes remarkably close to its grand aim: an actual justification of induction. This finding, however, is subject to two main qualifications, and still disregards one important challenge. The first qualification concerns the empirical success of induction. Even though, I argue, Schurz's argument does not need (...) to spell out what inductive method actually consists in, it does need to postulate that there is something like the inductive or scientific prediction strategy that has so far been significantly more successful than alternative approaches. The second qualification concerns the difference between having a justification for inductive method and for sticking with induction for now. Schurz's argument can only provide the latter. Finally, the remaining challenge concerns the pool of alternative strategies, and the relevant notion of a meta-inductivist's optimality that features in the analytic step of Schurz's argument. Building on the work done here, I will argue in a follow-up paper that the argument needs a stronger dynamic notion of a meta-inductivist's optimality. (shrink)

One of the most discussed issues in psychology—presently and in the past—is how to define and measure the extent to which human cognition is rational. The rationality of human cognition is often evaluated in terms of normative standards based on a priori intuitions. Yet this approach has been challenged by two recent developments in psychology that we review in this article: ecological rationality and descriptivism. Going beyond these contributions, we consider it a good moment for psychologists and philosophers to join (...) forces and work toward a new foundation for the definition of rational cognition. We take a first step in this direction by proposing that the rationality of both cognitive and normative systems can be measured in terms of their cognitive success. Cognitive success can be defined and gauged in terms of two factors: ecological validity (the system's validity in conditions in which it is applicable) and the system's applicability (the scope of conditions under which it can be applied). As we show, prominent systems of reasoning—deductive reasoning, Bayesian reasoning, uncertain conditionals, and prediction and choice—perform rather differently on these two factors. Furthermore, we demonstrate that conceptualizing rationality according to its cognitive success offers a new perspective on the time-honored relationship between the descriptive (“is”) and the normative (“ought”) in psychology and philosophy. (shrink)