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)

Surprisingly, modified versions of the confirmation theory (Carnap and Hempel) and truth approximation theory (Popper) turn out to be smoothly sythesizable. The glue between the two appears to be the instrumentalist methodology, rather than that of the falsificationalist. The instrumentalist methodology, used in the separate, comparative evaluation of theories in terms of their successes and problems (hence, even if already falsified), provides in theory and practice the straight road to short-term empirical progress in science ( à la Laudan). It is (...) also argued that such progress is also functional for all kinds of truth approximation: observational, referential, and theoretical. This sheds new light on the long-term dynamics of science and hence on the relation between the main epistemological positions, viz., instrumentalism (Toulmin, Laudan), constructive empiricism (Van Fraassen), referential realism (Hacking, Cartwright), and theory realism of a non-essentialist nature (constructive realism à la Popper). Readership: Open minded philosophers and scientists. The book explains and justifies the scientist's intuition that the debate among philosophers about instrumentalism and realism has almost no practical consequences. (shrink)

This article discusses the classical problem of zero probability of universal generalizations in Rudolf Carnap’s inductive logic. A correction rule for updating the inductive method on the basis of evidence will be presented. It will be shown that this rule has the effect that infinite streams of uniform evidence assume a non-zero limit probability. Since Carnap’s inductive logic is based on finite domains of individuals, the probability of the corresponding universal quantification changes accordingly. This implies that universal generalizations can receive (...) positive prior and posterior probabilities, even for (countably) infinite domains. (shrink)

This article discusses the problem of non-zero probabilities for non-tautologous universal generalizations in Rudolf Carnap’s inductive logic when the domain of discourse is infinite. A solution is provided for a generalization of the form “all Xs are Ys”, for example “all ravens all black”. The solution is based on assuming that a significant part of the domain consists of non-Xs. This assumption can often be justified as a kind of ceteris paribus principle.