Lectures on inductive logic (Q2825455)

This monograph is devoted to the quest of developing a ``general, reliable, applicable inductive logic'' (GRAIL). The author invites students of and researchers in philosophy, computer science and mathematics who are familiar with elementary logic and probability to join his quest.NEWLINENEWLINE The book is partitioned into ten chapters. The first chapter treats classical approaches to inductive logic due to Pólya and Wittgenstein and motivates the need for an inductive logic. Chapter 2 introduces parts of the formal apparatus required for a modern treatment of inductive logic: propositional and predicate logic, probabilities over logical languages and the notion of the entropy of a probability function. In the third chapter, the author describes how to combine probability and logic. The fourth chapter is devoted to the historically first main inductive logic: Carnapian inductive logic. The author argues that this inductive logic is not the desired GRAIL, since -- among other issues -- it fails to capture logical entailment.NEWLINENEWLINE In Chapter 5, Jon Williamson hence develops his own approach, objective Bayesian inductive logic, by appealing to an equivocation principle. This principle is cached out in terms of adopting the probability function with maximal entropy which satisfies all evidential constraints. In the next two chapters, the author shows that his approach captures logical and inductive entailment. In Chapter 8, the author's approach is defended against criticisms of inductive logic in general (language dependence, Goodman's riddle) and his approach specifically (principle of indifference). Chapter 9 puts forward a formal justification of the author's approach in terms of avoiding avoidable losses.NEWLINENEWLINE The brief last chapter takes stock and argues that objective Bayesian inductive logic promises to be a GRAIL.