The is-ought problem. An investigation in philosophical logic
This book is philosophical logic at its best. It applies the rigorous methods and results of formal alethic and deontic modal logic to the long-standing philosophical question of whether Ought is ever derivable from Is, i.e., whether normative statements are ever validly inferable from purely descriptive statements. By addressing this question at a high level of abstraction, the author is able to establish very general results. Chapter 1 sets up the philosophical background of the Is-Ought problem. Chapter 2 develops the formal languages that will be applied to analyzing this problem. These are first-order bi-modal, alethic-deontic languages with or without identity and interpreted in models with or without constant domains and with or without rigid designation. (Hence, there is a variety of languages with respect to which the problem must be addressed.) The alethic modal logic may vary in familiar ways; the deontic logic is based on standard assumptions, where statements \(OA\) are interpreted as true at a point just when \(A\) is true at all \textit{ideal} points. Chapter 3 articulates the Is-Ought problem precisely. There are four distinct `Special Hume Theses' (SH) that no purely normative statement \(N\), not logically true logically follows from a consistent, purely descriptive set of premisses, \({\mathbf D}\), depending on how `purely normative' is construed. There is a more interesting `General Hume Thesis' (GH) that no \textit{mixed} conclusion, \(A\), containing both descriptive and normative components, logically follows from a purely descriptive set of premisses, \({\mathbf D}\), unless \(A\) is `Ought-Irrelevant' to \({\mathbf D}\), i.e., unless the result of substituting any predicate for the predicates within the scope of the `ought'-operators of \(A\) would also follow from \({\mathbf D}\). Chapter 4 establishes precise conditions under which (GH) holds. Chapter 5 establishes conditions for (SH), connecting Hume's thesis with Halldén completeness. Chapter 6 examines weaker versions of Hume's thesis when certain bridge principles, like Ought implies Can and Necessary implies Ought, are adopted. Chapter 7 considers weak interpretations of the alethic operator, as either `belief' or as `desire'. Chapter 8 generalizes the results to non-normal (alethic) modal logics. Chapter 9 applies the results to philosophical arguments from ethical theory. Chapter 10 considers the special problems that arise in quantified modal logic with regard to identity and existence and how these bear on Hume's thesis. Because, as proved, normative statements are derivable from descriptive premisses only in the presence of ineliminable bridge principles, the last two chapters examine the standing of such principles. Here the arguments become more philosophical than formal. Chapter 11 argues against candidate bridge principles being analytic (except those considered in Ch. 6), while Chapter 12 addresses how synthetic principles might be confirmed, if at all. Throughout, this book establishes important conclusions regarding Hume's thesis. Equally important is the clarity it brings to the analysis of the problem itself, and how it demonstrates the fruitfulness of formal methods for philosophical inquiry.
scientific article; zbMATH DE number 1322227