Chapter 1 Overview
Chapter 1 Overview
The purpose of this study is to explore a new deontic logic for representing and reasoning about what agents ought to do, a notion that must be distinguished from that of what ought to be the case. The interplay between these two ideas, and the question of which should form the central focus for deontic logic, has long been a delicate problem in the area.
In his seminal article on the subject, Georg Henrik von Wright  first introduced the deontic operators as syntactic expressions applying, not to sentence letters standing for states of affairs, but instead to special symbols representing kinds of actions. The resulting formalism provided the resources for expressing the idea that certain actions are obligatory or permissible—that closing the window, for example, is obligatory. For a variety of reasons, several other early researchers in the area—Alan Anderson , Stig Kanger , Arthur Prior —felt that it was better to conform to the more usual style of modal syntax by allowing deontic operators to apply to arbitrary sentences. This perspective, which has shaped most subsequent work in the field, initiated a line of research that has led to the development of a number of formal systems capable of distinguishing among various aspects of the general idea that certain states of affairs ought or ought not to be—that it ought to be that the window is closed, for example.
Part of the reason for the popularity in deontic logic of the perspective that takes what ought to be as fundamental is sheer technical convenience, the ease of working with formalisms so closely analogous to ordinary modal systems. There is also, however, a philosophical thesis at work—sometimes defended, but often just taken for granted—according to which this perspective is supposed to be more general. The study of what agents ought to do, it is thought, can naturally be subsumed under the broader study of what ought to be, for the simple reason that among the various things that ought or ought not to be are the things that agents do, the actions they perform or refrain from. According to this thesis, saying that an agent ought to close (p.4) the window, for example, is equivalent to saying that it ought to be that the agent closes the window.
It has occasionally been argued, most notably by Peter Geach , that the emphasis in deontic logic on the notion of what ought to be leads to severe distortions when the resulting theories are applied to the task of analyzing what agents ought to do. And von Wright himself has always maintained that a deontic logic adequate for such a task must be built upon the foundation of a more general theory of action; in his own work, he has endeavored both to supply such a foundation  and to integrate it with deontic logic .
This book attempts a similar integration, relying, however, not on von Wright's theory of action, but instead on a more recent treatment developed by Nuel Belnap, Michael Perloff, and Ming Xu in an important series of papers beginning with Belnap and Perloff's  and culminating in Belnap, Perloff, and Xu's . This treatment of action, which is itself cast against the background of an indeterministic tense logic due to Prior , is known as stit semantics, because it concentrates on constructions of the form “α (an agent) sees to it that A,” usually abbreviated simply as [α stit: A]. The goal is to provide a precise semantic account of various stit operators within the overall setting of indeterministic time.
As it happens, Prior's indeterministic temporal framework allows for the introduction of a standard deontic operator ○, meaning “It ought to be that.” It is therefore natural to explore the interactions between this deontic operator and the stit operators representing agency; and it may seem reasonable to propose a logical complex of the form ○[α stit: A]—meaning “It ought to be that α sees to it that A”—as an analysis of the idea that seeing to it that A is something α ought to do. The motive for this analysis, of course, is the philosophical thesis mentioned above, according to which the notion of what an agent ought to do can be identified with the notion of what it ought to be that the agent does.
In this book, I set out what seems to be an incontestable objection to this philosophical thesis, at least as it might be developed using a standard deontic logic; and driven by this objection, I propose a new analysis of the notion of what an agent ought to do. The new analysis is based on a loose parallel between action in indeterministic time and choice under uncertainty, as it is studied in decision theory. Very broadly, a particular preference ordering—a kind of dominance ordering—is adapted from the study of choice under uncertainty to the present account of action, and then used to define both the optimal actions that an agent should perform and the propositions whose truth the agent should guarantee.
The overall structure of the book is as follows. Chapter 2 reviews the theory of indeterministic time that forms the general background and provides a self‐contained introduction to the underlying treatment of action, (p.5) focusing on a particularly simple stit operator. Chapter 3 then introduces a standard deontic operator into this framework, allowing for a precise formulation of the idea that what an agent ought to do can be identified with what it ought to be that the agent does; this idea is defended against certain objections found in the literature, and the new objection is set out. Chapter 4 is the heart of the work, introducing a dominance relation among actions and then using this relation to define a deontic operator that captures a new analysis of what agents ought to do. The remaining three chapters extend and develop this core analysis. Chapter 5 generalizes the account so that it applies to conditional as well as absolute oughts, and then explores certain forms of act utilitarianism. Chapter 6 generalizes the account so that it applies to the oughts governing groups of agents as well as individuals, and then explores a form of rule utilitarianism. Finally, Chapter 7 generalizes the account of oughts so that it applies over extended periods of time as well as to single moments, and then explores the debate between actualism and possibilism in the evaluation of actions.
For the sake of clarity, I have stated definitions and results precisely, but no real mathematical sophistication is involved; any reader with an understanding of elementary modal logic should be able to follow the entire discussion. To preserve readability, all formal proofs are collected into the Appendix.
Although this work is primarily concerned with deontic logic, the emphasis is conceptual rather than technical. I have attempted throughout to relate the various formal options considered to issues from the philosophical literature, showing how the framework developed here allows for a number of positions from recent moral theory to be set out clearly and discussed from a uniform point of view. In doing so, I am aware that I have followed a rather narrow path through some difficult terrain, leaving much of the surrounding territory unexplored. That is not always the right way to work, but in this case I thought it best simply to push ahead.