Deontic Logic and Imperative Logic, Introduction

The behavior of deontic predicates such as 'obligatory', 'permissible' and 'forbidden' has long been receiving philosophers' attention. As early as in the Middle Ages, it was observed that there exists a similarity between the concept obligation and the concept necessity on the one hand, and the behavior of the concept permission and of the concept possibility on the other. However, the philosophical treatment of these deontic concepts had been largely peripheral and made in passing until early this century when Ernst Mally tried to formalize systematically the deontic concepts.1 It was he who first used the word 'deontik' and called his study of these concepts 'Deontik Logik'.

Subsequently, a remarkable number of efforts have been made either directly in deontic logic or in fields closely related to it, e.g., in the logic of imperatives or in the logic of commands. Examples of these efforts made before 1950 can be found most significantly in the following literature: Kurt Grelling [1939], Karel Reach [1939], Karl Menger [1939], Albert Hofstadter and John Charles Chinoweth McKinsey [1939], Alf Ross [1941] and Herbert Gaylord Bohnert [1945].

It is perhaps sound to say, however, that the ice of modern deontic study was not really broken until the late 1950's when the Finnish logician Georg Henrik von Wright published his earliest studies on deontic logic with an effort to formalize the deontic concepts of permission, obligation, prohibition and commitment.2 Since the publication of the earliest papers by von Wright, the study of deontic concepts has received widespread philosophical attention both in the English-speaking world and in Scandinavian countries.3

Although hardly twenty years have elapsed, we find a wide range of deontic logics on display. Among them some systems are based upon standard propositional logic, 4others take alethic modal logics as their cornerstones. 5There are still others in which quantifiers play an indispensable role.6Besides, of all the varieties some systems are two-valued, 7others three-valued;8some systems formalize the relativized deontic concepts,9others incorporate tense-logical notions as their basic concepts.10Furthermore, some philosophers discuss deontic logic in the context of, or in coordination with, imperative logic or directive logic;11others base their deontic logics on another formalized or formalizable system, such as the "logic of better",12and so on. This list of variety in deontic logic can be extended considerably, and all of the deontic systems are devised to capture the formal structure of deontic concepts.

In the course of development of these various deontic systems, different types of procedure to single out the "deontic truths" have also been advanced. Among them, axiomatics is hardly a new technique as one may expect. The truth table or matrix method and the normal form method are also commonly used. In addition, Quine's truth-value analysis, Hintikka's model-set method, Kripkean model structure together with Beth's semantical tableaux, and Fitch's subordinate proof, all have found their ways into deontic logic.

This brief description of deontic logic may lead one to conclude that the modern development of deontic logic has now reached a mature and advanced stage. This conclusion, however, is too hasty if not totally unjustifiable. For one thing, logic may not be just a game of manipulating symbols. We usually intend a logic to be a formalization or systematization of a set of concepts of which the underlying "logic" is intuitively conceived. In our present case, this set of concepts is the so-called deontic concepts: obligation, permission, prohibition (forbiddance) and commitment . A deontic logic is meant to explicate these concepts. Hence, the success of a deontic logician depends not only on whether he has a syntactically well-built system, but also on whether his system admits of a sound semantical interpretation which is genuinely deontic. From this point of view, it is not without good reason that some philosophers also call deontic logic the logic of obligation. This reminds us from the very beginning what deontic logic aims at, and provides us with an intuitive ground to justify its degree of success.

It is a common belief, and a usual practice, too, among deontic logicians that the concepts of obligation, permission and prohibition are interdefinable with the help of some logical constants (e.g., the negation and conjunction connectives). 13It follows immediately that the logic of obligation, the logic of permission, and the logic of prohibition are or could be, one and the same logic. But what about the logic of commitment? Is the concept "commitment" definable in terms of one or several of the other deontic concepts with perhaps the help of certain logical constants? The answer is far less definite.

Von Wright first tried to formalize the concept of commitment in terms of obligation and the material conditional.14Since that proposal was put forward, criticism and new proposals have been mounting in the literature. But till now there seems to be no single satisfactory formulation which is commonly accepted by deontic logicians. To make the situation even worse, Roderick M. Chisholm introduced the so-called contrary-to-duty imperative into deontic studies,15thereby adding to the already puzzling problem a new dimension of difficulty.

This is just an indication of the semantic difficulties which a deontic logician encounters. In addition, the problems of deontic logic come from pragmatic considerations, too. Some philosophers tend to think that a sound deontic system should be able to function as a logic of imperative (or directive) inference which can be used to justify imperative reasoning just as ordinary logic has been used to justify descriptive or assertoric reasoning. Indeed, some philosophers, notably Ross [1968], even call a logic of imperatives deontic logic. And the problems of imperative logic have often been treated as the problems of deontic logic.

There are, then, two classes of problems we have so far mentioned. On the one hand, there are semantic problems of how to interpret a deontic logic as a sound logic of obligation and other deontic concepts. Or, what turns out to be the same thing, the problem of how to "correctly" formalize our intuitive deontic concepts. And, on the other hand, we have the pragmatic problems of how our logic can be used as a logic of imperatives. These are indeed, two set of problems we want to consider in this discussion.

But before we set out to discuss these problems, we shall first try to present some systems of deontic logic. We shall treat three systems OT*, OS4* and OS5* quite thoroughly, and compare them with von Wright's system vW, Fisher and Åqvist's system FA and Anderson's systems OM, OM' and OM". This will help us to locate our problems precisely in their proper contexts, and make us understand more adequately the nature of the problems.

1.See Mally [1926]. The author-cum-date reference is made to the bibliography at the end of this book.

2.In English, the word 'deontic' was coined, according to von Wright, by Charles Dunbar Broad. See von Wright [1951a].

3.See especially, von Wright [1951a] and [1951b].

4.For example, von Wright [1951a], [1951b], [1956], [1965a] and Fisher [1961b].

5.E.g.,Anderson [1956] and Prior [1957].

6.See Hintikka [1957].

7.Von Wright [1951b].

8.Fisher [1961b] and Åqvist [1963b].

9.Von Wright [1956] and Rescher [1958].

10.Von Wright [1965b] and Åqvist [1966]. cf.§14.

11.E.g., Geach [1958], Castañeda [1958], [1968], and Ross [1968].

12.Åqvist [1963c].

13.See, for example (D2.1)-(D2.3) in next section.

14.Von Wright [1951a].

15.Chisholm [1963a].

§1.Introduction