Free Deontic Logic

The main research goal of this project is to develop a formal system of deontic Logic. In opposition to the Standard approach to deontic Logic, the formal system in question does not use normative sentence operators, but normative predicates instead. Georg Henrik von Wright, the founder of modern deontic Logic, developed in his seminal paper "Deontic Logic" (1951) such a formal system. Nevertheless most philosophers working in this area do not follow von Wright in this respect. In von Wright`s system normative predicates are applied to action-types, denoted by general terms like `murder` er `Smoking`. With relative ease the following sentences are expressible within such a framework: `Murder is forbidden`, er `Smoking in public buildings is forbidden`. In ethics and jurisprudence, however, it is not only of interest to normatively evaluate action-types, but also action-tokens. Examples are: `Rabin`s murderer should be prosecuted`, or `Ethel Rosenberg`s electrocution an June 19, 1953 was wrong`. Von Wright`s System, however, does not permit a formalization of sentences of this kind, although they are ethically and legally relevant. Therefore, we develop a formal system with normative predicates that are applied to singular terms, not to general terms. We notice, first, that everything that is formalizable in von Wright`s System is also formalizable in this new approach, as long as a complete systems of first order predieate Logic with identity is available. Moreover, in normative contexts not only actiontokens of the past, but also action-tokens in the future must be discussed rationally and evaluated normatively. Examples are: `N.N.`s execution an July 25, 2004 in Beijing/China is forbidden`, er `The abortion ofN.N.`s embryo in two days is forbidden (i.e. morally wrong)`. In order to reach this goal in a quite natural way, we use a kind of free Logic, because in free Logic empty singular terms are allowed. This is the first attempt to apply free Logic in the field of deontic Logic. The major task in this project is then to develop a free deontic Logic with normative predicates. The following questions will be addressed: Can a system analogue to the Standard systems of deontic Logic be developed along this line? What does a system of this kind look like? Is it possible to establish an adequate formal semantics for a system of this kind? Can the paradoxes of deontic Logic be avoided within such a System?

Georg Henrik von Wright presented in his ground-breaking paper Deontic Logic (Mind 1951) a deontic logic that met the standards of modern logic. Von Wright`s calculus based on the basic expression permitted . Von Wright`s own position, however, left some range of interpretation, whether this basic expression should be viewed as a predicate or as a sentence-operator. Most researchers in the field of deontic logic interpreted his basic expression, e.g. permitted as a sentence-operator. The main goal of this research project was devoted to the development of a deontic logic with normative predicates. This goal has been achieved two-fold: (1) we developed a formal system - called LAN - in such a way that basic normative predicate is applied to names of concrete actions. Furhermore, (2) this approach was extendend (called LAN*) to deal with action-types too. Both systems, LAN and LAN*, have as a background a first order predicate logic. We introduced a calculus of alternatives that describes basic principles of a logic of actions. Informally, those axioms describe that an agent has the possibilty of choosing between at least two actions and that exactly one action will be performed by the cognitive agent. We have chosen the normative predicate permitted to be our basic functor of LAN. The normative axiom we put forward expresses the fact, that there is at least one permitted action. This seems to be a reasonable claim for any situation that can be accounted as moral. LAN has been proved sound and complete relative to the semantical account we have provided. Due to expressive limitations of LAN when dealing with action-types, we have extended the original approach LAN to LAN*. Thereby we provided principles in order to obtain action-types from concrete (but maybe) possible individual actions. As a further normative predicate, we have introduced permitted but here this predicate is applied to names of action-types and names of situtations. The additional normative axiom expresses, that in every situation there is at least one permitted action-type. Eventually, we modified the system LAN - including its language - in such a way that it is possible to state an explicit definition of moral dilemma. We also provided a logic - called NT - with a suitable semantics such that there is a model for NT and the definition of moral dilemma. This has the effect of providing for a consistent formal frame for dealing with moral dilemmas within a formal setting that includes first order logic and the modal logic T. Originally, we had planned to organize an international workshop with leading experts on the topic of the project. Unfortunately, this work-shop could not be realized during the term of the project for reasons that were outside our scope of influence. It is envisaged, however, to oranganize this conference in the near future.