On a Dilemma of Conditional Obligation

Conditional obligations play an important role in normative argumentation. A large number, if not the majority of norms have a conditional form: if p then it ought to be that q: An important class among the conditional obligations are the so-called commitments, that is, sentences of the form 'the performance of (the action described by) p commits one person to perform q'. The concept of conditional obligation has caused deontic logicians much trouble. Many proposals were made how to formalize the notion properly, but none of them has proved satisfactory. The dilemma can be summarized as follows: it seems necessary to have a form of detachment rule so that one can proceed from conditional to unconditional obligation, if the condition is satissed. On the other hand, if the rule of detachment is allowed, then in many cases one can deduce too much: from intuitively consistent premisses one can deduce contradictory consequences. The best-known example for such counter-intuitive results is Chisholm's contrary-to-duty paradox. The aim of my paper is to propose a simple solution to this problem. I shall show that Chisholm's contrary-to-duty paradox can be solved in a very simple way. In monadic deontic logic, there are two natural candidates for formalizing the notion of conditional obligation. Some authors suggest the formula "O(p q)", others the formula "p Oq" as the formalization of the sentence: "q ought to be under the condition p". The rst formula is favored, e.g., by von Wright ((7], 8]), and the second by, e.g. Chisholm ((4]) and Weinberger ((6].) Both suggestions have their own drawbacks. It is well-known that the following formulae are valid in standard deontic logic (SDL): Fp O(p q) (1) Oq O(p q) (2) Thus, if "O(p q)" is to be read as "p commits you to do q" then formula (1) suggests that doing something forbidden commits one to do anything, and formula (2) that anything commits one to do one's duty. One may try otherwise and use "p Oq" to formalize the notion of commitment. However, similar problems arise: the following formulae are valid for SDL: