Contrary-to-Duty Paradoxes and Counterfactual Deontic Logic

Abstract

In this paper, I will discuss some examples of the so-called contrary-to-duty (obligation) paradox, a well-known puzzle in deontic logic. A contrary-to-duty obligation is an obligation telling us what ought to be the case if something forbidden is true, for example: 'If she is guilty, she should confess'. Contrary-to-duty obligations are important in our moral and legal thinking. Therefore, we want to be able to find an adequate symbolisation of such obligations in some logical system, a task that has turned out to be difficult. This is shown by the so-called contrary-to-duty (obligation) paradox. I will investigate and evaluate one kind of solution to this problem that has been suggested in the literature, which I will call the 'counterfactual solution'. I will use some recent systems that combine not only counterfactual logic and deontic logic, but also temporal logic, in my analysis of the paradox. I will argue that the counterfactual solution has many attractive features and that it can give a fairly satisfactory answer to some examples of the contrary-to-duty paradox, but that it nevertheless has some serious problems. The conclusion is that, notwithstanding the many attractive features of the solution, there seem to be other approaches to the paradox that are more promising.

Defeasibility applied to Forrester’s paradox

“…is a contrary-to-duty obligation of ⃝(α 1 | β 1 ) if its antecedent, β 2 , is contradictory to the consequent of the first obligation, α 1 . Intuitively, this means an obligation that informs us what must be the case when something forbidden has been done (Rönnedal, 2019).…”