`Ought' and Extensionality

Abstract

In deontic logic it is widely assumed that 'ought'-contexts are nonextensional, just as contexts formed by necessity and belief operators are. Yet questions of quantification, referential transparency and opacity, extensionality, etc. are rarely examined closely in deontic logic. Perhaps that is because deontic logicians have concentrated on problems that arise at the level of propositional logic, and because it is easy to assume that the extension of propositional deontic logic to first-order systems will follow the pattern already established in other areas of modal logic. I will argue here, however, that such an extension is not as smooth as one might expect. In particular, I will argue that, contrary to expectation, there is good reason to consider deontic operators, unlike alethic and intentional modalities, to be fully extensional or referentially transparent with respect to singular terms. Yet if the deontic modalities are extensional, there is a serious risk that deontic logic collapses to triviality. To escape this dilemma, I propose a modification of the standard way of interpreting first-order deontic statements whereby 'ought'-statements are fully extensional for all singular terms and classical rules for quantification and identity apply to them without restriction, while the modalities retain their deontic character. The issue of extensionality arises when deontic operators are included in a first-order language including identity and definite descriptions, for which I will use the usual notation. Here it will be sufficient to focus on the single operator 0 which may apply to any sentence of the language. This is the deontic operator expressed in English by 'it ought to be that . . .' or 'it is obligatory that. . . 9. Since all of the cases I will be examining apply this operator to sentences that say a person performs some action or does something, it is appropriate to paraphrase locutions 'it ought to be that s does A' or 'it is obligatory that s A's' by 's ought to do A' or 's is obliged to A'. If one