Non - Kripkean Deontic Logic

Abstract

Deontic logic has as its defining characteristic that it treats the word ‘ought’ as a logical word. Although one might undertake such a project as a purely formal exercise, there is a much deeper philosophical motivation. It is accepted among moral philosophers that the word ‘ought’ must be interpreted in a way which makes certain inferences valid. One of the most notable of these is:

$$\frac{{It\,ought\,to\,be\,the\,case\,that\,\alpha }}{{It\,is\,\log ically\,possible\,that\,\alpha }}$$

which is a very weak version of the slogan that “ought implies can”.