A New System of Modal Logic

Abstract
This chapter differs from the traditional systems of modal logic in that it studies the various modalities as dyadic predicates or 'relations' between propositions. Such modalities may also be called relative modalities. Relative possibility is the one indefinable modal concept of this system. Absolute possibility is thus a species of the generic notion of relative possibility. It would be rash to maintain that the notions of the absolute modalities were the same as the modal notions of the traditional systems. It is an interesting fact that the laws of the 'classical' systems of modal logic can be interpreted as laws of absolute modalities within the new system. In a sense, therefore, the 'classical' systems may be regarded as special or limiting cases of the logic of dyadic modalities. In the monadic systems of modal logic the notion of a strict implication means a necessary material implication.