Possible worlds in 'The Craft of Formal Logic'

摘要

"The Craft of Formal Logic" is Arthur Prior's unpublished textbook, written in 1950-51, in which he developed a theory of modality as quantification over possible worlds-like objects. This theory predates most of the prominent pioneering texts in possible worlds semantics and anticipates the significance of its basic concept in modal logic. Prior explicitly defines modal operators as quantifiers of 'entities' with modal character. Although he talks about these 'entities' only informally, and hesitates how to name them, using alternately the phrases 'possible states of affairs', 'chances', 'cases' or 'peculiar objects', he is nevertheless very clear that they should be the fundamental concept of any theory of modality as a form of quantity. Without the assumption that modal operators quantify over such modal objects, the modal system will be incapable of distinguishing an actually true proposition from a necessarily true one. Due to the fact that Prior never made any direct reference to this theory in his subsequently published papers, it remained largely unknown. The comparison of "The Craft" with some of his papers on tense logic suggests that this early theory of modality underlies his later work on temporality.