Further Into the Abyss: Graham Priest’s Towards Non-Being

Abstract

This lightly revised but much expanded second edition of Graham Priest’s book reproduces, with only minor changes, the first edition (Chapters 1–8),1 and adds a further ten chapters. Of these, the first five treat in more detail of leading ideas and constructions deployed in the first edition, and include replies to many of its critics.2 The remaining five are more or less self-contained discussions of several topics closely related to the book’s main themes. The two central aims of TNB1 were to develop a semantics for intentionality and to defend a version of an ontological view which Priest, following Richard Routley (later Sylvan) calls noneism. Since these remain the central themes of TNB2, I shall discuss them at some length, before turning to a more summary discussion of what is new in this edition. Intentionality is the phenomenon of aboutness involved in mental states, acts, and attitudes as expressed or reported by verbs such as ‘know’, ‘believe’, ‘fear’, ‘hope’, ‘contemplate’, ‘worship’, etc. These verbs may govern clauses, as in ‘The ancient Greeks believed that Mount Olympus was inhabited by many gods, led by their king, Zeus’, or they may take direct objects (nouns or noun phrases), as in ‘The ancient Greeks worshipped Zeus and feared his wrath’. Such statements may be true, regardless of whether there exist objects named by the names or singular terms occurring in the clauses or phrases which complement the verbs. There are accordingly two main kinds of construction involving intentional verbs, those in which the verb is taken as the core of a sentence-forming operator on sentences, as in ‘Odysseus hoped that Polyphemus would not notice his men clinging beneath the cyclops’ sheep’, exemplifying the general form: |$a\Psi p$|⁠, where |$a$| is a term and |$p$| a sentence; and those in which it figures as a (first-level) predicate, as in ‘Homer worshipped Zeus’, exemplifying the general form |$a\Psi b$|⁠, where |$a$| and |$b$| are both terms. Such constructions give rise to a variety of well-known and much-discussed logical problems. These include: failures of the principle of substitutivity of identicals which holds for extensional contexts; the problem of logical omniscience, and more generally, failures of closure under logical consequence or entailment in intentional contexts; failures of the principle of existential generalization; and failures of other logical principles, such as the Barcan and Converse Barcan principles, which are often taken to hold good in modal contexts.