Logical and Extra-Logical Entailment

Abstract This chapter lays out, in an accessible fashion, what Beall takes to be the correct account of logic (-al consequence), as well as how logic relates to (and functions within) true theories. Specifically, Beall discusses the fundamental sematic properties (viz., truth and falsity) and ‘semantic statuses’ for sentences; the basic logical vocabulary and truth and falsity conditions for logical compounds; and logical consequence (entailment) and the space of logical possibilities. Additionally, Beall outlines the ingredients and mechanics of extra-logical (theory-specific) entailment relations under which true and complete theories are closed. The chapter sets the background framework on which Chapter 3’s account of identity relations (in general) and trinitarian identity (in particular) rest.