Falsity and untruth

Jc Beall's Divine Contradiction is a fascinating defence of the idea that contradictions are true of the tri-personal God. This project requires a logic that avoids the consequence that every proposition follows from a contradiction. Beall presents such a logic. This ‘gap/glut’ logic is the topic of this article. A gap/glut logic presupposes that falsity is not simply the absence of truth – for a proposition that is true may also be false. This article is essentially an examination of the idea that falsity is not simply untruth. The author rejects this position but does not claim to have an argument against it. In lieu of an argument, he presents three ‘considerations’. First, it is possible to give an intuitive semantics for the language of sentential logic that yields ‘classical’ sentential logic (including ‘p, ¬ p ⊢ q’) and which makes no mention of truth-values. Second, it is possible to imagine a race who manage their affairs very well without having the concept ‘falsity’. Third, it is possible to construct a semantics that yields a logic identical with the dialetheist logic and which makes no mention of truth-values – and which, far from being plausible, seems pointless.