From Explosion to Implosion: A New Justification for the Ex Falso Quodlibet Rule

In this paper, we consider the ex falso quodlibet rule (EFQ) as a derived rule and propose a new justification for it based on a rule we call the collapse rule. The collapse rule is a mix between EFQ and disjunctive syllogism (DS). Informally, it says that a choice between a proposition A and \(\bot \) $\perp$ , which is understood as nullary disjunction, is no choice at all and it defaults to A. Thus, we can regard it as capturing the idea of an implosion principle in contrast to EFQ’s explosion principle. Furthermore, we show that the collapse rule can also be used to justify DS and that all these three rules have the same deductive strength: they are all interderivable. Thus, the discussions about the justification of EFQ or DS be reduced to a discussion about the justification of the collapse rule.