On the Relationship Between Logic’s Neutrality and Theory Closure

Logic is often considered neutral, imposing no significant constraints on the world. In this paper, we explore how this purported neutrality can be understood, focusing on a proposal originally sketched by Jc Beall for another purpose. Accordingly, suggesting that logic should be viewed as a tool for theory building, we argue that mere theory closure can be interpreted as a hallmark of logic’s neutrality. The proposal can be connected with a sharp distinction between validity and truth and approached through a metalinguistic framework. We then discuss some complications and possible objections to the account, which gives us the opportunity to further deepen our treatment and connect the proposal with some important issues in the philosophy of logic. In particular, we consider the role of the deduction theorem and the relationship between entailment and implication. We conclude that once correctly interpreted, logic’s neutrality can indeed be understood in terms of theory closure.