Arguments by Leibniz’s Law in Metaphysics

Abstract

Leibniz’s Law (or as it sometimes called, ‘the Indiscerniblity of Identicals’) is a widely accepted principle governing the notion of numerical identity. The principle states that if a is identical to b, then any property had by a is also had by b. Leibniz’s Law may seem like a trivial principle, but its apparent consequences are far from trivial. The law has been utilised in a wide range of arguments in metaphysics, many leading to substantive and controversial conclusions. This article discusses the applications of Leibniz’s Law to arguments in metaphysics. It begins by presenting a variety of central arguments in metaphysics which appeal to the law. The article then proceeds to discuss a range of strategies that can be drawn upon in resisting an argument by Leibniz’s Law. These strategies divide into three categories: (i) denying Leibniz’s Law; (ii) denying that the argument in question involves a genuine application of the law; and (iii) denying that the argument’s premises are true. Strategies falling under each of these three categories are discussed in turn.