Remarks on the Principle of the Identity of Indiscernibles

Abstract

The essay to follow is one in good, old-fashioned Metaphysics. I wish to take a fresh look at an old principle which has had a venerable history in the philosophic tradition. Partly, this is because in this century that old principle has received some newer formulations, thanks to developments in logic, and these newer formulations deserve some comment. It is partly because old metaphysical issues have thus reappeared in new guises that it will be instructive to point out some of the connections between the new and the old. This examination is itself a part of a program in metaphysics.1 For the sake of having a formulation before us, let us begin, as is customary, with that due to Leibniz: no two substances are completely similar, or differ solely numerically.2 Later on, we shall be interested in ways in which this statement may be reformulated so as to be susceptible of more precise analysis. For the moment, however, I wish to draw attention to a battery of concepts and distinctions which form the context in which all discussions of this principle take place. To begin with, there is the grammatical distinction between subject and predicate. A subject is that to which many predicates may apply, in particular the identity predicate, but which is itself not predicated of anything else. Predicates, on the other hand, qualify a subject as being of a certain kind, as belonging to a particular class or classes. Corresponding to this distinction, although not exactly, is that between substance and property. Substance is that which may be referred to, or named, by a subject term, while its properties are that which characterize it as a certain kind of entity. Properties are what predicates designate.3 A proper subset of subject terms are singular terms-those referring to exactly one substance (whether contingently or necessarily). The remainder of the subject terms I shall call, for want of a better name, plural terms. The correspondence between subject and predicate terms on the one side, and substances and properties on the