identity, theoretical See PHILOSOPHY OF MIND. identity of indiscernibles, any of a family of principles, important members of which include the following: (1) If objects a and b have all properties in common, then a and b are identical. (2) If objects a and b have all their qualitative properties in common, then a and b are identical. (3) If objects a and b have all their non-relational qualitative properties in common, then a and b are identical. Two questions regarding these principles are raised: Which, if any, are true? If any are true, are they necessarily true?
Discussions of the identity of indiscernibles typically restrict the scope of the principle to concrete objects. Although the notions of qualitative and non-relational properties play a prominent role in these discussions, they are notoriously difficult to define. Intuitively, a qualitative property is one that can be instantiated by more than one object and does not involve being related to another particular object. It does not follow that all qualitative properties are non-relational, since some relational properties, such as being on top of a brown desk, do not involve being related to some particular object. (1) is generally regarded as necessarily true but trivial, since if a and b have all properties in common then a has the property of being identical with b and b has the property of being identical with a. Hence, most discussions focus on (2) and (3). (3) is generally regarded as, at best, a contingent truth since it appears possible to conceive of two distinct red balls of the same size, shade of color, and composition. Some have argued that elementary scientific particles, such as electrons, are counterexamples to even the contingent truth of (3). (2) appears defensible as a contingent truth since, in the actual world, objects such as the red balls and the electrons differ in their relational qualitative properties. It has been argued, however, that (2) is not a necessary truth since it is possible to conceive of a world consisting of only the two red balls. In such a world, any qualitative relational property possessed by one ball is also possessed by the other. Defenders of the necessary truth of (2) have argued that a careful examination of such counterexamples reveals hidden qualitative properties that differentiate the objects. See also IDENTITY, INDIVIDUATION, LEIB- NIZ , PROPERTY , SUBSTANC. A.C.