Identity of Indiscernibles

Leibniz’ principle of the “identity of indiscernibles” implies that things are distinct if they do not share all possible relationships or properties. Distinctness means having distinct relationships to the rest of the world and thus at least one differing property. Whether things can be held to be identical depends therefore on the possibility to exhaustively enumerate a finite list of those properties or relationships. But such a complete list is possible only for deductive systems, where the properties and relationships are definitional. That is, they are made not found. As a principle, the identity of indiscernibles already assumes that the world is such a system.

The identity of an individual thing is relative to its parts as well as to the wholes of which it is a part. The collected properties or parts of a natural thing do not (as assumed in reductionism) constitute the thing as a whole. But they do constitute an artifact and in fact define an artifact. Thus an artifact can be exhaustively described, while a natural thing cannot. Two artifacts can be identical because it is possible to exhaustively search and compare their lists of defining properties. Any list of properties which thought could assign to a natural thing, however, cannot exhaust its being, since it may have indefinite properties.

The fact that elementary particles cannot be marked or tagged as individuals leads to a characteristically different statistics for quantum entities. In quantum physics, there are difficulties of principle involved in locating the set of all objects that satisfy the definition of a given particle type. In fact, in creating the statistics, it is not objects that are counted, but measurement events—which may not represent objects at all, but merely quantities. Quantum “objects” tread a line between natural things, with indefinite properties, and artifacts that are no more than what they are defined to be.