Identity of indiscernibles (metaphysics)

The principle that no two distinct objects share every property. It is often associated with Leibniz and is distinct from the claim that identical objects share their properties.

Leibniz's Law: The principle that identical objects share all their properties. It is often confused with this principle, but runs in the opposite direction.
Gottfried Wilhelm Leibniz: A German philosopher and mathematician whose metaphysics includes monads and the principle of sufficient reason. He formulated and defended the principle as part of his account of individual substances.
Numerical identity: The relation each object bears only to itself, expressed by the claim that it is one and the same object. The principle concerns whether two numerically distinct objects can be qualitatively indistinguishable.
Black's two-sphere argument: Max Black's thought experiment about a possible universe containing only two identical, symmetrically placed spheres. It challenges the principle by describing distinct spheres with no qualitative differences.
Bare particulars: Particulars conceived as underlying subjects that need not be bundles of properties. They allow individuals to differ without any qualitative property distinguishing them.
Indiscernibility of identicals: The principle that if two objects are identical, they share every property. This converse principle is usually accepted even by philosophers who reject identity of indiscernibles.
Principle of sufficient reason: The principle that every fact has a sufficient reason why it is so rather than otherwise. Leibniz connected the absence of discernible differences between individuals to the lack of a reason to distinguish them.
Indiscernibility: The condition of having no difference with respect to a specified range of properties. The principle turns on whether indiscernibility is possible for distinct objects.
Symmetry: A property of a system that remains unchanged under specified transformations. A perfectly symmetric arrangement can make distinct objects appear to share every qualitative feature.
Bundle theory: The view that an object consists in a bundle of properties rather than an underlying substratum. If objects are bundles, the principle can follow from how individuality is defined.

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