identityofindiscernibles

Identity of indiscernibles is a principle in metaphysics attributed to Leibniz. It states that if any two objects x and y share all the same properties, then they are the same object. In logical form: if for every property P, P(x) is true exactly when P(y) is true, then x = y. It is often described as the converse of the indiscernibility of identicals, which holds that if x = y then they have all the same properties.

Formulations of the principle vary in what counts as a property. Some accounts require all intrinsic properties, while others allow relational properties such as “being taller than” or “being located at the same place.” If all properties are included, the principle makes a strong claim about identity; if only a subset of properties is considered, the claim is correspondingly weaker.

The identity of indiscernibles has played a central role in debates about ontology and individuation. It is not universally accepted, and several objections have been raised. A common challenge is the possibility of two distinct objects that are indiscernible by all properties, known as the problem of indiscernibles. In the philosophy of physics, indistinguishable quantum particles have fueled discussions about whether the principle can or should apply at the fundamental level. Respondents have offered various replies, including appeals to weak discernibility (where objects are distinguishable by asymmetrical relations they bear to other objects) or to restricting the domain of properties considered relevant for identity. Some philosophers accept a more modest view, treating identity as determined by a framework that may go beyond straightforward property attribution.