identity of indiscernibles (redirected from Leibniz's law)

identity of indiscernibles

Principle enunciated by G.W. Leibniz that denies the possibility of two objects being numerically distinct while sharing all their non-relational properties in common, where a relational property is one that involves bearing a relation to another object. More formally, the principle states that if x is not identical to y, then there is some non-relational property P such that P holds of x and does not hold of y, or that P holds of y and does not hold of x. Equivalently, if x and y share all their non-relational properties, then x is identical to y. Its converse, the principle of the indiscernibility of identicals (also known as Leibniz's Law), asserts that if x is identical to y, then every non-relational property of x is a property of y, and vice versa.