Indiscernibles

In mathematical logic, indiscernibles are objects which cannot be distinguished by any property or relation defined by a formula. Usually only first-order formulas are considered. For example, if {a, b, c} is a set of indiscernibles, then for each 2-ary formula φ, we must have φ(a,b) ⇔ φ(b,a) ⇔ φ(c,a) ⇔ φ(a,c) ⇔ φ(b,c) ⇔ φ(c,b). Historically, the identity of indiscernibles was one of the laws of thought of Gottfried Leibniz.