indiscernibles

In mathematical logic, indiscernibles are objects that cannot be distinguished by any property or relation defined by a formula. Usually only first-order formulas without equality are considered. ==Examples== If a, b, and c are distinct and {a, b, c} is a set of indiscernibles, then, for example, for each binary formula \beta , we must have [ \beta (a, b) \land \beta (b, a) \land \beta (a, c) \land \beta (c, a) \land \beta (b, c) \land \beta (c, b) ] \lor [ \lnot \beta (a, b) \land \lnot \beta (b, a) \land \lnot \beta(a, c) \land \lnot \beta (c, a) \land \lnot \beta (b, c) \land \lnot \beta (c, b) ] \,.

Historically, the identity of indiscernibles was one of the laws of thought of Gottfried Leibniz.