Bishop's Set Theory

A set is not an entity which has an ideal existence. A set exists only when it has been defined.
To define a set we prescribe, at least implicitly,
  1. what we (the constructing intelligence) must do in order to construct an element of the set,
  2. and what we must do to show that two elements of the set are equal.
-- Errett Bishop, A Constructivist Manifesto