 A simple illustration of explication is provided by the definition of ordered pair in set theory. Here, the pair \(\langle x,y\rangle\) is defined as the set \(\{\{x\}, \{x,y\}\}\). Viewed as an explication, this definition does not purport to capture all aspects of the antecedent uses of ‘ordered pair’ in mathematics (and in ordinary life); instead, it aims to capture the essential uses. The essential fact about our use of ‘ordered pair’ is that it is governed by the principle that pairs are identical iff their respective components are identical: