 The non-logical terminology of the language consists of its individual constants and predicate letters. The symbol “\(=\)”, for identity, is not a non-logical symbol. In taking identity to be logical, we provide explicit treatment for it in the deductive system and in the model-theoretic semantics. Most authors do the same, but there is some controversy over the issue (Quine [1986, Chapter 5]). If \(K\) is a set of constants and predicate letters, then we give the fundamentals of a language \(\LKe\) built on this set of non-logical terminology. It may be called the first-order language with identity on \(K\). A similar language that lacks the symbol for identity (or which takes identity to be non-logical) may be called \(\mathcal{L}1K\), the first-order language without identity on \(K\).