 Strictly speaking, truth in an interpretation is a purely mathematical relation between the formulas of a formal language and rigorously defined mathematical objects of a certain type. However, in practice, most formal languages are applied languages and this will enable us to define an objective notion of truth simpliciter for classical predicate logic. More specifically, an applied formal language \(\scrL\) is designed to clearly and unambiguously formalize a range of discourse about some real world domain (e.g., the stars and planets, the US electorate on 6 November 2020, the natural numbers, etc)—call this the intended domain of \(\scrL\). Hence, each constant of \(\scrL\) symbolizes a name in the given discourse and each predicate of \(\scrL\) symbolizes a predicate of the  discourse.[32]  An interpretation \(\calI\) for \(\scrL\) will be intended, then, just in case its universe \(D\) comprises exactly the individuals in the intended domain of \(\scrL\) and \(\calI\) assigns to the constants and predicates of \(\scrL\) the actual semantic values of the names and natural language predicates they are meant to symbolize. The compositional truth condition of a sentence \(\varphi\) in an intended interpretation thus traces \(\varphi\)’s truth value down to the basic atomic facts on which it ultimately depends or, as we might put it, the atomic facts on which its truth value is grounded. Thus, a sentence \(\varphi\) of an applied language \(\scrL\) will be true just in case it is true\(^\calI,\) for some intended interpretation \(\calI\) for \(\scrL\).