Editing Metalogic (section)

=== Formal language ===
{{Main|Formal language}}

A ''formal language'' is an organized set of [[symbol (formal)|symbols]], the symbols of which precisely define it by shape and place. Such a language therefore can be defined without [[reference]] to the [[meaning (linguistics)|meanings]] of its expressions; it can exist before any [[Interpretation (logic)|interpretation]] is assigned to it—that is, before it has any meaning. [[First-order logic]] is expressed in some formal language. A [[formal grammar]] determines which symbols and sets of symbols are [[well-formed formula|formulas]] in a formal language.

A formal language can be formally defined as a set ''A'' of strings (finite sequences) on a fixed alphabet α. Some authors, including [[Rudolf Carnap]], define the language as the ordered pair <α, ''A''>.<ref name="itslaia">[[Rudolf Carnap]] (1958) ''[https://books.google.com/books?id=hAvVAgAAQBAJ Introduction to Symbolic Logic and its Applications]'', p.&nbsp;102.</ref> Carnap also requires that each element of α must occur in at least one string in ''A''.