How does metamathematical formalism interpret the statement “4 is even”?

In the philosophy of mathematics, metamathematical formalism interprets mathematical statements not as descriptions of objective entities, but as expressions within a formal system.12

Under this view, the statement “4 is even” is not interpreted as a literal claim about the properties of a number existing in the real world. Instead, it is understood as a claim about the syntax and deductive structure of arithmetic. Specifically, the statement is interpreted to mean that the string of symbols “4 is even” is a theorem that can be derived from the established axioms of the system.12

By focusing on the manipulation of formulas rather than their external meaning, metamathematical formalism treats mathematical practice as a formal game of symbols governed by rules, rather than as a study of abstract objects.132