How did Rudolf Carnap explain the difference between an object language and a metalanguage?

Rudolf Carnap, a prominent figure in logical positivism, utilized the distinction between an object language and a metalanguage as a fundamental tool for the logical analysis of language.12

In Carnap’s framework, the object language refers to the language being analyzed, which is used to discuss objects and states of affairs in the world. The metalanguage is the language in which that analysis is formulated; it is essentially a language used to talk about another language.12

Carnap argued that philosophical problems could be resolved by examining them within a formal, syntactical framework rather than relying on nonformal or actual meanings. By employing symbolic notation within a metalanguage and adhering to strict rules of logic, he believed it was possible to avoid metaphysical judgments, which he considered invalid. This rigorous approach allows for the analysis of language structures without falling into a vicious infinite regress, as a metalanguage can itself become the object of a "metametalanguage" if necessary.12