Why did Rudolf Carnap believe logic and mathematics could be known a priori?

Rudolf Carnap, along with other logical empiricists, maintained that logic and mathematics are known a priori because he considered their statements to be analytic propositions.12

Unlike empirical statements, which are grounded in observation, Carnap argued that logical and mathematical truths are true solely by virtue of the meanings of their constituent terms and the rules of the language in which they are formulated. Because these statements are essentially definitions or conventions, they are valid independently of experience; their denial would result in a self-contradiction.123

Carnap viewed these disciplines as formal systems where truth is established through deductive inference based on specified syntactic and semantic rules. Consequently, he believed that experience could not refute these truths, as they do not provide information about the physical world but rather clarify the structure and usage of the language itself.123