Why is formal logic often compared with pure mathematics?

Formal logic is often compared to pure mathematics because both disciplines rely on the construction of formal systems. In these systems, symbols are manipulated according to precise, predefined rules to derive theorems from a set of axioms, independent of any specific subject matter or interpretation.12

The comparison is rooted in several key similarities:

• Abstract Structure: Just as algebra uses variables to represent numerical values, formal logic uses variables to represent placeholders for expressions. This allows logicians to analyze the structure of thought and deduction in a way that mirrors the abstract manipulation of mathematical formulas.12
• Calculi: Because a logician’s handling of proposition forms is analogous to a mathematician’s work with numerical formulas, the systems they construct are frequently referred to as logical calculi.12
• Foundational Links: Historically, the philosophy of mathematics has been deeply intertwined with logic. Schools of thought like logicism have even argued that all mathematical truths are ultimately reducible to logical laws.34

Ultimately, both fields focus on the validity of structures rather than the truth of specific empirical content.12