Why did 17th-century logicians begin using symbols like those in algebra?

In the 17th century, logicians began adopting algebraic symbols to transform logic into a mechanical or algorithmic "calculus of reason" (calculus ratiocinator). By representing concepts and their relationships with symbols—such as letters, lines, or circles—thinkers like Gottfried Wilhelm Leibniz aimed to perform logical operations with the same precision and reliability as arithmetic.12

This shift was driven by several key motivations:

• Algorithmic Reasoning: Logicians sought a system where valid inferences could be checked or discovered through explicit, rule-based manipulations of symbols, effectively removing the potential for human error or failures of ingenuity.12
• Universal Language: Many, including Leibniz and René Descartes, envisioned a "universally characteristic language" (lingua characteristica universalis) that could represent concepts notationally, allowing for clear communication independent of native tongues.12
• Structural Parallels: Mathematicians observed deep parallels between the structure of traditional syllogistic logic and the operations of algebra. By treating concepts as "composite" entities—collections of more basic properties—they could use algebraic substitutions and operations to derive conclusions from premises.12

While these early efforts laid the philosophical groundwork for symbolic logic, they remained largely uninfluential until the 19th century.12