Why did Leibniz compare logic to a mathematical calculus?

Gottfried Wilhelm Leibniz compared logic to a mathematical calculus because he envisioned a "calculus of reason" (calculus ratiocinator) that would allow human reasoning to function mechanically or algorithmically, much like performing large sums.1

By developing a symbolic logic where concepts were represented by symbols and manipulated according to established rules, Leibniz aimed to create a system where new truths could be discovered and proposed conclusions could be verified for validity. He believed that such a system would eliminate individual mistakes and failures of ingenuity, as derivations could be checked by others or even performed by machines.1

This ambition was part of his broader rationalist project to establish a "universal mathematics" (mathesis universalis), which would serve as a foundational language for reasoning across all sciences. By treating logical relationships as equations—where the concepts within a predicate are "included in" the concept of the subject—Leibniz sought to transform philosophical inquiry into a rigorous, indubitable process similar to the precision found in mathematics and geometry.123