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Why did logical symbolism become more important in the 17th century?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Applied logic Aristotle, marble portrait bust, Roman copy (2nd century bce) of a Greek original (c. 325 bce); in the Museo Nazionale Romano, Rome.

In the 17th century, the growing importance of logical symbolism was primarily driven by a desire to emulate the success of mathematics. Logicians observed the significant progress achieved in mathematical fields after they adopted the systematic use of special symbols and abbreviations, and they hoped to replicate this success within the study of logic.12

This shift was characterized by several key factors:

Algebraic Inspiration: Logicians began using letters—similar to the practice in algebra—to represent propositions, concepts, classes, properties, and relations, alongside specialized symbols for logical notions.12
New Logical Goals: Beyond mere training in "natural" reasoning, 17th-century thinkers sought to develop an ideal logical language that was more precise than natural languages. They also aimed to create methods of discovery that could accelerate human thought or even allow reasoning to be performed mechanically or algorithmically, a concept notably explored by Gottfried Wilhelm Leibniz in his pursuit of a calculus ratiocinator.312
Systematic Progress: The application of symbols was fueled by the conscious hope that such formalization would lead to significant advancements in human reasoning, distinguishing this era as a foundational period for modern formal logic.12