How did Stoic logic differ from Aristotle’s term logic?

The primary difference between Aristotelian and Stoic logic lies in their fundamental focus: Aristotle developed a term logic, while the Stoics developed a propositional logic.12

Aristotelian Term Logic

Aristotle’s system, known as syllogistic, centers on the internal structure of categorical propositions. He used variables (Greek letters) as placeholders for terms or names to identify valid patterns of inference, such as: "If every $\beta$ is an $\alpha$ and every $\gamma$ is a $\beta$, then every $\gamma$ is an $\alpha$." His logic focuses on the relations between these terms as they function as subjects or predicates within propositions.34

Stoic Propositional Logic

In contrast, the Stoics neglected term logic to concentrate on inferences derived from hypothetical propositions. Instead of analyzing the internal structure of simple propositions, they studied how to combine propositions using logical connectives like "if...then," "or," and "and."12

The Stoics used ordinal numerals as variables to represent whole propositions rather than terms. For example, their basic inference schemata included: "Either the first or the second; but not the second; therefore, the first." While Aristotle’s work was often tied to scientific demonstration, the Stoics focused heavily on debate, disputation, and the resolution of paradoxes.12