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

The primary difference between Aristotelian and Stoic logic lies in their fundamental units of analysis and their approach to inference.

Aristotle’s Term Logic

Aristotle’s system, known as term logic, focused on the internal structure of categorical propositions. He analyzed how terms (subjects and predicates) relate to one another within a syllogism. Using variables (Greek letters) to represent these terms, he established rules for valid inferences based on the quantity and quality of propositions—such as whether they were universal or particular, and affirmative or negative.12

Stoic Propositional Logic

In contrast, the Stoics, led by Chrysippus, developed propositional logic. Rather than breaking down propositions into terms, they treated entire propositions as atomic units. They focused on how these units are combined using logical connectives like "if...then," "and," and "or". Instead of term variables, they used ordinal numerals (e.g., "the first," "the second") as placeholders for whole propositions. Their system centered on valid inference schemata, such as the five "indemonstrable" arguments, which rely on the truth-functional relationships between propositions rather than the internal categorical structure of the statements.34