This article records tradition as it has been passed down and reported. Its sources are not yet part of the atlas's verified catalogue.
Chrysippus is remembered by later antiquity as the man who rebuilt Stoic logic almost single-handedly, credited with a system that departs sharply from Aristotle's syllogistic in a way that anticipates modern propositional logic. Where Aristotle reasoned about classes of things, Chrysippus reasoned about whole propositions, which the Stoics called sayables. He identified five basic argument forms, called indemonstrables, that he treated as self-evidently valid and not reducible to anything simpler. The first is the familiar pattern of affirming the antecedent, if p then q, p, therefore q. The second reverses it by denying the consequent, if p then q, not q, therefore not p. A third and fourth work with disjunction, either p or q, p, therefore not q, and either p or q, not q, therefore p. A fifth handles negated conjunctions, not both p and q, p, therefore not q. Every other valid argument, on Chrysippus's account, could in principle be reduced to some chain of these five, which gave Stoic logicians a genuinely systematic apparatus for testing inference rather than relying on intuition.
The details of how Chrysippus defined the connectives show a mind unwilling to settle for a merely mechanical truth table. A disjunction, for him, was true only when its disjuncts genuinely conflicted, one true and the other false, not merely when at least one happened to be true. A conditional was true when the contradictory of the consequent was actually incompatible with the antecedent, a much stronger requirement than the material conditional of later logic, which counts a conditional true whenever the antecedent is false regardless of any real connection between the two clauses. Chrysippus wanted logic to track genuine conceptual relationships, not just the distribution of truth values, and this concern for real connection over formal coincidence runs through the rest of his philosophy as well.
That same rigor served an ethical purpose, since Chrysippus held that logic was not a specialist's game but training for the sage. He identified happiness entirely with virtue, insisting that living viciously simply is living unhappily, with no gap between the two that fortune could open up. Virtue itself he treated as fundamentally a form of knowledge, following the Socratic line that had run through Stoicism from Zeno onward. Prudence is knowledge of what to choose, temperance is knowledge of what to hold firm against, and each apparent virtue turns out on inspection to be wisdom applied to a particular domain of life. A person could not possess courage while lacking justice, since both were finally the same rational understanding viewed from different angles. This is why the discipline of valid inference mattered so much to Chrysippus. A mind that assents carelessly to false or poorly connected propositions is a mind that will eventually assent carelessly to the wrong action, and the sage's famous imperturbability was, on this view, downstream of a logic trained never to accept more than the premises actually secure. Even his account of fate reflects this taste for real necessity over loose coincidence, describing it as a natural, everlasting ordering in which one thing follows another through genuine interconnection rather than accident. For Chrysippus, getting an argument right and living rightly were two applications of a single rational discipline.