Aristotle is history’s first great logician and Chrysippus is the second. We know more of Aristotle’s work than Chrysippus’ (whose works have been almost entirely lost), but we have enough at hand to identify the principal achievements of each. Aristotle’s logical particles of the syllogistic were ‘all’, ‘no’, ‘some’, and ‘non-’. Chrysippus’ were ‘if-then’, ‘it is not the case’, and ‘or’. This inclines the modern reader to see in Aristotle’s term-logic a precursor of predicate logic, and in Chrysippus’ logic the precursor of propositional logic. Because space is limited, I shall take the ancient logic of this chapter to be Aristotelian and Chrysippean logics.