Propositional logic
Validity depends on the form connecting propositions, not on terms. The five indemonstrables anticipate modern logic.
Ancient Greece & Rome · c. 279–206 BCE
克吕西波 · Χρύσιππος
The second founder of Stoicism, author of over seven hundred books, who built propositional logic and defended the compatibility of fate and freedom.
Had there been no Chrysippus, there would have been no Stoa.
Source: Diogenes Laërtius 7.183 (a saying about him)
Chrysippus came from Soli in Asia Minor and was reportedly a long-distance runner before coming to Athens, where he first studied sceptical dialectic in the Academy, then joined the Stoa as pupil and successor of Cleanthes. The ancients said that without Chrysippus there would have been no Stoa. He wrote seven hundred and five books, at times five hundred lines a day, but none survives whole; we know him only through quotation.
His greatest contribution was logic. Where Aristotle's logic dealt with terms, Chrysippus' dealt with propositions: forms such as 'if p then q; p; therefore q' were his discovery, and he listed five basic indemonstrable argument schemes. The system was forgotten in the Middle Ages, and only when Frege rebuilt modern logic in the nineteenth century did people see that the Stoics had been there first.
In physics he defended strict determinism: everything is fixed by prior causes, the universe an unbreakable causal chain. Yet he also insisted that we are responsible for our actions. His image was a cylinder: the push that starts it is external, but how it rolls depends on its own shape. Likewise impressions come from fate, but assent depends on our character. This is the first explicit statement of compatibilism.
Validity depends on the form connecting propositions, not on terms. The five indemonstrables anticipate modern logic.
Everything is determined, yet the proximate cause of action is our own character, so responsibility remains ours.
Fear, grief and desire are not irrational forces but mistaken judgements about good and evil, and so can be cured by reason.