What contributions did Stoics make to the study of logic?

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Stoicism was a school of philosophy that developed in Athens, Greece, in 300 BCE. The founder of the movement was Zeno of Citium in Cyprus. His thinking was developed further and was organized by his followers Cleanthes and Chrysippus. Other Stoics who refined Zeno’s metaphysical doctrines were Panaetius of Rhodes and Posidonius. They brought Stoicism to Rome in the second century BCE. Later, Seneca and Epictetus and the Emperor Marcus Aurelius were well-known Stoic philosophers of Imperial Rome. It is only from these later Stoics that complete works remain. There are only fragments of works from the earlier Stoics. The “Meditations” of Marcus Aurelius shows how the Stoic philosophy was considered to be a way of life. It reveals how the emperor worked on himself to live by the Stoic creed and remain free from all negative emotions in order to remain pure and rational.

The Stoics believed that emotions such as fear or jealousy arose from mistaken judgments. A virtuous man could be happy and remain immune to these emotions if he acted morally. They believed that only a sage could be perfect and free from distracting emotions, while all others were slaves to their feelings. Their ethical theory derived from the earlier philosophical ideas of Plato and Aristotle.

The Stoics made distinctive contributions to the fields of logic and ethics. Their logical theories were divided into two branches, rhetoric and dialectic. The Stoics interpreted logic very widely to include more than just analyzing the form of arguments. Logic for the Stoics also included rhetoric, grammar and the philosophy of language. It also encompassed theories of thought and concepts, what is known as epistemology. Stoic logic maintains that an argument is valid if it can be reduced to one of five “indemonstrable forms”. These are: 1) modus ponens, which maintains that if p then q; p; therefore q. 2) Modus tollens: if p then q; not q; therefore not p; 3) it is not the case that both p and q; therefore not q; 4) either p or q; therefore not q; and 5) either p or q; therefore q.

Other contributions to logic included their views on modality and bivalence. Chrysippus presented the view that bivalence and the law of the excluded middle apply to future events. Bivalence maintains that a connective, like “or”, contains only two values, true or false. The law of the excluded middle states that for a proposition p, both p and not p, its contradictory, must both be necessarily true.

The Stoics believed in causal determinism but not in fatalism. They held that when a person acts, he could have done something else. They interpret “could have” as a modal concept which perceives that there may be a conflict between universal causation and human freedom. The Stoics maintained that when a person’s moral character determines his actions, these actions are “up to him.” A person is responsible for those actions. They believed that everything comes about by fate. But this depends on how a person determines his or her own fate by moral beliefs and by actions. However, there is a chain of cause and effect that does not result from a person’s beliefs and desires but comes about by a natural flow of events. This is known in modern philosophy as “soft determinism.”

The Stoics argued with the philosophical school known as the Skeptics about the criterion of truth. The Skeptics denied the very existence of cognitive impressions and said that they did not constitute knowledge. However, Chrysippus articulated the Stoic belief that truth is determined by a cognitive impression which definitely determines that something is true. Zeno defined this as something which “arises from that which is, and is stamped and impressed by that very thing, and could not arise from what is not”. The Stoics believed that if a person is disciplined enough, he or she will never make a mistake about a cognitive impression.

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