Stoic logic

Stoic logic is the system of propositional logic developed by the Stoic philosophers in ancient Greece.

It was one of the two great systems of logic in the classical world. It was largely built and shaped by Chrysippus, the third head of the Stoic school in the 3rd-century BCE. Chrysippus's logic differed from Aristotle's term logic because it was based on the analysis of propositions rather than terms. The smallest unit in Stoic logic is an assertible (the Stoic equivalent of a proposition) which is the content of a statement such as "it is day". Assertibles have a truth-value such that they are only true or false depending on when it was expressed (e.g. the assertible "it is night" will only be true if it is true that it is night).^[1] In contrast, Aristotelian propositions strongly affirm or deny a predicate of a subject and seek to have its truth validated or falsified independent of context. Compound assertibles can be built up from simple ones through the use of logical connectives. The resulting syllogistic was grounded on five basic indemonstrable arguments to which all other syllogisms were claimed to be reducible.^[2] The linguistic orientation of Stoic logic made it difficult for its students even within the Stoic school.^[3]

Towards the end of antiquity Stoic logic was neglected in favour of Aristotle's logic, and as a result the Stoic writings on logic did not survive, and the only accounts of it were incomplete reports by other writers. Knowledge about Stoic logic as a system was lost until the 20th century, when logicians familiar with the modern propositional calculus reappraised the ancient accounts of it.