Logic as a discipline starts with the transition from the more or less unreflective use of logical methods and argument patterns to the reflection on and inquiry into these methods and patterns and their elements, including the syntax and semantics of sentences. In Greek and Roman antiquity, discussions of some elements of logic and a focus on methods of inference can be traced back to the late 5^th century BCE. The Sophists, and later Plato (early 4^th c.) displayed an interest in sentence analysis, truth, and fallacies, and Eubulides of Miletus (mid-4^th c.) is on record as the inventor of both the Liar and the Sorites paradox. But logic as a fully systematic discipline begins with Aristotle, who systematized much of the logical inquiry of his predecessors. His main achievements were his theory of the logical interrelation of affirmative and negative existential and universal statements and, based on this theory, his syllogistic, which can be interpreted as a system of deductive inference. Aristotle’s logic is known as term-logic, since it is concerned with the logical relations between terms, such as ‘human being’, ‘animal’, ‘white’. It shares elements with both set theory and predicate logic. Aristotle’s successors in his school, the Peripatos, notably Theophrastus and Eudemus, widened the scope of deductive inference and improved some aspects of Aristotle’s logic.

In the Hellenistic period, and apparently independent of Aristotle’s achievements, the logician Diodorus Cronus and his pupil Philo (see the entry Dialectical school) worked out the beginnings of a logic that took propositions, rather than terms, as its basic elements. They influenced the second major theorist of logic in antiquity, the Stoic Chrysippus (mid-3^rd c.), whose main achievement is the development of a propositional logic, crowned by a deductive system. Regarded by many in antiquity as the greatest logician, he was innovative in a large number of topics that are central to contemporary formal and philosophical logic. The many close similarities between Chrysippus’ philosophical logic and that of Gottlob Frege are especially striking. Chrysippus’ Stoic successors systematized his logic, and made some additions.

The development of logic from c. 100 BCE to c. 250 CE remains mostly in the dark, but there can be no doubt that logic was one of the topics regularly studied and researched. At some point Peripatetics and Stoics began taking notice of each other’s logical systems, and we witness some conflation of both terminologies and theories. Aristotelian syllogistic became known as ‘categorical syllogistic’ and the Peripatetic adaptation of Stoic syllogistic as ‘hypothetical syllogistic’. In the 2^ndcentury CE, Galen attempted to synthesize the two traditions; he also professed to have introduced a third kind of syllogism, the ‘relational syllogism’, which apparently was meant to help formalize mathematical reasoning. The attempt of some Middle Platonists (1^st c. BCE–2^nd c. CE) to claim a specifically Platonic logic failed, and in its stead, the Neo-Platonists (3^rd–6^th c. CE) adopted a scholasticized version of Aristotelian logic as their own. In the monumental—if rarely creative—volumes of the Greek commentators on Aristotle’s logical works we find elements of Stoic and later Peripatetic logic as well as Platonism, and ancient mathematics and rhetoric. Much the same holds for the Latin logical writings by Apuleius (2^nd c. CE) and Boethius (6^th c. CE), which pave the way for Aristotelian logic, thus supplemented, to enter the Medieval era.

More at:  https://plato.stanford.edu/entries/logic-ancient/

(Contributed by Heather Williams, H.W., M.)