The principle of explosion in the stoic logic

The Stoic philosophers developed a formal propositional language during the Hellenistic period, which included propositional variables and propositional connectives. In this language, ordinal numerals serve as propositional variables: the first (sentence), the second (sentence), etc. Compound sentences are constructed from simple ones and connectives according to the following patterns: – Negation: not the first; – Conjunction: both the first and the second; – Disjunction: either the first or the second; – Implication: if the first then the second; where the first and the second can be any sentences, whether simple or compound. Therefore, the propositional syntax of the Stoics can be reliably and directly transposed into contemporary logic. Following Jan Łukasiewicz’s seminal lecture On the Stoics’ Logic (delivered in 1923), and for most of the 20th century, it was widely believed that Stoic propositional logic was simply an early or premature version of classical propositional calculus. However, at the turn of the 20th and 21st centuries, several works were published arguing that Stoic logic was either relevantistic or paraconsistent. This view became widely accepted in the 21st century.