From Exposition to Existential Introduction and Elimination

The purpose of current article is to report and to analyze a part of the history of Exposition specially, and the history of logic in Islamic civilization generally. Aristotle uses the exposition in several places of his syllogistic, including in the proof of E-conversion. The problem of current article is the recent application. Since Theophrastus there have been many challenges in the proof of E-conversion by exposition. Alexander of Aphrodisias tries to resolve the challenges and, in order of it, propose two different interpretations about the mentioned exposition the second of which, on the basis of our analysis, is a reductio ad absurdum in which existential introduction, commutation, and existential elimination have been used. The fact shows that Aristotle’s logic, in this part, depends both on propositional and predicate logic. Again this interpretation considers the exposition as a non-syllogistic proof because of its usage from singular term, and shows that Alexander who counts the Aristotle’s syllogistic as the logic of universal terms is right. In Islamic world, Ibn Sina, Kunaji, and Tusi follow the same interpretation and even offer a more clear understanding of the mentioned rules, so that Ibn Sina and Tusi expressly talk about a distinction which today is made between proper name and arbitrary name. But Suhrawardi and Fakhr al-Din Razi who are influenced by Alexander’s first interpretation expose no brilliant acuity, not in understanding the nature of Aristotle’s logic, and not in understanding the rules involved in the proof of E-conversion by exposition.