Axiomatic or Natural Deduction: A study of Aristotle's Syllogistic System

Abstract

In 20th century, Classic Logic allowed logicians to look at Aristotelian Logic from a broader perspective. With the fruition of the studies and research of Lukasiewicz about Aristotelian Logic in the first half of the 20th century, a new path opened for logicians. In the framework of Classic Logic and using its rules and principles, Lukasiewicz introduced Aristotelian syllogisms as Axiomatic System, providing a detailed explanation of his method. In this approach, Barbara and Datisi beside the Identity are axioms; therefore, other moods are deducible by applying these two and borrowing inference rules from Propositional Logic. Later, in the early 1970s, Smiley and Corcoran disagreed with Lukasiewicz’s view. Smiley and Corcoran introduced Aristotelian syllogism as Natural Deduction System, The upcoming research aim is to present reasons based on the deductive nature of the Aristotelian Logical System after introducing each approach and comparing them with Aristotle's statements .