Deficiencies of Aristotelian Logic from the Perspective of Symbolic Logic

Abstract

Ancient logic in general, and Aristotelian logic in particular, have been subject to several criticisms due to its dominance from its emergence until the 19th century. After prominent mathematicians discovered a new logic that used a precise symbolic language, its premises and methods of proof underwent changes, leading to the emergence of different logical frameworks. One of the key points on which symbolic logicians agree, and which has sparked considerable debate, is Aristotle's ignorance of empty categories and personal boundaries. This includes the direct and indirect transitions in his arguments, such as reasoning by contradiction, reasoning by intersection, or the four types of propositions containing the letter "P", which represent universal questions indicating presupposition to particular questions indicating existence. Symbolic logic rejects these aspects.