With the presentation of a new logic system entitled modern logic or mathematical logic, the Aristotelian logic has encountered appreciation and criticism of some Islamic and Western thinkers. The cyclicality of the principles of classical logic, non-inclusiveness of all relations, non-fruitfulness, and speaking in general terms are among the most important of these criticisms. These two logical systems have differences with each other. The importance and genuineness of expressions and avoidance of verbal fallacies, generality of the inclusiveness of analogies, referent-orientedness, ability to present complex conclusions, and application in many sciences are among the distinguishing features of modern logic comparing classical logic. These two are also different from each other in terms of fundamental postulate. In this writing, while referring to the short history of modern logic and the shortcomings and criticisms directed at the classical logic, the differences between these two logical systems are explained.