Reflection on Set theory: Is the barber example a genuine illustration of Russell's paradox?

Abstract

Since the formulation of Russell’s paradox, many people have created more accessible models while trying to understand and solve the paradox. The Barber paradox is the most famous one, but it is not the case that this paradox was not proposed by Russell. This paper will demonstrate the nature of both paradoxes through truth-functional language and propose possible solutions (theory of types) for Russell’s paradox. The reason why the Barber paradox is a pseudo paradox will also be illustrated with a possible solution. There is a huge difference between the paradoxes due to the fundamental difference in the set, and more reasons will be clarified in the paper.