The teachability of virtue is an issue on which were crossed swords during the struggle for supremacy between two basic principles of ancient Greek spirit - sophistry and ancient Greek ethics. Two great representatives of these opposite principles, Plato and Protagoras, confronted their arguments in Plato's dialog named after the great sophist. Paradoxically, during this philosophical struggle, Protagoras, who at the beginning supposed that virtue is teachable, later, on the contrary, states that virtue is not knowledge and this would make it least likely to be teachable. On the other hand Plato, who is trying to preserve the ancient Greek principle that virtue is innate, claims that virtue is knowledge. The solution of this great dispute between two principles of antiquity Plato sees in philosophical theoretization of ancient Greek mythical worldview.