In Alexandre Kojéve’s Introduction to Hegel, the author is explaining, in the first chapter, about the self-consciousness of a human as it is originated only in the presence of another human. He says that self-consciousness is achieved when a human desires of being desired by the other human. After a little more explanation on this part, the author says that in this way there develops a relationship of Master and Slave between two humans and this relation is always the result of the fight for recognition (being desired).
On page 9 of his book, we find these lines:
... if Desire must end in satisfaction, if the science of man must possess the quality of definitively and universally valid truth —the interaction of Master and Slave must finally end in the “dialectical overcoming” of both of them.
I cannot understand what the author meant by “dialectical overcoming”. As far as my search is concerned, I have found that dialectic is a way of reaching the truth by proper methods of argumentation and reasoning, but it is not helping in understanding that.