Koznyshev is Constantine Levin's half-brother and an enthusiastic intellectual. He spends six years working on a book about the contemporary state of Russia. When nobody reads his book, he immediately jumps on the bandwagon of another cause (Slavic nationalism) because he really likes to stay current. Koznyshev's enthusiasm is for intellectual fads, and he doesn't seem to have real convictions that have grown out of his own experience. He likes to argue and he's good at it, but there's no real belief or faith behind it all.
Koznyshev is one of Levin's favorite conversational partners, but their big stumbling block is that Koznyshev is interested in big questions of "the peasants" and "the common good" in the abstract. Levin feels, by contrast, that you can't talk abstracting about these issues with any real meaning.
For Levin, all reform has to follow the particular, individual interests of the reformer. Intellectual abstraction has no meaning for Levin, so he usually loses his arguments with Koznyshev even when he's right.