According to metaphysical realism, we would have to compare our thought with mind-independent reality, if we want to gain knowledge about the world. Such a comparison is impossible. Yet we can gain knowledge about the world. So metaphysical realism is false. — I take this to be the historically most influential argumentative line opposing metaphysical realism. The paper develops this argument, the Main Anti-Realist Argument, in more detail and offers a brief critical discussion of its crucial assumptions.