According to constructivism, the world we can know is a construction and it is not possible to gain knowledge about the world as it is in itself. This thesis of constructivism has been criticized as being self-refuting. It is discussed whether this criticism is sound. Constructivists have tried three ways in order to avoid self-refutation. It is argued that the first two ways are unconvincing. The third solution is tenable. However, at a closer look the third solution turns out as a moderate kind of realism since it gives up the central claim of constructivism.