ABSTRACT. We follow Ludwig Wittgenstein: "How can the all-embracing logic which mirrors the world use such special catches and manipulations? Only because all these are connected into an infinitely fine network, the great mirror." (Tractatus Logico-Philosophicus 5.511) Teaching logic means therefore to teach how surprisingly straightforward insights generate the most abstract structures known. In this lecture we intend to develop tools to motivate this generation for beginners.