Formal semantics, the discipline for systematic theories about meaning in formal and natural languages, has developed into an extremely rich and diversified field. It uses a variety of formal methods and attempts to live up to a variety of formal, empirical, and metaphysical desiderata. But the researchers in the field do not agree on these desiderata. One classical principle of semantics is the principle of compositionality: (PC) The meaning of a complex expression is a function of the meanings of its parts and its mode of composition. Although several generations of researchers have subscribed to the principle, it is controversial and it is in some – real or apparent – conflict with other some desiderata of formal semantics for natural language. It seems that it can come into conflict with procedural aspects of a semantics, with computational aspects, with intuitive and philosophically motivated types of linguistic meaning, and with uniformity of meaning representations. Which way should we go? It is high time to confront these questions among researchers with different technical and philosophical orientation. That is the motivation of the present symposium.