Conceptual modeling is a strongly interdisciplinary field of research. Although numerous proposals for axiomatic foundations of the main ideas of the field exist, there is still a lack of understanding main concepts such as system, process, event, data, and many more. Against the background of the tremendously gaining importance of digital phenomena, we argue that axiomatic foundations are needed for our discipline. Besides the general call, we provide a particular case study using HERAKLIT. This modeling infrastructure encompasses the architecture, statics, and dynamics of computer-integrated systems. The case study illustrates how axiomatically well-founded conceptual models may look like in practice. We argue that axiomatic foundations do not only have positive effects for theoretical research, but also for empirical research, because, for instance, assumed axioms can explicitly be tested. It is now time to spark the discussion on axiomatic foundations of our field.