Carl Adam Petri is well known for introducing the nets having his name. It is less known that net theory was, for Petri, the kernel of a radical shift in scientific knowledge. Carl Adam Petri has not written extensively during his life and this may have been an important reason that only the most applied part of his approach, the use of nets for designing concurrent systems, has become largely popular. In this paper, I try to popularize in a larger community the radical novelty and the relevance of the approach Petri used for developing scientific knowledge of physical and social phenomena. In short, we can say that Petri’s approach assumes that knowledge, even scientific knowledge, is rooted in human experience and there is no way, and no necessity, to connect it directly to an external reality.This has, as we will see, much to do with the concept of computing and, indirectly, with the relations between science and philosophy. This paper will summarize three aspects of Petri’s thinking, which deserve a wider attention: the notion of model, the new algebraic foundations for a theory of modeling (whose main example are Petri Nets) and its application to Human Communication Pragmatics.