What is a Complex System, After All?

The study of complex systems, although an interdisciplinary endeavor, is considered as an integrating part of physical sciences. Contrary to the historical fact that the field is already mature, it still lacks a clear and unambiguous definition of its main object of study. Here, I propose a definition of complex systems based on the conceptual clarifications made by Edgar Morin about the bidirectional non-separability of parts and whole produced by the nature of interactions. Then, a complex system is defined as the system where there is a bidirectional non-separability between the identities of the parts and the identity of the whole. Thus, not only the identity of the whole is determined by the constituent parts, but also the identity of the parts are determined by the whole due to the nature of their interactions. This concept allows, as shown in the paper, to derive some of the main properties that such systems must have as well as to propose its mathematical formalization.