Abstract

In the philosophy of science, increasing attention has been given to the methodological novelties associated with the study of complex systems. However, there is little agreement on exactly what complex systems are. Although many characterizations of complex systems are available, they tend to be either impressionistic or overly formal. Formal definitions rely primarily on ideas from the study of computational complexity, but the relation between these formal ideas and the messy world of empirical phenomena is unclear. Here, I give a definition of complex systems that draws on algorithmic complexity theory, but also provides a way of interpreting the formal idea in an empirical setting. I then use the definition to show that two canonical forms of scientific idealization are empirically inade- quate when applied to complex systems. The inadequacy of these forms of idealization is shown to be the primary reason that complex systems require novel methods. Moreover, this demand for novel methods helps explain the rise of complex systems science as an autonomous discipline.