Abstract
In the study of complex systems, scientific explanations typically emphasize organizational properties and ignore causal and material details. One might think that the reason for this emphasis is pragmatic. Since those causal and material details are beyond our epistemic reach, one might think, we must make do with what we can. In this dissertation, I defend the alternative view that the emphasis on organizational properties is justified on rational, epistemic grounds. The reason that organizational properties are emphasized is that, in the domain of complex systems, organizational properties are the ones that tend to have the most explanatory import.
This justification for the emphasis on organizational properties is one of the main themes of the dissertation. Another theme concerns the new forms of representation that are needed to reason productively about such organizational properties. These new forms of representation—of which the central example is graph theory—suggest new views about the applicability of mathematics to science, and also about how the depth of scientific explanations ought to be assessed.
The dissertation is organized into four chapters. In Chapter One, I give an account of what complex systems are, and why they force us to adopt new methods of representation and explanation. The account draws on algorithmic complexity theory to define complex systems, and then shows that two classical kinds of scientific idealization are empirically inadequate when applied to systems that satisfy the definition. The inadequacy of these forms of representation is shown to be one of the primary reasons that organizational properties must be taken into account.
In Chapter Two, I introduce the methods of network science—a subfield of complex systems that offers a particularly refined version of the explanatory strategy that I claim is novel. An argument is given that many complex systems are non-decomposable, and that therefore standard forms of mechanistic explanation are inappropriate in this domain. Whereas mechanistic approaches idealize away from the properties in virtue of which a system is complex, network science represents those properties explicitly, and exploits them for explanatory purposes.
In Chapter Three, I discuss the manner in which scientists justify the application of mathematical devices to complex systems. Since general theories and laws are typically unavailable when dealing with complex systems, the application of mathematics must be justified on the basis of system-specific considerations. This system-specific orientation makes it difficult to specify the empirical content of certain complex systems models. This difficulty is used to motivate a worry that such models are capable of teaching us mathematical truths, but not scientific ones. I defend the view that even if it is impossible to confirm that such models accurately describe the empirical phenomena that inspired their construction, they do have empirical content, and therefore have the potential to serve an explanatory function.
In Chapter Four, I defend an account of explanatory depth that is appropriate in the domain of complex systems, and contrast that account with traditional views. It is argued that in the domain of complex systems, the breadth of applicability of a model cannot serve as a metric of explanatory depth. On the alternative view I defend, a central role is assigned to the reliability of the mathematical model over perturbations in the empirical details. An important consequence of this view is that the addition of system-specific difference-making properties does not necessarily result in an increase in explanatory depth. It is often the case that the best way of explaining the behavior of a complex system is to represent the generating conditions that preserve its organization in a highly generic, domain-neutral manner.
