Luca Rivelli

This work is mainly concerned with the notion of hierarchical modularity and its use in explaining structure and dynamical behavior of complex systems by means of hierarchical modular models, as well as with a concept of my proposal, antimodularity, tied to the possibility of the algorithmic detection of hierarchical modularity. Specifically, I highlight the pragmatic bearing of hierarchical modularity on the possibility of scientific explanation of complex systems, that is, systems which, according to a chosen basic description, can be considered as composed of elementary, discrete, interrelated parts. I stress that hierarchical modularity is also required by the experimentation aimed to discover the structure of such systems. Algorithmic detection of hierarchical modularity turns out to be a task plagued by the demonstrated computational intractability of the search for the best hierarchical modular description, and by the high computational expensiveness of even approximated detection methods. Antimodularity consists in the lack of a modular description fitting the needs of the observer, a lack due either to absence of modularity in the system’s chosen basic description, or to the impossibility, due to the excessive size of the system under assessment in relation to the computational cost of algorithmic methods, to algorithmically produce a valid hierarchical description. I stress that modularity and antimodularity depend on the pragmatic choice of a given basic description of the system, a choice made by the observer based on explanatory goals. I show how antimodularity hinders the possibility of applying at least three well-known types of explanation: mechanistic, deductive-nomological and computational. A fourth type, topological explanation, remains unaffected. I then assess the presence of modularity in biological systems, and evaluate the possible consequences, and the likelihood, of incurring in antimodularity in biology and other sciences, concluding that this eventuality is quite likely, at least in systems biology. I finally indulge in some metaphysical and historical speculations: metaphysically, antimodularity seems to suggest a possible position according to which natural kinds are detected modules, and as such, due to the computational hardness of the detection of the best hierarchical modular description, they are unlikely to be the best possible way to describe the world, because the modularity of natural kinds quite probably does not reflect the best possible modularity of the world. From an historical point of view, the growing use of computational methods for modularity detection or simulation of complex systems, especially in certain areas of scientific research, hints at the envisioning of a multiplicity of emerging scientific disciplines guided by a self- sustained, growing production of possibly human-unintelligible explanations. This, I suggest, would constitute an historical change in science, which, if has not already occurred, could well be on the verge of happening.

Empirical philosophers of science aim to base their philosophical theories on observations of scientific practice. But since there is far too much science to observe it all, how can we form and test hypotheses about science that are sufficiently rigorous and broad in scope, while avoiding the pitfalls of bias and subjectivity in our methods? Part of the answer, we claim, lies in the computational tools of the digital humanities, which allow us to analyze large volumes of scientific literature. Here we advocate for the use of these methods by addressing a number of large-scale, justificatory concerns—specifically, about the epistemic value of journal articles as evidence for what happens elsewhere in science, and about the ability of DH tools to extract this evidence. Far from ignoring the gap between scientific literature and the rest of scientific practice, effective use of DH tools requires critical reflection about these relationships.

This work is concerned with hierarchical modular descriptions, their algorithmic production, and their importance for certain types of scientific explanations of the structure and dynamical behavior of complex systems. Networks are taken into consideration as paradigmatic representations of complex systems. It turns out that algorithmic detection of hierarchical modularity in networks is a task plagued in certain cases by theoretical intractability and in most cases by the still high computational complexity of most approximated methods. A new notion, antimodularity, is then proposed, which consists in the impossibility to algorithmically obtain a modular description fitting the explanatory purposes of the observer for reasons tied to the computational cost of typical algorithmic methods of modularity detection, in relation to the excessive size of the system under assessment and to the required precision. It turns out that occurrence of antimodularity hinders both mechanistic and functional explanation, by damaging their intelligibility. Another newly proposed more general notion, explanatory emergence, subsumes antimodularity under any case in which a system resists intelligible explanations because of the excessive computational cost of algorithmic methods required to obtain the relevant explanatory descriptions from the raw data. The possible consequences, and the likelihood, of incurring in antimodularity or explanatory emergence in the actual scientific practice are finally assessed, concluding that this eventuality is possible, at least in disciplines which are based on the algorithmic analysis of big data. The present work aims to be an example of how certain notions of theoretical computer science can be fruitfully imported into philosophy of science.

In this paper I will reconstruct and analyze a famous argument by Stuart Kauffman about complex systems and evolution, in order to highlight the use in theoretical biology of a kind of non-mechanistic and non-causal explanation which I propose to call, following Kauffman, ensemble explanation. The aim is to contribute to the ongoing philosophical debate about non-causal explanations in the special sciences, kinds of explanation apparently extraneous to the received causal-mechanistic view. Ensemble explanations resemble quite closely the explanations of the structural kind proposed by Philippe Huneman, which—unlike mechanistic explanations—do not explain by exposing the causal structure of a phenomenon, but...