Multilevel Ensemble Explanations: a Case from Theoretical Biology

Multilevel Ensemble Explanations: A Case from Theoretical Biology Luca Rivelli University of Padua, Philosophy Department (FISPPA) I analyze a well-known argument by Stuart Kauffman about complex systems and evolution to show it contains a hierarchy of non-mechanistic, non- causal explanations—which I would call, following Kauffman, “ensemble explanations”—quite closely resembling the explanations of the structural kind proposed in Huneman (2017), but lacking their absolute mathematical certainty, being based on results of non-exhaustive computer simulations. In Kauffman’s core argument ensemble explanations form an explanatory chain along a hierarchy of levels, where each explanans at one level gets itself recursively explained at the lower level. Explanations at adjacent levels turn out to be related not by mereological containment as in a multilevel mechanistic explanation, but by an analog to the relationship between two specifications at different levels of a specification/implementation hierarchy as understood by computer science. A mechanistic explanation grounds the whole hierarchy enabling the explanatory chain. Interestingly, the preliminary production of ensemble explanations enables the multilevel mechanistic explanations of systems manifesting what Bedau (1997) defines as weak emergence. 1. Introduction 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 Perspectives on Science 2019, vol. 27, no. 1 © 2019 by The Massachusetts Institute of Technology doi:10.1162/posc_a_00301 88 Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/posc_a_00301 by guest on 26 September 2021 Perspectives on Science 89 explanations resemble quite closely the explanations of the structural kind proposed by Philippe Huneman (2017), which—unlike mechanistic explanations—do not explain by exposing the causal structure of a phenomenon, but by virtue of structural-mathematical “laws” (theorems) holding for all abstract models of a certain class, a class to which a valid abstract model of the phenomenon to explain turns out to belong. Simi- larly, ensemble explanations explain by virtue of a law holding for a class of abstract models, with the difference that the law is not ascertained deduc- tively, but is inductively derived via non-exhaustive sets of computer-based simulations on random samples taken from the class under consideration. This circumstance renders such law only probably true, setting ensemble explanations apart from structural explanations. I will show how in Kauffman’s work ensemble explanations form an explanatory chain structured along a hierarchy of levels, in which each explanans at one level, becoming in turn an explanandum, gets recursively explained at a progressively lower level, until the hierarchy bottoms out into a classic mechanistic explanation. I argue that the nature of this hierarchy is not part-whole composition as in mechanistic multilevel explanations, but an analog to the specification/implementation hierarchy of computer science: along it, ensemble explanations fulfill the rather peculiar role of specifications explaining other specifications, while the same hierarchy, if needed, would allow for the production of a corresponding full functional explanation making explicit the details of the implementation at each level. Interestingly, it turns out that, far from being hard compet- itors, ensemble explanations coordinate with mechanistic explanations fruitfully: while a mechanistic explanation grounds the whole hierarchy at its lowest-level step, the production of ensemble explanations constitute in turn an enabling preliminary step for a further multilevel mechanistic explanation of those complex systems manifesting what Bedau (1997) calls a weakly emergent dynamics. It is safe to say that any attempted general- ization, based on the single case studied in this work, is risky. I do not claim to have highlighted a universal articulation between ensemble, functional, and mechanistic explanations, but, at least, a possible way in which these explanation kinds can be related. 2. Topological and Structural Explanations Since the late 1990s, the received view on explanations in the special sciences has been the so-called new mechanical philosophy, introduced by seminal works such as Bechtel and Richardson (1993) and Machamer, Darden, and Craver (2000): for mechanists, to explain a phenomenon con- sists in presenting the mechanism producing it, that is, showing in detail how a coordinated ensemble of parts and activities engaging in causal Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/posc_a_00301 by guest on 26 September 2021 90 Multilevel Ensemble Explanations interactions brings about the phenomenon.1 More recently, a variety of non-causal and non-mechanistic explanations in the special sciences have caught the attention of philosophers. Huneman (2010) and Huneman (2015) are among the first philosophical works to identify in the biological literature cases of recourse to a specific type of non-mechanistic scientificexpla- nation based on topological properties of abstract representations of a system, that is, properties invariant under a class of possible continuous deformations. The idea comes from mathematical topology, a discipline studying, intuitively, invariant properties of the “form” of an object, or the structure of connectivity of networks. To clarify, a network is a mathematical structure2 constituted by a set of items, the nodes, variously connected with one another by links, or edges. In a directed network links have a direction, so they can be plausibly seen as inputs going into nodes or outputs coming out of them. As a dynamics can occur on the network when nodes represent active elements capable of changing state and of reciprocal influence through input and output signals, networks have been more and more employed as theoretical dynamical models of a multitude of empirical phenomena. Of course, the connectivity structure of the network, its topology, constrains the possible dynamics. Topology changes only by connecting or disconnecting nodes, not by deforming the network. Certain networks show a form of modularity called community structure, a topological property consisting in the fact that the network can be partitioned into subnetworks, the modules or communities, with sparse connections between communities, and a higher density of connections among nodes internal to communities. An example is in fig. 1. Mechanistic explanations explain by citing how the coordinated causal interactions between the relevant physical parts that make up the overall mechanism produce the mechanism’s behavior to be explained. When possible, these explanations proceed by individuating a multi-level structure of nested mechanisms, where each of the parts composing the encompass- ing mechanism is itself a whole mechanism, possibly in turn composed of parts at the lower level and so on, until the hierarchy bottoms-out in a level—determined by pragmatic considerations—of what are considered elementary parts. While mechanistic explanations explain by citing causal chains of events involving physical parts embedded in a multilevel containment constitutive structure, in topological explanations the properly explanatory role is fulfilled by topological facts, which are mathematical facts. Huneman (2017) expands this pioneering topological conception outlining a more general theory of non-mechanistic structural explanations 1. For reasons of space, I take for granted that the reader is well acquainted with this established theoretical position. An outstanding overview is Glennan 2017. 2. Properly, a graph. Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/posc_a_00301 by guest on 26 September 2021 Perspectives on Science 91 Figure 1. A network with modularity by community structure. Colored discs surround the modules. where what is explanatory is the reference to formal or structural mathematical properties of a model of the system. Here is an outline of Huneman’s view: i. Structural explanations omit specific causal spatio-temporal trajec- tories of entities—that is, they omit the core of any mechanistic explanation—and explain instead by means of some mathematical feature of a representation of the system. ii. As mathematical properties—and not simply abstract representations of physical features—these explanatory features endow structural explanations with the modal force of a mathematical statement, whose truth traverses possible worlds, as opposed to empirical laws, which concern only the actual world. Specifically, this mathematical modal force out- classes the force of causal explanations, marking the different nature of structural explanations with respect to causal-mechanistic ones.3 3. This does not mean that mathematically certain explanations are to be preferred to causal explanations: it is a fact in certain cases of scientific explanation of empirical phenomena reported in the literature, that what does the explaining is not a causal connection, but some mathematical truth. Some examples are

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