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Bowtie Structures, Pathway Diagrams, and Topological Explanation

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Abstract

While mechanistic explanation and, to a lesser extent, nomological explanation are well-explored topics in the philosophy of biology, topological explanation is not. Nor is the role of diagrams in topological explanations. These explanations do not appeal to the operation of mechanisms or laws, and extant accounts of the role of diagrams in biological science explain neither why scientists might prefer diagrammatic representations of topological information to sentential equivalents nor how such representations might facilitate important processes of explanatory reasoning unavailable to scientists who restrict themselves to sentential representations. Accordingly, relying upon a case study about immune system vulnerability to attacks on CD4+ T-cells, I argue that diagrams group together information in a way that avoids repetition in representing topological structure, facilitate identification of specific topological properties of those structures, and make available to controlled processing explanatorily salient counterfactual information about topological structures, all in ways that sentential counterparts of diagrams do not.

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Notes

  1. Specifically, given an abstract space E for representing relations among the parts of systems and a set of particular relations S′ in E representing the relations among the parts of a particular system S, the topological properties of S are the properties that are invariant under continuous transformations of S′ in E (Huneman 2010: 216).

  2. According to Mach, the “goal which [physical science] has set itself is the simplest and most economical abstract expression of facts” (1895: 207; see also Duhem 1991: 21–24). Insofar as biological science aims for this economy of thought, there is an important sense in which Kitano and Oda's diagram marks scientific progress. For their diagram brings order to the facts about the immune system cellular interaction pathway, and it does so in a way superior to its sentential counterpart. I thank an anonymous referee for this observation.

  3. The strongly connected components of a graph are its strongly connected subgraphs; a subgraph is strongly connected just in case each of its nodes is reachable from every other node; and a node w is reachable from a node v just in case there is a path from v to w, where a path from v to w is a sequence of nodes v = v o , v 1 , …, v n  = w (distinct except for the possibility that v = w) such that, for each i = 0, 1, …, n, (v i , v i+1 ) is an arc (Yang et al. 2011).

  4. I thank an anonymous referee for this observation.

  5. Topological properties do not always carry the explanatory burden. For many mechanistic explanations, topological properties do minimal explanatory work. For example, we explain how an odorant produces an olfactory signal by appealing to the mechanism for the olfactory system. In doing so, however, we appeal primarily to specific activities and interactions among the olfactory system's components, and only secondarily (if at all) to properties of the olfactory system pathway that are invariant under continuous transformations. I thank an anonymous referee for prompting this clarification.

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Acknowledgments

I thank William Bechtel, Philippe Huneman, Daniel Pearlberg, audiences at University of Nebraska - Omaha and the Alabama Philosophical Society, as well as two anonymous referees for helpful comments on prior versions of this paper.

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    Nicholaos Jones

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Jones, N. Bowtie Structures, Pathway Diagrams, and Topological Explanation. Erkenn 79, 1135–1155 (2014). https://doi.org/10.1007/s10670-014-9598-9

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