Recent philosophical work has explored the distinction between causal and non-causal forms of explanation. In this literature, topological explanation is viewed as a clear example of the non-causal variety–it is claimed that topology lacks temporal information, which is necessary for causal structure (Pincock in Mathematics and scientic representation, Oxford University Press, Oxford, 2012; Huneman in Synthese 177:213–245, 2010). This paper explores the distinction between topological and causal forms of explanation and argues that this distinction is not as clear cut as the literature suggests. One reason for this is that some explanations involve both topological and causal information. In these “borderline” cases scientists explain some outcome by appealing to the causal topology of the system of interest. These cases help clarify a type of topological explanation that is genuinely causal, but that differs from standard topological and interventionist accounts of explanation (Woodward in Making things happen, Oxford University Press, Oxford, 2003).
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Königsberg is a former German city, which is now Kalingrad, Russia.
The Königsberg bridge system fails to meet the second condition, as all of its four nodes are of odd degree.
As best I know, this interpretation of “level” and “higher-level” originates in the multiple-realizability literature. In this literature, when some property A can be realized or instantiated by a variety of different physical details, the multiply-realized property is said to be at a “higher-level” than its “lower-level” realizers (Putnam 1975). This characterization of “level” helps clarify one form of “abstraction” in these cases–namely, a higher-level property can “abstract” from the lower-level details that instantiate it.
If the bridge’s higher-level topology is realized by some microstructure–and realization relations are not causal–how does this capture abstraction from causal detail? Although Pincock and others are not explicit about this, one charitable interpretation is that the bridge’s lower-level details consist of molecular interactions, which are causal in nature. These lower-level causal interactions differ across bridges made of different materials and they are omitted from representations of the system’s topology.
One example of this is the use of arrows in conveying relationships of priority, such as trail signs representing “user hierarchy” (arrows capture who yields to who among pedestrians, cyclists and cars). Alternatively, a figure or diagram can represent causality without using either arrows or edges or all. For example, it has been argued that diagrams such as the periodic table represent causal information, despite lacking these symbols (Ross 2018a).
Even Jones’s description reveals the causal nature of this case. He states that “[t]he directionality of cellular interactions within the immune system pathway determines the pathway’s bowtie structure: various stimuli activate pathways that converge to activate naive CD4+ T cells, which in turn activate a variety of responses” (Jones 2014, p. 1139). It should be clear that terms such as “interaction,” “activation,” and “directionality” are referring to causal relationships in this system.
This captures a way that the connections to the T cell variable differs from connections to other variables in the system.
I would like to thank Carlos Santana for insightful comments regarding this objection. For helpful discussion of the centrality feature, see (Jackson 2008, pp. 61–65).
For example, we do not need to know if T cells are triggered by the upstream cell (i) sending a chemical signal, (ii) physically manipulating an extracellular receptor, or any other causal process. It does not matter how these upstream cells trigger T cells, it just matters that they trigger them.
For example, in the first step of glycolysis the substrate glucose is converted into glucose-6-phosphate (G-6P) by a particular enzyme (a variety of hexokinase isozymes catalyze this reaction). The framework in Fig. 3 would represent this in the following way: glucose would be the upstream node, G-6P would be the downstream node, and the enzyme would be the directed edge between them.
For a detailed analysis of the relevant causal factors in these biochemical processes and their role in explanation, see (Ross 2018b).
Technically, these letters do not represent the species themselves, but changes in their energy levels. This allows them to be interpreted with an interventionist framework. For more on this see (Ross forthcoming).
It is easy to imagine ordinary life examples that are similar to this case. Suppose Fig. 4 represents a set of flowing rivers, with the letters and nodes as locations and arrows as segments of river. If one drops a basket of bread into the river at location A it will ultimately end up at location C, as opposed to locations D or E. This, of course, is because C is causally connected to A, while D and E are not.
For example, a gene that explains a disease does not involve sets of causal connections in the way that the “bow tie topology” that explains some systemic property does.
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I would like to thank Nicholas Jones, Philippe Huneman, Daniel Kostic, two anonymous reviewers, and audience members at the “Scientific Explanations, Competing and Conjunctive” conference, held at the University of Utah, for helpful feedback on this paper.
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Ross, L.N. Distinguishing topological and causal explanation. Synthese 198, 9803–9820 (2021). https://doi.org/10.1007/s11229-020-02685-1