General theory of topological explanations and explanatory asymmetry

Abstract

In this paper, I present a general theory of topological explanations, and illustrate its fruitfulness by showing how it accounts for explanatory asymmetry. My argument is developed in three steps. In the first step, I show what it is for some topological property A to explain some physical or dynamical property B . Based on that, I derive three key criteria of successful topological explanations: a criterion concerning the facticity of topological explanations, i.e. what makes it true of a particular system; a criterion for describing counterfactual dependencies in two explanatory modes, i.e. the vertical and the horizontal and, finally, a third perspectival one that tells us when to use the vertical and when to use the horizontal mode. In the second step, I show how this general theory of topological explanations accounts for explanatory asymmetry in both the vertical and horizontal explanatory modes. Finally, in the third step, I argue that this theory is universally applicable across biological sciences, which helps in unifying essential concepts of biological networks. This article is part of the theme issue ‘Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

The Network Theory of Psychiatric Disorders: A Critical Assessment of the Inclusion of Environmental Factors

“…But what exactly is meant by explain in this context? 15 According to Kostić (2020) , a topological explanation supports counterfactuals that describe a counterfactual dependency between a system’s topological properties and its network dynamics (i.e., if the topological property would not have been there, the network dynamics would have been different). He distinguishes two ways in which topological explanations may describe counterfactual dependency relations: a vertical explanation in which a global topological property (characteristic of the whole network) determines certain general properties of the real-world system, and a horizontal explanation in which a local topological property (characteristic of a part of the network) determines certain local dynamical properties of the real-world system.…”

“…He distinguishes two ways in which topological explanations may describe counterfactual dependency relations: a vertical explanation in which a global topological property (characteristic of the whole network) determines certain general properties of the real-world system, and a horizontal explanation in which a local topological property (characteristic of a part of the network) determines certain local dynamical properties of the real-world system. Kostić (2020) illustrates the difference between these two modes of explanation by focusing on the question of cognitive control, i.e., how the brain as a dynamical system efficiently transitions between internal states. If the explanation-seeking question is: “why can the brain achieve cognitive control?,” the relevant vertical counterfactual is: if the brain would not have been a small-world network, it would not have been able to achieve cognitive control.…”

“…How can counterfactual dependence account for explanatory asymmetry, i.e., the topological property explaining the phenomenon and not vice versa? Kostić (2020) suggests three ways in which this can be done. First, the phenomenon that the topological property wants to explain is not a mathematically quantified property, hence there is property asymmetry .…”

“…The topological explanatory strategy does pose some difficulties in the context of psychiatric disorders, however. First, providing the right topological explanations depends on the topological property (and the phenomenon it aims to explain) to be “approximately true” ( Kostić, 2020 , p. 2). We can estimate topological properties using network analysis, but as highlighted previously, we should critically examine the data and statistical methods used to substantiate theoretical claims.…”

Unifying the essential concepts of biological networks: biological insights and philosophical foundations

“…The contributions in this theme issue are organized thematically, starting with a philosophical analysis of what constitutes a successful distinctively topological explanation [8]. Kostic´ [8] provides a set of epistemic norms that govern a successful network/topological explanation, that is, the set of norms that helps to distinguish explanatory from merely predictive or descriptive network models.…”