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Otávio Bueno, Melisa Vivanco, Resisting Non-causal Explanations, Analysis, Volume 79, Issue 3, July 2019, Pages 550–559, https://doi.org/10.1093/analys/anz050
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1. Introduction
In Because Without Cause: Non-causal Explanations in Science and Mathematics, Marc Lange provides an analysis of scientific and mathematical explanations that do not derive their explanatory power from the description of the world’s network of causal relations (xi).1 He offers a formidable challenge to the predominant causal accounts of explanations in science and (applied) mathematics that insist that scientific explanations require the identification of the causes of the phenomena to be explained (e.g., Salmon 1984, 1989; Cartwright 1989; Woodward 2003; Strevens 2008). As Lange argues, most such accounts cannot even recognize the existence, let alone the significance, of non-causal explanations at all.
Lange’s approach focuses on three central areas: non-causal explanations in the sciences; non-casual explanations in mathematics, and the relations between them. We will focus on the first two.
2. Non-causal explanations in the sciences
Among scientific non-causal explanations, Lange identifies a particularly important class formed by explanations by constraints. These constraints involve a variety of necessity that is stronger than ordinary natural necessity, such as mathematical necessity. Distinctively mathematical explanations are non-causal explanations that account for a certain phenomenon by highlighting its inevitability. The sense that the phenomenon under consideration could not be otherwise provides a stronger kind of necessity than causal necessity. If such a necessity is of a purely mathematical sort, the explanation will be distinctively mathematical. Although Lange does not provide a definition of such explanations, he does offer a variety of examples to illustrate them. What is important for the present purposes is that distinctively mathematical explanations are non-causal because they do not work by supplying information about the world’s network of causal relations. The idea is that such explanations work by showing that the fact to be explained could not have been otherwise.
