Marc Lange: Because Without Cause: Non-causal Explanations in Science and Mathematics
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Marc Lange’s book provides an analysis of non-causal explanations starting from the consideration that causal explanations—those which work by “describing the world’s network of causal relations (xi)”—have almost monopolized the attention of philosophy of science. The book, which is composed of four main parts, shows how non-causal explanations play an important role in both mathematics and the sciences. In undertaking such an enterprise, Lange provides a plethora of examples, many of which turn out to be clear and helpful even for those who do not possess a mathematical education.
Chapter 1, and part I in general (chapters 1–4), presents the notion of distinctively mathematical explanations which “are non-causal because they do not work by supplying information about a given event’s causal history […] A distinctively mathematical explanation works instead (I will argue) roughly by showing how the fact to be explained could not have been otherwise” (5). The aforementioned definition is...