The way some scientific explanations work is not by describing causal connections between events or by describing the world’s overall causal structure. Furthermore, mathematicians regard some proofs as not merely proving some theorems but also explaining why those theorems hold—and these explanations do not work by supplying information about causes. This book proposes philosophical accounts of many kinds of non-causal explanations in science and mathematics. One important kind of non-causal scientific explanation is termed “explanation by constraint.” These explanations work by providing info ... More

The way some scientific explanations work is not by describing causal connections between events or by describing the world’s overall causal structure. Furthermore, mathematicians regard some proofs as not merely proving some theorems but also explaining why those theorems hold—and these explanations do not work by supplying information about causes. This book proposes philosophical accounts of many kinds of non-causal explanations in science and mathematics. One important kind of non-causal scientific explanation is termed “explanation by constraint.” These explanations work by providing information about what makes certain facts especially inevitable—that is, what makes them possess greater necessity than ordinary laws of nature (connecting causes to their effects) do. This book presents an original account of explanations by constraint, offering many examples from classical physics and special relativity. This book also offers original accounts of several other varieties of non-causal scientific explanation. “Dimensional explanations” work by showing how some law of nature arises merely from the dimensions of the quantities involved. “Really statistical explanations” include explanations that appeal to regression toward the mean and other canonical manifestations of chance. This book also provides an original account of what makes certain mathematical proofs but not others explanatory, thereby connecting mathematical explanation to a host of other important but underexplored mathematical ideas, including coincidences in mathematics, the importance of giving multiple proofs of the same result, impure proofs that explain, and natural properties in mathematics.