Not all scientific explanations work by describing causal connections between events or the world's overall causal structure. Some mathematical proofs explain why the theorems being proved hold. In this book, Marc Lange proposes philosophical accounts of many kinds of non-causal explanations in science and mathematics. These topics have been unjustly neglected in the philosophy of 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 - more necessary than the ordinary laws of nature connecting causes to their effects. Facts explained in this way transcend the hurly-burly of cause and effect. Many physicists have regarded the laws of kinematics, the great conservation laws, the coordinate transformations, and the parallelogram of forces as having explanations by constraint. This book presents an original account of explanations by constraint, concentrating on a variety of 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 dimensional relations among the quantities involved. Really statistical explanations include explanations that appeal to regression toward the mean and other canonical manifestations of chance. Lange provides an original account of what makes certain mathematical proofs but not others explain what they prove. Mathematical explanation connects to a host of other important mathematical ideas, including coincidences in mathematics, the significance of giving multiple proofs of the same result, and natural properties in mathematics. Introducing many examples drawn from actual science and mathematics, with extended discussions of examples from Lagrange, Desargues, Thomson, Sylvester, Maxwell, Rayleigh, Einstein, and Feynman, Because Without Cause's proposals and examples should set the agenda for
future work on non-causal explanation.
Industry Reviews
"With this book Lange really raises the bar for those involved in the study of explanation(s) in science and mathematics." -- Daniele Molinini, Philosophia Mathematica
"Marc Lange provides an elaborate philosophical analysis of non-causal explanations in the (natural) sciences and in pure mathematics...This is an original and thought-provoking contribution to the current debate on non-causal explanations in philosophy of science and philosophy of mathematics...Lange's work -- including this book and a number of papers -- is one of the driving forces and highly original voices in the debate...Lange's book is an excellent,
creative and thought-provoking scholarly contribution to the current debate on explanation. In particular, I believe it is likely the book will have a stimulating and fruitful effect on the literature." --
Notre Dame Philosophical Reviews
