Because without Cause
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Because Without Cause: Non-Causal Explanations in Science and Mathematics

by Marc Lange

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.

Reviews for Because Without Cause

I think that even the (partially or totally) unconvinced reader will agree on the exceptional quality and ‘mighty’ character of Because Without Cause

• Molinini in Philosophia Mathematica

Lange’s book is the ideal starting point for building further bridges between philosophical debates — inside and outside of philosophy of science — that are largely disconnected: work on explanations in science, mathematics, and philosophy… Even if one is ultimately not convinced by Lange’s pluralism, any other approach to non-causal and causal explanations (such as monism and particularism) will have to be developed in response to Lange’s splendid work.

• Reutlinger in Notre Dame Philosophical Reviews

This is a tremendous book. It brings together and synthesises Marc Lange’s highly original work over the past decade on non-causal explanation in science and mathematics. Like much of Lange’s oeuvre, it represents naturalistic metaphysics of science that draws inspiration and support from a wealth of detailed, carefully researched examples from the sciences, going back to the early nineteenth century and beyond. … The way in which these examples are coupled with open-minded—dare I say adventurous—metaphysics of modality makes for an exciting and thought-provoking read.

• Saatsi in Metascience

It exemplifies the methodology of integrating history and philosophy of science to full effect. Almost every example, of literally dozens, is new to the discussion and shows both careful attention to historical detail and impressive familiarity with the finer points of the relevant mathematics and physics. … It is a fully prepared feast of new material for philosophers, especially but not only philosophers of science, to dive into, argue against, add to, refine, or apply to further discussions.

• Andersen in Mind