Because Without Cause: Non-Causal Explanations in Science and Mathematics (Oxford Studies in Philosophy of Science)

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. 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. -- Provided By Publisher. What Makes A Scientific Explanation Distinctively Mathematical? -- There Sweep Great General Principles Which All The Laws Seem To Follow -- The Lorentz Transformations And The Structure Of Explanations By Constraint -- The Parallelogram Of Forces And The Autonomy Of Statics -- Really Statistical Explanations And Genetic Drift -- Dimensional Explanations -- Aspects Of Mathematical Explanation : Symmetry, Salience, And Simplicity -- Mathematical Coincidences And Mathematical Explanations That Unify -- Desargues's Theorem As A Case Study Of Mathematical Explanation, Existence, And Natural Properties -- Mathematical Coincidence And Scientific Explanation -- What Makes Some Reducible Physical Properties Explanatory? Marc Lange. Includes Bibliographical References And Index. 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. "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" -- University Press Scholarship Online Not all scientific explanations work by describing causal connections between events or the world's overall causal structure. In addition, mathematicians regard some proofs as explaining why the theorems being proved do in fact hold. This book proposes new philosophical accounts of many kinds of non-causal explanations in science and mathematics.