Description
Book SynopsisNot 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.
Trade ReviewThis is a tremendous book. It brings together and synthesizes 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 adventurousmetaphysics of modality makes for an exciting and thought-provoking read.Juha Saatsi, Metasicence *
[This book] 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. * Holly Andersen, Mind *
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 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. * Alexander Reutlinger, Notre Dame Philosophical Reviews *
The book has plenty to recommend it: broadness of vision and ambition-he covers a lot of ground (both scientific and philosophical)-as well as a wealth of examples (several original, all worked out in detail)... My overall assessment is that this is a substantial book well worth studying. It will elicit interesting debates in the years to come. * Sorin Bangu, British Journal of Philosophy of Science *
Table of Contents0. Preface 0.1 Welcome 0.2 What this book is not about 0.3 Coming attractions Part 1: Scientific Explanations by Constraint 1. What Makes a Scientific Explanation Distinctively Mathematical? 1.1 Distinctively mathematical explanations in science as non-causal scientific explanations 1.2 Are distinctively mathematical explanations set apart by their failure to cite causes? 1.3 Mathematical explanations do not exploit causal powers 1.4 How these distinctively mathematical explanations work 1.5 Elaborating my account of distinctively mathematical explanations 1.6 Conclusion 2. "There Sweep Great General Principles Which All The Laws Seem To Follow" 2.1 The task: to unpack the title of this chapter 2.2 Constraints versus coincidences 2.3 Hybrid explanations 2.4 Other possible kinds of constraints besides conservation laws 2.5 Constraints as modally more exalted than the force laws they constrain 2.6 My account of the difference between constraints and coincidences 2.7 Accounts that rule out explanations by constraint 3. The Lorentz Transformations and the Structure of Explanations by Constraint 3.1 Transformation laws as constraints or coincidences 3.2 The Lorentz transformations given an explanation by constraint 3.3 Principle versus constructive theories 3.4 How this non-causal explanation comes in handy 3.5 How explanations by constraint work 3.6 Supplying information about the source of a constraint's necessity 3.7 What makes a constraint Appendix: A purely kinematical derivation of the Lorentz transformations 4. The Parallelogram of Forces and the Autonomy of Statics 4.1 A forgotten controversy in the foundations of classical physics 4.2 The dynamical explanation of the parallelogram of forces 4.3 Duchayla's statical explanation 4.4 Poisson's statical explanation 4.5 Statical explanation under some familiar accounts of natural law 4.6 My account of what is at stake Part 2: Two Other Varieties of Non-Causal Explanation in Science 5. Really Statistical Explanations and Genetic Drift 5.1 Introduction to Part 2 5.2 RS (Really Statistical) explanations 5.3 Drift 6. Dimensional Explanations 6.1 A simple dimensional explanation 6.2 A more complicated dimensional explanation 6.3 Different features of a derivative law may receive different dimensional explanations 6.4 Dimensional homogeneity 6.5 Independence from some other quantities as part of a dimensional explanans Part 3. Explanation in Mathematics 7. Aspects of Mathematical Explanation: Symmetry, Salience, and Simplicity 7.1 Introduction to proofs that explain why mathematical theorems holds 7.2 Zeitz's biased coin: A suggestive example of mathematical explanation 7.3 Explanation by symmetry 7.4 A theorem explained by a symmetry in the unit imaginary number 7.5 Geometric explanations that exploit symmetry 7.6 Generalizing the proposal 7.7 Conclusion 8. Mathematical Coincidences and Mathematical Explanations That Unify 8.1 What is a mathematical coincidence? 8.2 Can mathematical coincidence be understood without appealing to mathematical explanation? 8.3 A mathematical coincidence's components have no common proof 8.4 A shift of context may change a proof's explanatory power 8.5 Comparison to other proposals 8.6 Conclusion 9 Desargues' Theorem as a Case Study of Mathematical Explanation, Existence, and Natural Properties 9.1 Introduction 9.2 Three proofs - but only one explanation - of Desargues' theorem in two-dimensional Euclidean geometry 9.3 Why Desargues' theorem in two-dimensional Euclidean geometry is explained by an exit to the third dimension 9.4 Desargues' theorem in projective geometry: unification and existence in mathematics 9.5 Desargues' theorem in projective geometry: explanation and natural properties in mathematics 9.6 Explanation by subsumption under a theorem 9.7 Conclusion Part 4: Explanations in Mathematics and Non-Causal Scientific Explanations -- Together 10 Mathematical Coincidence and Scientific Explanation 10.1 Physical coincidences that are no mathematical coincidence 10.2 Explanations from common mathematical form 10.3 Explanations from common dimensional architecture 10.4 Targeting new explananda 11 What Makes Some Reducible Physical Properties Explanatory? 11.1 Introduction 11.2 Centers of mass and reduced mass 11.3 Reducible properties on Strevens's account of scientific explanation 11.4 Dimensionless quantities as explanatorily powerful reducible properties 11.5 My proposal 11.6 Conclusion: all varieties of explanation as species of the same genus References Index
