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Viser: Because Without Cause - Non-Causal Explanations in Science and Mathematics
Because Without Cause
Non-Causal Explanations in Science and Mathematics
Marc Lange
(2016)
Sprog: Engelsk
Detaljer om varen
- Hardback: 512 sider
- Udgiver: Oxford University Press, Incorporated (November 2016)
- ISBN: 9780190269487
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.
Part 25.2 RS (Really Statistical) explanations5.3 Drift6. Dimensional Explanations6.1 A simple dimensional explanation6.2 A more complicated dimensional explanation6.3 Different features of a derivative law may receive different dimensional explanations6.4 Dimensional homogeneity6.5 Independence from some other quantities as
part of a dimensional explanansPart 3. Explanation in Mathematics7. Aspects of Mathematical Explanation: Symmetry, Salience, and Simplicity7.1 Introduction to proofs that explain why mathematical theorems holds7.2 Zeitz''s biased coin: A suggestive example of mathematical explanation7.3 Explanation by symmetry7.4 A theorem explained by a symmetry in the unit imaginary number7.5 Geometric explanations that exploit symmetry7.6 Generalizing the proposal7.7 Conclusion8. Mathematical Coincidences and Mathematical Explanations That Unify8.1 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 proof8.4 A shift of context may change a proof''s explanatory power8.5 Comparison to other proposals8.6 Conclusion9 Desargues'' Theorem as a Case Study of Mathematical Explanation, Existence, and Natural Properties9.1 Introduction9.2 Three proofs - but only one explanation - of Desargues'' theorem in two-dimensional Euclidean geometry9.3 Why Desargues'' theorem in two-dimensional Euclidean geometry is explained by an exit to the third dimension9.4 Desargues'' theorem in projective geometry: unification and existence in mathematics9.5 Desargues'' theorem in projective geometry: explanation and natural properties in mathematics9.6 Explanation by subsumption under a theorem9.7 ConclusionPart 4: Explanations in Mathematics and Non-Causal Scientific Explanations -- Together10 Mathematical Coincidence and Scientific Explanation10.1 Physical coincidences that are no mathematical coincidence10.2 Explanations from common mathematical form10.3 Explanations from common dimensional architecture10.4 Targeting new explananda11 What Makes Some Reducible Physical Properties Explanatory?11.1 Introduction11.2 Centers of mass and reduced mass11.3 Reducible properties on Strevens''s account of scientific explanation11.4 Dimensionless quantities as explanatorily powerful reducible properties11.5 My proposal11.6 Conclusion: all varieties of explanation as species of the same genus ReferencesIndex