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E-grāmata: Because Without Cause: Non-Casual Explanations In Science and Mathematics

4.00/5 (8 ratings by Goodreads)
(Chair of the Philosophy Department, University of North Carolina at Chapel Hill)
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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.

Recenzijas

This 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 *

Preface xi
PART I Scientific Explanations by Constraint
1 What Makes a Scientific Explanation Distinctively Mathematical?
3(43)
1.1 Distinctively Mathematical Explanations in Science as Non-Causal Scientific Explanations
3(9)
1.2 Are Distinctively Mathematical Explanations Set Apart by Their Failure to Cite Causes?
12(10)
1.3 Mathematical Explanations Do Not Exploit Causal Powers
22(3)
1.4 How These Distinctively Mathematical Explanations Work
25(7)
1.5 Elaborating My Account of Distinctively Mathematical Explanations
32(12)
1.6 Conclusion
44(2)
2 "There Sweep Great General Principles Which All the Laws Seem to Follow"
46(50)
2.1 The Task: To Unpack the Title of This
Chapter
46(3)
2.2 Constraints versus Coincidences
49(9)
2.3 Hybrid Explanations
58(6)
2.4 Other Possible Kinds of Constraints besides Conservation Laws
64(4)
2.5 Constraints as Modally More Exalted Than the Force Laws They Constrain
68(4)
2.6 My Account of the Difference between Constraints and Coincidences
72(14)
2.7 Accounts That Rule Out Explanations by Constraint
86(10)
3 The Lorentz Transformations and the Structure of Explanations by Constraint
96(54)
3.1 Transformation Laws as Constraints or Coincidences
96(4)
3.2 The Lorentz Transformations Given an Explanation by Constraint
100(12)
3.3 Principle versus Constructive Theories
112(11)
3.4 How This Non-Causal Explanation Comes in Handy
123(5)
3.5 How Explanations by Constraint Work
128(8)
3.6 Supplying Information about the Source of a Constraints Necessity
136(5)
3.7 What Makes a Constraint "Explanatorily Fundamental"?
141(4)
Appendix: A Purely Kinematical Derivation of the Lorentz Transformations
145(5)
4 The Parallelogram of Forces and the Autonomy of Statics
150(39)
4.1 A Forgotten Controversy in the Foundations of Classical Physics
150(4)
4.2 The Dynamical Explanation of the Parallelogram of Forces
154(5)
4.3 Duchayla's Statical Explanation
159(8)
4.4 Poisson's Statical Explanation
167(6)
4.5 Statical Explanation under Some Familiar Accounts of Natural Law
173(5)
4.6 My Account of What Is at Stake
178(11)
PART II Two Other Varieties of Non-Causal Explanation in Science
5 Really Statistical Explanations and Genetic Drift
189(15)
5.1 Introduction to Part II
189(1)
5.2 Really Statistical (RS) Explanations
190(6)
5.3 Drift
196(8)
6 Dimensional Explanations
204(27)
6.1 A Simple Dimensional Explanation
204(5)
6.2 A More Complicated Dimensional Explanation
209(6)
6.3 Different Features of a Derivative Law May Receive Different Dimensional Explanations
215(4)
6.4 Dimensional Homogeneity
219(2)
6.5 Independence from Some Other Quantities as Part of a Dimensional Explanans
221(10)
PART III Explanation in Mathematics
7 Aspects of Mathematical Explanation: Symmetry, Salience, and Simplicity
231(45)
7.1 Introduction to Proofs That Explain Why Mathematical Theorems Hold
231(3)
7.2 Zeitz's Biased Coin: A Suggestive Example of Mathematical Explanation
234(4)
7.3 Explanation by Symmetry
238(1)
7.4 A Theorem Explained by a Symmetry in the Unit Imaginary Number
239(6)
7.5 Geometric Explanations That Exploit Symmetry
245(9)
7.6 Generalizing the Proposal
254(14)
7.7 Conclusion
268(8)
8 Mathematical Coincidences and Mathematical Explanations That Unify
276(38)
8.1 What Is a Mathematical Coincidence?
276(7)
8.2 Can Mathematical Coincidence Be Understood without Appealing to Mathematical Explanation?
283(4)
8.3 A Mathematical Coincidence's Components Have No Common Proof
287(11)
8.4 A Shift of Context May Change a Proof's Explanatory Power
298(6)
8.5 Comparison to Other Proposals
304(7)
8.6 Conclusion
311(3)
9 Desargues's Theorem as a Case Study of Mathematical Explanation, Existence, and Natural Properties
314(35)
9.1 A Case Study
314(1)
9.2 Three Proofs---but Only One Explanation---of Desargues's Theorem in Two-Dimensional Euclidean Geometry
315(8)
9.3 Why Desargues's Theorem in Two-Dimensional Euclidean Geometry Is Explained by an Exit to the Third Dimension
323(4)
9.4 Desargues's Theorem in Projective Geometry: Unification and Existence in Mathematics
327(8)
9.5 Desargues's Theorem in Projective Geometry: Explanation and Natural Properties in Mathematics
335(6)
9.6 Explanation by Subsumption under a Theorem
341(4)
9.7 Conclusion
345(4)
PART IV Explanations in Mathematics and Non-Causal Scientific Explanations---Together
10 Mathematical Coincidence and Scientific Explanation
349(22)
10.1 Physical Coincidences That Are No Mathematical Coincidence
349(1)
10.2 Explanations from Common Mathematical Form
350(11)
10.3 Explanations from Common Dimensional Architecture
361(7)
10.4 Targeting New Explananda
368(3)
11 What Makes Some Reducible Physical Properties Explanatory?
371(30)
11.1 Some Reducible Properties Axe Natural
371(7)
11.2 Centers of Mass and Reduced Mass
378(3)
11.3 Reducible Properties on Strevens's Account of Scientific Explanation
381(3)
11.4 Dimensionless Quantities as Explanatorily Powerful Reducible Properties
384(2)
11.5 My Proposal
386(8)
11.6 Conclusion: All Varieties of Explanation as Species of the Same Genus
394(7)
Notes 401(60)
References 461(22)
Index 483
Marc Lange is a philosopher of science. He serves as Chair of the Philosophy Department at the University of North Carolina at Chapel Hill, where he is the Theda Perdue Distinguished Professor. His previous books include Laws and Lawmakers (OUP 2009), An Introduction to the Philosophy of Physics: Locality, Fields, Energy, and Mass (2002), and Natural Laws in Scientific Practice (OUP 2000).
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