Because without cause : non-causal explanations in science and mathematics / Marc Lange.

Format:

Book

Author/Creator:

Lange, Marc, 1963- author.

Series:

Oxford studies in philosophy of science

Language:

English

Subjects (All):

Probabilities--Philosophy.

Probabilities.

Conditional expectations (Mathematics).

Science--Philosophy.

Science.

Mathematics--Philosophy.

Mathematics.

Physical Description:

xxii, 489 pages ; 25 cm.

Place of Publication:

New York, NY : Oxford University Press, [2017]

Summary:

Oxford Studies in Philosophy of Science, 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. Book jacket.

Contents:

Part I Scientific Explanations by Constraint

1 What Makes a Scientific Explanation Distinctively Mathematical? 3

1.1 Distinctively Mathematical Explanations in Science as Non-Causal Scientific Explanations 3

1.2 Are Distinctively Mathematical Explanations Set Apart by Their Failure to Cite Causes? 12

1.3 Mathematical Explanations Do Not Exploit Causal Powers 22

1.4 How These Distinctively Mathematical Explanations Work 25

1.5 Elaborating My Account of Distinctively Mathematical Explanations 32

1.6 Conclusion 44

2 "There Sweep Great General Principles Which All the Laws Seem to Follow" 46

2.1 The Task: To Unpack the Title of This Chapter 46

2.2 Constraints versus Coincidences 49

2.3 .Hybrid Explanations 58

2.4 Other Possible Kinds of Constraints besides Conservation Laws 64

2.5 Constraints as Mo dally More Exalted Than the Force Laws They Constrain 68

2.6 My Account of the Difference between Constraints and Coincidences 72

2.7 Accounts That Rule Out Explanations by Constraint 86

3 The Lorentz Transformations and the Structure of Explanations by Constraint 96

3.1 Transformation Laws as Constraints or Coincidences 96

3.2 The Lorentz Transformations Given an Explanation by Constraint 100

3.3 Principle versus Constructive Theories 112

3.4 How This Non-Causal Explanation Comes in Handy 123

3.5 How Explanations by Constraint Work 128

3.6 Supplying Information about the Source of a Constraint's Necessity 136

3.7 What Makes a Constraint "Explanatorily Fundamental"? 141

Appendix: A Purely Kinematical Derivation of the Lorentz Transformations 145

4 The Parallelogram of Forces and the Autonomy of Statics 150

4.1 A Forgotten Controversy in the Foundations of Classical Physics

4.2 The Dynamical Explanation of the Parallelogram of Forces 154

4.3 Duchayla's Statical Explanation 159

4.4 Poisson's Statical Explanation 167

4.5 Statical Explanation under Some Familiar Accounts of Natural Law

4.6 My Account of What Is at Stake 178

Part II Two Other Varieties of Non-Causal Explanation in Science

5 Really Statistical Explanations and Genetic Drift 189

5.1 Introduction to Part II 189

5.2 Really Statistical (RS) Explanations 190

5.3 Drift 196

6 Dimensional Explanations 204

6.1 A Simple Dimensional Explanation 204

6.2 A More Complicated Dimensional Explanation 209

6.3 Different Features of a Derivative Law May Receive Different Dimensional Explanations 215

6.4 Dimensional Homogeneity 219

6.5 Independence from Some Other Quantities as Part of a Dimensional Explanans 221

Part II Explanation in Mathematics

7 Aspects of Mathematical Explanation: Symmetry, Salience, and Simplicity 231

7.1 Introduction to Proofs That Explain Why Mathematical Theorems Hold 231

7.2 Zeitz's Biased Coin: A Suggestive Example of Mathematical Explanation 234

7.3 Explanation by Symmetry 238

7.4 A Theorem Explained by a Symmetry in the Unit Imaginary Number 239

7.5 Geometric Explanations That Exploit Symmetry 245

7.6 Generalizing the Proposal 254

7.7 Conclusion 268

8 Mathematical Coincidences and Mathematical Explanations That Unify 276

8.1 What Is a Mathematical Coincidence? 276

8.2 Can Mathematical Coincidence Be Understood without Appealing to Mathematical Explanation? 283

8.3 A Mathematical Coincidence's Components Have No Common Proof 287

8.4 A Shift of Context May Change a Proof's Explanatory Power 298

8.5 Comparison to Other Proposals 304

8.6 Conclusion 311

9 Desargues's Theorem as a Case Study of Mathematical Explanation, Existence, and Natural Properties 314

9.1 A Case Study 314

9.2 Three Proofs-but Only One Explanation-of Desargues's Theorem in Two-Dimensional Euclidean Geometry 315

9.3 Why Desargues's Theorem in Two-Dimensional Euclidean Geometry Is Explained by an Exit to the Third Dimension 323

9.4 Desargues's Theorem in Projective Geometry: Unification and Existence in Mathematics 327

9.5 Desargues's Theorem in Projective Geometry: Explanation and Natural Properties in Mathematics 335

9.6 Explanation by Subsumption under a Theorem 341

9.7 Conclusion 345

Part IV Explanations in Mathematics and Non-Causal Scientific Explanations-Together

10 Mathematical Coincidence and Scientific Explanation 349

10.1 Physical Coincidences That Are No Mathematical Coincidence 349

10.2 Explanations from Common Mathematical Form 350

10.3 Explanations from Common Dimensional Architecture 361

10.4 Targeting New Explananda 368

11 What Makes Some Reducible Physical Properties Explanatory? 371

11.1 Some Reducible Properties Are Natural 371

11.2 Centers of Mass and Reduced Mass 378

11.3 Reducible Properties on Strevens's Account of Scientific Explanation 381

11.4 Dimensionless Quantities as Explanatorily Powerful Reducible Properties 384

11.5 My Proposal 386

11.6 Conclusion: All Varieties of Explanation as Species of the Same Genus 394.

Notes:

Includes bibliographical references and index.

ISBN:

9780190269487

0190269480

OCLC:

956379140

Publisher Number:

99970220088