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A Primer on Determinism (The Western Ontario Series in Philosophy of Science)

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The title of this work is to be taken seriously: it is a small book for teaching students to read the language of determinism. Some prior knowledge of college-level mathematics and physics is presupposed, but otherwise the book is suitable for use in an advanced undergraduate or beginning graduate course in the philosophy of science. While writing I had in mind primarily a philosophical audience, but I hope that students and colleagues from the sciences will also find the treatment of scientific issues of interest.

Though modest in not trying to reach beyond an introductory level of analysis, the work is decidedly immodest in trying to change a number of misimpressions that pervade the philosophical literature. For example, when told that classical physics is not the place to look for clean and unproblematic examples of determinism, most philosophers react with a mixture of disbelief and incomprehension. The misconceptions on which that reaction is based can and must be changed. In addition to embodying falsehoods about the implications of modern physics for the truth of the doctrine of determinism, the literature also fails to convey a sense of how determinism actually works or fails to work in physics; how delicate the doctrine is in some respects, requiring a host of enabling assumptions for it to stand a chance of being true, and yet how robust it is in other respects, not only surviving but absorbing and growing stronger from potential counterexamples; how straightforward and mundane it is in some ways, and yet how subtly and exquisitely connected it is to a complex of issues about the nature of space and time, about the ultimate furniture of the universe, and about the concept of physical possibility. Further, the meaning of determinism is often mangled in the process of philosophical ax-grinding, the worst offenders being those Libertarians who, fearful that determinism will undermine human freedom and dignity, are careful to define it so that it can't be true. And finally, and most distressingly of all, the literature conveys the false impression that outside of the quantum domain determinism is a dead issue, whereas in fact it continues to throw off new problems and challenges for philosophy and for science. The main burdens of this Primer, then, are to say what determinism is and to describe in a way that is both introductory and realistic the problems and prospects of determinism in various branches of modern physics and at the same time to reveal how advances in understanding those problems and prospects are bound up with advances in mathematics, physics, philosophy of science, and metaphysics. I do not claim to have succeeded but only to have made a long overdue start on this neglected task. The challenge of completing the task will have to be left to abler hands.

Table of Contents

PREFACE

I. INTRODUCTION: DEFINING DETERMINISM

1. Classical Determinism: the Vision and the Context

2. What Determinism is Not: Cause and Effect

3. Predictability: Laplace's Demon

4. Predictability: Popper's Demon

5. Russell's Definition

6. What Determinism Is

7. Fear and Loathing

8. Democracy and Symmetry

9. Non-Laplacian Varieties of Determinism

10. Che Sara Sara

11. Deterministic Theories

12. Conclusion

DETERMINISM IN CLASSICAL PHYSICS

1. Classical Worlds

2. The Apparent Failure of Determinism in Leibnizian Physics

3. Leibniz's Response

4. Newtonian Space-time

5. Newtonian Particle Mechanics

6. Determinism at Bay

7. Determinism at Sea

8. Life Rafts

9. Infinite Billiards

10. Heat

11. Walling Out

12. Old Heat

13. Don't Fence Me In

14. Classical Electromagnetism

15. Shock(ing) Waves

16. Viscous fluids

17. Conclusion

DETERMINISM IN SPECIAL RELATIVISTIC PHYSICS

1. Special Relativistic Worlds

2. Domains of Dependence

3. The Relativistic Formulation of Laplacian Determinism

4. Laplacian Determinism — At Last!

5. Higher Dimensions and Weak Solutions; Huygens' Principle

6. Domains of Prediction

7. Particle Motion: Retarded and Advanced Action-at-a-distance

8. Instantaneous Action-at-a-distance

9. Tachyons

10. Conclusion

V. DETERMINISM AND LAWS OF NATURE

1. Hume's Definitions of 'Cause'

2. The Naive Regularity Account

3. The Empiricist Constraints

4. Mill, Ramsey, and Lewis

5. Deductive Systematization: a Closer Look

6. Laws as Universal and Eternal Truths

7. Defeasibility and Degrees of Lawfulness

8. Challenges to the Regularity Account of Laws

9. Dispositions: the Garden Variety Type

10. Tooley's Case

11. Nomic Necessity

12. Laws as Contingent Relations Among Universals

13. Conclusion

DETERMINISM, MECHANISM, AND EFFECTIVE COMPUTABILITY

1. Turing Machines

2. Determinism and Effective Computability: First Try

3. Grzegorczyk Computability

4. Determinism and Effective Computability: Ordinary Differential Equations

5. Determinism and Effective Computability: Partial Differential Equations

6. Extended Computability

7. Generalized Computability

8. Objections; Church's Thesis Revisited

9. Conclusion

DETERMINISM AND TIME SYMMETRIES

1. The Received View

2. Time Translation Invariance

3. Recurrence: Conditional and Unconditional

4. Time Reversal Invariance

5. Time Reversal Invariance and Futuristic and Historical Determinism

6. Determinism Plus Time Translation Invariance Imply Periodicity

7. Mill, Russell, Feigl, and Nagel: Vindicated?

8. Mill, Russell, Feigl, and Nagel: Refuted?

9. Russell and Feigl: Defended

10. Mill, Russell, Feigl, and Nagel: Modified and Qualified

11. Preview: General Relativity and Time Symmetries

DETERMINISM, RANDOMNESS, AND CHAOS

1. Defining Randomness

2. Randomness, Disorder, and Computational Complexity

3. Biased Coins

4. Utter Chaos

5. Determinism and Performance Randomness

6. Physical Probabilities: Frequencies or Propensities?

DETERMINISM, INSTABILITY, AND APPARENT RANDOMNESS

1. Stability and Instability for Fields

2. Classical Dynamical Systems

3. Macro-randomness: What We Want

4. Macro-randomness: Can We Have What We Want?

5. Instability in Classical Particle Systems

6. Strange Attractors

7. Conclusion.

Appendix: the Baker's Transformation

DETERMINISM IN GENERAL RELATIVISTIC PHYSICS

1. General Relativistic Worlds

2. Time Slices

3. Partitioning by Time Slices

4. Causality Conditions

5. The Status of Causality Conditions

6. Cauchy Surfaces

7. The Cauchy Initial Value Problem

8. The Significance of the Cauchy Initial Value Problem

9. Laplacian Determinism in the Medium and the Small

10. Singularities

11. Cosmic Censorship

12. Prediction

13. Geometrodynamics

14. The Characteristic Initial Value Problem

15. Conclusion

DETERMINISM IN QUANTUM PHYSICS

1. Quantum Mechanics as More Deterministic than Classical Mechanics

2. The Quantum State: a Closer Look

3. The Projection Postulate

4. The Incompleteness of Quantum Mechanics: Joint Probabilities

5. The Theorems of Gleason and Kochen-Specker

6. Bell's Theorem

7. Realism and the Incompleteness of Quantum Mechanics

8. The Problem of Measurement

9. The Insolubility of the Measurement Problem

10. Determinism and Quantum Mechanics

11. Indeterminism, Randomness, and Stochasticity

12. Conclusion

XII. DETERMINISM AND FREEWILL

1. Moral and Legal Responsibility and the Compatibilist Position

2. Tropisms

3. Indeterministic Actions and the Possibility of a Science of Human Behavior

4. Conclusion

FINAL EXAM

BIBLIOGRAPHY

INDEX OF NAMES

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