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THEORY REDUCTION: The Case of the Kinetic Theory of Gases

Soshichi Uchii, Kyoto University, Japan

(Acknowledgments: This paper was written in 1991 while I was a visiting fellow at the Center for Philosophy of Science, University of Pittsburgh. I wish to thank the Center for its generosity. This paper was read in a lunchtime colloquium at the Center, and also in Jim Joyce's seminar at the Philosophy Department of the University of Michigan; I also wish to express my thanks to the Philosophy Department and Prof. A. W. Burks in particular, for arranging that opportunity.)

CONTENTS

1. What is Theory Reduction?

2. What is the problem with the Kinetic Theory?

3. A Quick Review of Thermodynamics

4. Mechanics and Probability: Maxwell's Adventure

5. Mechanics and Irreversibility

6. Can we define Probability in the Kinetic Theory?

7. Ergodic Hypothesis

8. Division between Mechanics and Probability

9. Probability Applicable when we are Ignorant

10. The Case for or against Reductionism?

Bibliography / Appendix

1. What is Theory Reduction?

It is often said that the kinetic theory of gases is one of the best examples of the reduction of one theory into another; that is, the classical theory of thermodynamics [or to be more exact, a significant portion of it] is alleged to be reduced to the kinetic theory, which is based on the Newtonian mechanics and the atomistic view of the matter.

But what is the nature of this alleged "reduction"? If you want to know the right answer to this, the best way is to examine the historical development of the kinetic theory. The kinetic theory is a theoretical attempt to explain the nature of gases and heat processes, in general, in terms of the movements of numerous molecules constituting a gas. Its major advocates were James Clerk Maxwell (1831-79) and Ludwig Boltzmann (1844-1906); in the course of their work on the kinetic theory, they had to struggle with several conceptual problems, as well as with many empirical problems, and these conceptual problems have something to do with our question of theory reduction. And you will see that these problems center on the concept of probability.

ｪｬ 2. What is the problem with the Kinetic Theory?

The Sites of Phil. Hist. Science, Kyoto Univ.

March 1, 1999; last modified March 26. (c) Soshichi Uchii