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The Axiomatization of Classical Mechanics

Published online by Cambridge University Press:  14 March 2022

Herbert A. Simon
Herbert A. Simon*
Affiliation:
Carnegie Institute of Technology
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Extract

The purpose of this note is to examine a recent axiomatization of classical particle mechanics, and its relation to an alternative axiomatization I had earlier proposed. A comparison of the two proposals casts some interesting light on the problems of operationalism in classical celestial mechanics.

1. Comparison of the Two Axiomatizations. The basic differences between the two proposals arise from the nature of the undefined terms. Both systems take the set of particles, time, and position as primitive notions. Both systems assume that there exists a set of particles having continuous, twice-differentiable paths over some time interval. In addition, CPM takes mass and force as primitive notions, and assumes that with each particle there is associated a mass and a set of forces such that Newton's Second Law is satisfied (Axiom P6). A system with these properties is called in CPM “a system of particle mechanics.” If, in addition, the set of forces in the system satisfies Newton's Third Law, the system is called in CPM “Newtonian.”

Type
Discussion
Information
Philosophy of Science , Volume 21 , Issue 4 , October 1954 , pp. 340 - 343
Copyright
Copyright © Philosophy of Science Association 1954

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References

(CPM) McKinsey, J. C. C., Sugar, A. C., and Suppes, Patrick, “Axiomatic Foundations of Classical Particle Mechanics,” Journal of Rational Mechanics and Analysis, 2: 253–272 (April 1953).Google Scholar
(NM) Simon, Herbert A., “The Axioms of Newtonian Mechanics,” Philosophical Magazine, Ser. 7, 38: 888–905 (December 1947).Google Scholar
[1] Filon, L. N. G., “Mass and Force in Newtonian Mechanics,” Mathematical Gazette, 22: 9–16 (1938).Google Scholar
[2] Hood, William, and Koopmans, T. C. (eds.) Studies in Econometric Method. New York: Wiley, 1953.Google Scholar
[3] Margenau, Henry, The Nature of Physical Reality. New York: McGraw-Hill, 1950.Google Scholar