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Fundamental Measurement of Force and Newton's First and Second Laws of Motion

Published online by Cambridge University Press:  14 March 2022

David H. Krantz
David H. Krantz*
Affiliation:
University of Michigan
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Abstract

The measurement of force is based on a formal law of additivity, which characterizes the effects of two or more configurations on the equilibrium of a material point. The representing vectors (resultant forces) are additive over configurations. The existence of a tight interrelation between the force vector and the geometric space, in which motion is described, depends on observations of partial (directional) equilibria; an axiomatization of this interrelation yields a proof of part two of Newton's second law of motion.

The present results (which were derived from a curious and deep isomorphism between force measurement and trichromatic color measurement) yield a kind of subunit, which needs to be incorporated into more complete axiomatizations of mechanics that would fulfill the Mach–Kirchhoff program.

Type
Research Article
Information
Philosophy of Science , Volume 40 , Issue 4 , December 1973 , pp. 481 - 495
Copyright
Copyright © 1973 by The Philosophy of Science Association

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Footnotes

†

This paper was written when I was a Fellow at the Center for Advanced Study in the Behavioral Sciences, 1970 to 1971. I wish to thank Patrick Suppes for useful discussions and encouragement.

References

REFERENCES

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